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Learning efficient in-store picking strategies to reduce customer encounters in omnichannel retail

Authors:

Abstract

Omnichannel retailers are reinventing stores to meet the growing demand of the online channel. Several retailers now use stores as supporting distribution centers to offer quicker Buy-Online-Pickup-In-Store (BOPS) and Ship-From-Store (SFS) services. They resort to in-store picking to serve online orders using existing assets. However, in-store picking operations require picker carts traveling through store aisles, competing for store space, and possibly harming the offline customer experience. To learn picking policies that acknowledge interactions between pickers and offline customers, we formalize a new problem called Dynamic In-store Picker Routing Problem (diPRP). This problem considers a picker that tries to pick online orders (seeking) while minimizing customer encounters (hiding) – preserving the offline customer experience. We model the problem as a Markov Decision Process (MDP) and solve it using a hybrid solution approach comprising mathematical programming and reinforcement learning components. Computational experiments on synthetic instances suggest that the algorithm converges to efficient policies. We apply our solution approach in the context of a large European retailer to assess the proposed policies regarding the number of orders picked and customers encountered. The learned policies are also tested in six different retail settings, demonstrating the flexibility of the proposed approach. Our work suggests that retailers should be able to scale the in-store picking of online orders without jeopardizing the experience of offline customers. The policies learned using the proposed solution approach reduced the number of customer encounters by up to 50%, compared to policies solely focused on picking orders. Thus, to pursue omnichannel strategies that adequately trade-off operational efficiency and customer experience, retailers cannot rely on actual simplistic picking strategies, such as choosing the shortest possible route.




INESC TEC, Faculty of Engineering, University of Porto, Porto 4200–465, Portugal
 !"#$ "% &'! #!
Keywords:
%
 "



(
 )

%        )  (  
* ' )+&,
%"'-&%'. ''-''.*!,
/* 0)    + 
      (  ,1
 /* !     )  ) 
 1  ) (2  )   3, "  
 - .* !           -seeking .
)2 -hiding . 4  1/* 5
    3 -3.    ,
     (  *
#/  ,       
 * 5 ,      / (   $ 
        (    
* !       /    
6/, (*%)  
  (   ) 72  / ( 1 *
!           ( 
 ,   89:   , (   *! 
   +,   ,  
/   ,      
*
1.
Introduction
!   ,
, -#*;9;9.*
! /
    1  
*   1   
)     (, 
 -  * ;9;;.* 5   
,  ,  <<==   , 
 (    ),(
/ 
 -3 ;9>?.*   , 
  (     
 -&  * ;9;>.*    
 
)(@ (
-#2*;9;A.*
!   )  , 
2 (  ),
-#;9;9.*
! 
,        
 ,-B';9>C.*3
   (   
    (*  /    
)((-** 
.  1  -B  ' ;9>C. 
)     D*
-;9;>. )
1 -#*;9;>.*
 /(    &,
% "' -&%'.* # @ 
      
,-B* ;9>EFG,*;9;;.*
   &%'    
 (  -H*C: (    
>*?: (, . - I2 ;9;;.*
!  ,   7 
&%'/)(
# *
E-mail addresses:
(**J* -* . J(** -* .*
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
;
HH:;9>K  E9: ,;9;H  L' - ;9>E.*
& &%'     
(@  -** &%' '(, ;9;; '
'-''. &;9;;+  ,;9;9.
       
 ( 1     
 *
(@
      /
(-,. (@ 
-5*;9>?.* #+,
 (   )  
 (    (  , 
 ,*,
(   ,     
,-M;9;;. (
)(+ (@
  , * "   ) ( 
 -,.,)
/ ,(*
 ,  ( 
(@ ) ( )
 ,(
-  ;9;9.*  ,   
   ) 2
(  
-* ;9;>.*     
,        
), +,)(
(,* 
2      
-3(  * ;9;;.*    -;9;;. <<Picking
online orders is still causing headaches for grocers on multiple fronts, with
(...) in-store shoppers jostling with e-commerce workers to select products in
the aisles==* %    )  
   -1.  / )
 ,-I;9;A.*
      
(
 ,    
/ )      (
1 = /* !   ,
       ( 
       ( 1
  -  . ) 
  (  (   +, ( 
1  /  )  
  ,    
-  .*  ,    ( 
$(
 (((
  ) )    1
=/* !    
)(F,   
, 
*
5,(
 1   ( 
    /   
      * !
7)( 
)) ) ,, )   ( 
    )  
 (    (@  * 
)  1    @*
0     (@ )
1 / -3,
 2 ;9;;F 0N  * ;9>K.*   
/ +,    
-3  * >EE8F #  * ;9;>.   
 /   ) 7,  )
-3);9;>.*
!         
, 6)(
   )  )  
3, "    - .* !
+   ,  
*"@,  /2
  (   ) 2 
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
A
 (  *  
6)      ( 
*! (
) ,
/"-". 
      , ( +
 * !(    
3   -3.  
)) (  +* !
    , ,  , O
 /2   (
) -**))
     )   ) 
1    ** . ,
-**. 
(,*!7
  (  - ,. )
 -/.*
5   )@(
)   
 + 
    P
 * ! @  (  ) 
(Q
>* 5(2  )   
)     
)  , 
P *
;* 5   ,   , O
  ) " 3
   , 
  ,  (  
*
A* 5   /  
    , 
     ( 
    ) 
 )  $ *
, )      /
     
6/, (  * !   

      
   ) (@   
/*
!  (    2  ()*
';) 
*'A 
      
,*'H
O *
' 8    /
(  ,   ) ) 
 * ' K /  )
$
 /   * , ' C
   @ (  )  
(*
2.
Literature
review
%  )   Q
  
 *!()
  ) (    
  -' ;*>.* ! ) ) 
)-' 
;*;.,   -' ;*A. ,
   -' ;*H.* 5  
 ,)
  +
       )(
, ),
(*
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
H
2.1. In-store picking strategies
!     (( 
  ) 
- *;9>9F*;9>>F
0N*;9>K.*") 
  (@ ( )   
 * "     
(@, /*#,)
    -.  
- *;9>?.*
"     
  7(,*
,,/ ,+
 )(*'  )
) )     
,)
 -0N  * ;9>K.* !   &%'
 ''    ) +  
) 6)-) . ) 
,/,*
     
 * (@,
  , )  ,  - 
).*! ,
,, (  
/-*;9>9.*',
  /     , )
 (     
 ) )      
-#2* ;9;A.* !,
() 
)(-0N*;9>K.*
)
 ,(
    *   * -;9;>.
 ) 2  (  
,* !
     , 
2     &%' ,*
3(  * -;9;>.    (@
 (     '' , 
(@    * %( 
        ) )
       
* 3,  @  ,  
    * #2 *
-;9;A.  (    
(    , *
!,( -
.F       -
.F (  (@ (  
( (-.F
       
,   - .* !  (
   2 (    
( *
   (@  ) 
    &%'    
*0) )
&%' ) ) *) (
   ( (@   
,(&%'-* ;9;>F  
I2;9;;.* #,/
&%' (-**
 
 +,.* '    2 
-# *;9;>.*
!    @    ) ) 
   (   ),
 1  /*5 (
   (  )  / 
) )   
*5@ /
,)() 
,/*
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
8
2.2. Picker routing problems
!),
 ->E?A.,,
! '  -!'.  ' 
-(  * ;9>AF #2  # ;9>?F
R2  * ;9>E.* ' 
/   
    )  ) @
  -#  * ;9>CF O 
#G ;9>?F 7  * ;9>?.  
 +     
 - B  * ;9>?.* "  ( 
  ,  )
-!,*;9>9. )
    , ( / 
   ( -#S7  *
>E?8F  * ;9>?.* , ) (
       2 ( 
  /, -'2  * ;9>K.  
)
 ,  -   * ;9>8.  
 )
*      ,,
 ))  )-  
I;99>F I;99>FI
* ;99CF#* ;9>?F*;9;9.
  * # ,   
2( ))
)/  
*"
, ,,
     *
 
)apriori  
more ,*
2.3. Dynamic routing problems
  ,   A9,
,      @  *
%((  )(L
 * -;9;9.    ( ;9>9* %
 )       ,
&  * -;9>9.   * -;9>A. 2 
* -;9>K. (  * -;9>K.  %7   *
-;9;>.*") -**
 )    
,.    -** 
,    .  ( 
() ,
-'G5 ;9>K.*!
   @ () ( 
  , ) -;9>E.  
       
 ,    3* ! 
,      )
  / , 
  )-;99C.
6( @*
,
     3 
( + -2*;9>?F
 * ;9;>F I  * ;9;;.* 0) 
)/ 
  ( / ,   , 
 ,0*-;9;>.*
2.4. Dynamic picker routing problem
"   /      
,  (    * !
  ) ) ( ) ( 
/(  -**)
 .* # ,  
    , * B  I
-;99?.    ) 
(  ,,    ,*
& ,   
   
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
K
*
* -;9>K.,
)      *
!)( 2
       +,
)( *
!,(
, *0))
,(  (Q1 
* (
=   , (   *
!   ) ,   *
0)   )   
1      ,* " 
)      (  
, *
3  ,   )  
      )
    (* " 
/ ( ;9;9  )   
 )    )
7*
 (   (   ,  
      
= 
,( -0*
;9>AF &* ;9>8F 0  ;9;>.* $
        
 @  *!( 
)  /  (     
,  + (-
*;998. 6) (  
  (   -#  * ;9>8F  * ;9>C.*
!)apriori )
  (      @ - 
.* !( ( )    
   =/
 
*!) )*
3.
Problem description
"   ) (2    ,  
 
     )  
3 
 , * 5    )
  )  
  ,    *
,) ))
)         
,(( *
0' A*>    
      (  
( , 
(( *'A*;
@( (
-**()  
,  ,.* ' A*A 
3    ,  )   
      
()7 (*
3.1. Retail store environment
!       ) 
 
, 
 *!
= (F, £) )   (  - . 
/0)
   (   )    

{1, , 𝑣}
𝑣
/
𝑣+1
)    )    
-** 
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
C
2.*,
 ())
(
𝜆𝑆𝑡𝑜𝑟𝑒
   * $ ,

𝑐
T C   
 (      
 
𝑠𝑝𝑒𝑒𝑑𝐶𝑢𝑠𝑡𝑜𝑚𝑒𝑟
     
𝜃𝑐
 + (

*
,


𝑠𝑒𝑟𝑣𝑖𝑐𝑒U𝑡𝑖𝑚𝑒𝐶𝑢𝑠𝑡𝑜𝑚𝑒𝑟

*!
/ (
 , (   |C|   /
(
  𝑚* !   (    

)())
  (
𝜆
𝑂𝑛𝑙𝑖𝑛𝑒

*$ 

𝑜
T U (( G𝑜
F  **
>  ( 
*
3.2. Picker agents
5
𝑜

  *     +
𝜃𝑜
 @       -**
 ,@
(2.*"))
 + 2   
**     /2 
,),* !
()  + ,   
      
 /* !( ) ,  (
      
), *
!, (   
 ( ,   *!
(       
 (  (     () 
@+( 
,,-**
.V
 ) ) *! (
  ) 
,  )      *
$ 
,  +,   + 
/*
3.3. Dynamic picker routing problem as a Markov decision process
! (     @ 2 3 )
𝑇
   
𝑘
T 0, 1, ,
𝑇

)( 
/*
) 
𝑘
)
  ) * $  
𝑘

)
𝑠𝑘*
    𝑠0    
𝑘
= 0 

      0*   
 
𝑘
=
𝑇
@
𝑣
+ 1
(
   , * 

𝑠𝑘
,
  (  
(
(7-,
.* &   , (  

𝑎𝑘
-**

/







.

  * $      
 
,(*
!(  @ 
+   ) 2   (
 * !   , )
(*%(,
3((
 ,->.(SF-;.(
AF-A.)(
𝑅F𝑃 *
Decision epochs  
𝑘
 ) 
 )*
States !(,
𝑘
@,


𝑠𝑘
=
(𝑛𝑘, 𝑧𝑘, 𝑡𝑘)
)
𝑛𝑘
T
F


=


F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
?
/ig. 1.
!            ( &%'  '' )  ,  ( 
 *
𝑧𝑘
=
(𝑧𝑘(1), 𝑧𝑘(2), ,
𝑧𝑘(|G𝑜|))
(
 ( 
𝑜
 𝑘
𝑡𝑘
[0T,
𝑇
]
𝑛𝑘*
(  𝑧𝑘(.) 
{0, 1}Q{
0, (  ,
𝑡
(( 
,𝜙1 (
,𝜙2 ( ,,𝜙3 
      , 𝜙4* ! (
7)
𝑤1

𝑤4
,*
!
)
𝑟𝑘(𝑠𝑘, 𝑎𝑘, 𝜔𝑘+1)
)


𝑧𝑘(.)
=
𝑘
1, (,

𝑡𝑘
->
.
@
"𝑠0 = (0, 𝑧0, 0)
  2  𝑧0(𝑛)  0  1 (  

𝑛
T F {0}* ! @    
)

𝑠𝐾
{(0,
𝑧𝑘,
𝑡𝑘)
𝑡𝑘
[0T,
𝑇
],
𝑧𝑘
{0T, 1}|
G𝑜|}
)        2
,
𝑇

( (
9 >*!S = F × [0,
𝑇
] × {0,
1}|G𝑜|*
Actions 
𝑘
(
       F* 5 
   
𝑠𝑘
  ( ( 

𝑛𝑘
𝑟𝑘(𝑠𝑘,
𝑎𝑘,
𝜔𝑘+1)
=
𝑤1
𝜙1(𝜔𝑘+1) −𝑤2
𝜙2(𝜔𝑘+1) −𝑤3
𝜙3(𝜔𝑘+1) +𝑤4
𝜙4(𝜔𝑘+1)
-A.
Objective !7  /2 /  (
)      ( ) 
,, ,)
2
*
𝜋
+(𝑎0, 𝑎1, ,
𝑎𝑇
(,


𝑘
=
0,
,
𝑇
* !    @  
,
𝜋
/2
/)*!7(
 𝑠0()
 ,
A(𝑠𝑘)
=
{𝑎𝑘
T
{𝑛 T
F
(𝑠𝑘, 𝑛)
T
£}}
-;.
min
E
𝜋
[
𝑇
𝑘=0
𝑟𝑘|𝑠0
]
-H.
Transitions )(
𝑎𝑘
(
𝑠𝑘
 )
𝑠𝑘+1

𝑘
+ 1* !   ,    
) ) 
/ *0) )(

  (    * !
(
2
(
𝛺𝑘+1



,
𝜔𝑘+1*

𝑅 𝑘+1(𝑠𝑘, 𝑎𝑘, 𝜔𝑘+1)


  )    
𝑘
)


𝑎𝑘
(

𝑠𝑘



(
𝜔𝑘+1*
Rewards 5  
𝑠𝑘
(

𝑎𝑘
T A)   (

 ) * !)
(
(->.@/)(
-;. (  
(
-A. ( 
( -H.)
(*!
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
E
4.
Solution approach
!   @  ' A  
+ )    Q ->.
)      ' 
 -' .   "     
  +   @
 F  -;. (   + 
,  (    + +
     ,   
,   O * * ;  
) (  ) ) 
+   )   
)*
" ' H*> )    
 (     
     +  (  
*"'H*;)  
O    ,
( ,   )  
*'H*A
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>9
/ig.
2.  )  )( *
/()
  / () , ) O
*
4.1. SRP definition
! '   
 'A*>*$
(,𝑖
𝑗)
T£ 
(  )+ (
 ) 
𝑖

𝑗*
$),(
𝑤𝑖𝑗
,,=*
G𝑜
4.1.2. SRP solution approach
"/( ' 
( ( *   
-( 2.)
    (   ( '  *
, ,       
), 
( * !( )    ) 
 /  +,
 (     
* 5 ,     ) 
(( 
(/->.*
F  (   
𝑜*!
7 (          
  )
2-.(*
4.1.1. SRP mathematical formulation
!


' 
)

,


𝑥𝑖𝑗
(
(
Algorithm 1 #
>Q procedure CUTTInGPLAnEs(F, G𝑜)
;Q
𝐶𝑢𝑡𝑠𝐴𝑑𝑑𝑒𝑑
𝑇
𝑟𝑢𝑒;
𝑋
;
𝑌
;
𝑍
0;
AQ
while
𝐶𝑢𝑡𝑠𝐴𝑑𝑑𝑒𝑑
do
HQ 𝑋'  -8.-C.  F 
G𝑜;
8Q
𝑌
'  (F

*

𝑥
𝑖𝑗
,
)
KQ 𝑍#  (   MF
CQ if
𝑍
=
1
then
(,𝑖 𝑗) *!(
()Q
' Q
?Q
𝐶𝑢𝑡𝑠𝐴𝑑𝑑𝑒𝑑
𝐹
𝑎𝑙𝑠𝑒;
EQ else
2
(,𝑖 𝑗)T£
**
𝑤𝑖𝑗
𝑥𝑖𝑗
-8
.
>9Q   -?.   F
>>Q
𝐶𝑢𝑡𝑠𝐴𝑑𝑑𝑒𝑑
𝑇
𝑟𝑢𝑒;
>;Q
if
𝐶𝑢𝑡𝑠𝐴𝑑𝑑𝑒𝑑
then
>AQ 𝑋# F
>HQ else
𝑖TF
𝑖TF
𝑥𝑗𝑖
= 1
W
𝑗
T
G𝑜
X {0}
-K.
𝑥𝑖𝑗
= 1
W
𝑗
T
G𝑜
X {𝑣 + 1}
-C.
>8Q if then
>KQ
𝜃𝑜
!+(
 YF
>CQ return 𝜃𝑜*
𝑖TU
𝑗TU
𝑥𝑖𝑗
≤ |U| − 1
W U ⊂ F,
𝑖
𝑗
-?.
!,/
- > H.
-
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>>
𝑥
T {0, 1}.-E.
%7 ( -8. 2    -
.( *!6)
     @
   , 
-K.-C.*#-?.*
,  -E. @, (
*
>  8.* '      
 * "      
->>9. 
 - >  >>.*5   
  )      
* !        
( /
     
(>>C.*
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>;
)
𝑘 𝑘
4.2. Q-learning
!      ' H*>*;
 +
𝜃𝑜
(    (  (
  𝑜* 0)     
(
 * "  '  ( )  
   ()
(,𝑖
𝑗)
 )
𝑖

𝑗
-
    .* !(    
   ,  @  (

)

(
𝑖

𝑗



)


(*
Algorithm 2 O 
>Qprocedure QLEARnInG(𝑀𝐷𝑃 , 𝛼, 𝛾, 𝜖)
;Q "2𝑄(,𝑠 𝑎) F
AQ for do
HQ "2   )    𝑠0 -
  .F
8Q while
𝑠𝑘
 @ -  .do
KQ #
𝑎𝑘
(
𝑠𝑘
() 𝜖,,F
CQ $/𝑎𝑘)𝑟𝑘)

𝑠𝑘+1
F(
?Q
L
O(
,

𝑄(𝑠𝑘, 𝑎𝑘)
𝑄(𝑠𝑘, 𝑎𝑘)
+
𝛼
𝑟𝑘
+
!    ,  ()   
+   )  O
-5 >E?E.
𝛾
/
𝑄(𝑠𝑘+1
𝑎
)
,
𝑎)
𝑄(𝑠𝑘,
𝑎𝑘)
  3,  '
A*A*! +(
(/
, * "     
 (

(
𝑄(𝑠𝑘, 𝑎)


(
/
)
(
𝑎
(
𝑠𝑘*
  
𝑉𝜋 (𝑠𝑘)
   (  
 
EQ if 𝑄  then
>9Q &F
>>Q return O
H.)@

𝑠
-;8.

/)()(
𝑠𝑘
(),
𝜋*!     )  

𝑘
+ 1
  / )     (  
@ 
𝑇
* % 7   @  
,  /2   )  
  * #  & $+
-) ;99C. 𝑉 (𝑠𝑘) = max𝑎 A(𝑎 ){𝑟𝑘+1 +
E[𝑉 (𝑠𝑘+1)|𝑠𝑘, 𝑎]}



𝑎𝑘


,


()/
𝑎𝑘
=

/{𝑟𝑘+1
+
E[𝑉
(𝑠𝑘+1)|𝑠𝑘, 𝑎]}
->9.
𝑎𝑘TA(𝑠𝑘)
")
 (,) 
   * !( , ,
  6  
/   , )     

𝑠𝑘
(𝑎𝑘*𝑄𝜋 (𝑠𝑘,
𝑎𝑘)
(
-O(.
  +, ( 
𝑎𝑘
) 
     
𝑠𝑘
 () , 𝜋* 5 
@O(
𝑄
(𝑠𝑘, 𝑎𝑘)*
!

)
𝑉
(𝑠𝑘)

𝑄
(𝑠𝑘, 𝑎𝑘)


,

()/
𝑇
   /     O(
- ;  K  ?.* !  (   
(   𝜖,    
 ) ,𝜖 
 )   O    ) , 1 𝜖*
(
@   @(  O(

-**(/))
+  )    .* "(  
 O(*%)
/*
4.3. Illustrative example
!   )
   , ( 
, )*
* A  )  )   
* "  @ 2 (  
(
* 5  
 ))
  * ! SP , - .
    
*%QL ,-O
𝑉
(𝑠𝑘)
=
max
𝑎TA(𝑠𝑘)
𝑄
(𝑠𝑘,
𝑎)
->>.
.@
 ()*
!(   , 𝜋 (   )  

  ()/
𝜋
(𝑠𝑘)
=
 / 𝑄
(𝑠𝑘, 𝑎)
->;.
𝑎TA(𝑠𝑘)
"( )  (, 𝑄) ,  
 (        
) )*
!,(O
   & +  / 𝑄*
! & +   O(  
/,,
𝑄(,𝑠 𝑎)
=
𝑅
+
𝛾
max
𝑄(𝑠, 𝑎)
->A.
𝑎
!O+  , /𝑄 
,
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>A
!     , () ,
/( O * * H   /
(   (  O-.*
$) 
  - ?8.     -
>;A.* $     
    (  * 
@ )CC
EA*'O(CC 
CC*
5.
Algorithm convergence
")/
 /  ,  , (  
  ,
𝑄
𝑛𝑒𝑤
(,𝑠
𝑎)
=
𝑄(,𝑠
𝑎)
+
(
𝛼
𝑅
+ 𝛾
max
𝑄(𝑠, 𝑎)
𝑄(,𝑠 𝑎
)
->H.
𝑎
*,)
,  * ', ) (  
   
)   
𝛼
7 )  
)O
  (  *    ,
/ /𝑄𝑛𝑒𝑤 )
  𝑄* ! /    , ( 
 )
 ;* !   , 2  O
() -;;.*
!     / ( )
*! ,    (  
( -;A.* 
   2     𝑠0
-;
  @   (   
 
𝜖 (
 2*
5.1. Synthetic instances
',  )    
   ,   
 * 5   ( (
,)  2
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>H
/ig. 3.
" / (  SP -.   QL  -.* -  (  (     @     (
  )  (  *.
/ig. 4.
/) ( OO /*
*
     ,   
 (=
     
 (  * !  (  =
()() 
(1 /(10 *! 
 +  ,   
()    )  (  
    * !   (
,2 (
9*;*" (8 
/(
|C| 50*!/(
𝑚 5
    30     * !
) 
1 m∕s*!>2(
)
  12 ,* 
) 
  ,  ) 
      )
   
2, 3 *"(, -**
       ,  . 
 2 ,1 * 2,
1 
))100 *
5.2. Q-learning training and results
3   ( ( 
    (   
*!  ,  
    /  , * !
   )   
@    (  ,
*$ @)(5000 
* )"YJ;*8
B02  
+(
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>8
Table 1
' (       *
', {!,, ', ,
}
#  {$, , &}
,    {2}
%    {0.2}
%  -. {8}
/  (  
{50} /  (   

{5}    -.
{30}
5  -V. {1}
#  , ->. {3}
#  , -;. {1}
' , -A. {1}
 ) -H. {100}
Table 2
' ( (      
(*
  -𝛼.{0.95, 0.97, 0.99}
3  -𝛾.{0.50, 0.70, 0.90}
𝜖 -𝜖.{0.01}
) B E*8* ! ;   
 @*
!  )  (  
 !A*!@)
<<,==<<== ,(
 , (   ( ,  *
!   <<& ==  

 (  -𝛼|𝛾|𝜖.    

)*#(/

/)

F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>K
/ig. 5.
# )  ,    @   ,  -@ 899  (   .*
-
 (  (     @     (   )  (  *.
Table 3
# )      -8999 .*
,  &
-𝛼|𝛾|𝜖.
# )
* * /* #G - 89
*.
!,

0.97 | 0.9 | 0.01
28 989*54 29 262*92
;EHH9*K9
9*>>
!, 
0.99 | 0.7 | 0.01
27 240*37 28 563*90
;E
;K;*>9
9*>>
!, 
0.95 | 0.9 | 0.01
28 325*40 28 810*05
;E9CA*A8
9*>9
'

0.97 | 0.9 | 0.01
23 471*06 26 828*68 ;?8KE*??
9*>>
' 
0.97 | 0.9 | 0.01
8 571*05 21 363*16 ;?
AK;*C> 9*>9
' 
0.97 | 0.9 | 0.01
11 729*02 22 830*18 ;?;AK*HA
9*>9


0.99 | 0.9 | 0.01
−249 624*48 −74 201*81
;K
CH>*>> 9*>>
 
0.99 | 0.9 | 0.01
−280 708*50 −136 167*61
;KA8;*HH
9*>;
 
0.97 | 0.9 | 0.01
−275 092*86 −144 711*93
;8
CAA*A>
9*9?


0.95 | 0.9 | 0.01
−282 733*08 −172 079*58
;;8?H*A?
9*>9
 
0.95 | 0.9 | 0.01
−286 259*32 −152 702*76
>CAC>*H;
9*>?
 
0.97 | 0.9 | 0.01
−285 686*24 −180 264*63
;>8;H*9E
9*>A
@* !   )   (
 50 *
5)
/ )(
,*    2 (
    (   *
 /   )   
    
(,)V
      2*  )
 (  50    (
 (  )  ) (   2
(         (
*        
 )*8*
!  )    
  () * /  2 (
      
  (   )  * 5 
 )   , )  
 (() )  
,)2( 200
*   (,
       
)*
6.
Real-world application
!  /(
 $*!)
  , (  )   
   (     
 )  ( , 
,*
   ( 
 +)*!(
O    ,   ( (  O
-.
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>C
 -** 3.*
 1
( )(
      O* "  
O( (
,)6)
,*
6.1. Real-world instance
! @,  
  / )
) * !  ,
     (   
  * )  2
,   , )
   * 0)   
   (,  ,*
"    , 
 , ( ,  -**  
 )     .
)    (  
(    *  )
   , 
 * * K    ,  
)*
" @     
       
 *5(   )
    ,  
  (   (  * " 
    )   
 ,  *(
, ,(/
  * ! + ( 
,, )
       , 
* !     ) 
 (   
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>
9
/ig. 6.
 (   ,      ) * -  (  (     @
    (   )  (  *.
/ig.
7. )  *
   )    
(37 * ! )
   )    *
! (,
𝜆𝑆𝑡𝑜𝑟𝑒



10




(


𝜆𝑂𝑛𝑙𝑖𝑛𝑒



0.2*!/() 

300  )     /  ( 

  * $   30   
  )  1 m∕s* !    ( 8 * !
) 50 (F
2 , 3  (   
2,1 ( 
7*
! (   )  
  )    )
 * C   ( 
( )
 -  (  
.  / ( ,  ( ,
,-(2.
 (,,,*
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>
9
5     ,  ( 5
 15 * !)  
(  (   ,   (
     (   
 ( (*!
2()
  (  *!  ,
)   )   
( 3"M * 5   ()
,     ( ,   ()
V*
6.2. Training in a real-world context
!      )  )
      ' 8*;*  )
   
    (
( ,
𝛼   𝛾/  𝜖* !
(
!H*
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>>
/ig. 8.
)(10   @ )*
Table 4
' ( (     
@ (  ) *
  -𝛼.{0.1, 0.5, 0.9, 0.95, 0.97,
0.99}
3  -𝛾.{0.1, 0.5, 0.9, 0.95, 0.97,
0.99}
𝜖 -𝜖.{0.01, 0.03, 0.05, 0.07, 0.09}
(30 000 )(@*
     ) ) 
,1000 * !10 -
).       
       *?*$,
1000 )( 
 )*   (  @ 1000 
 ) ,(   
* B,     ( 20
000   *  ()  
   ( (  (
30 000 *
"  (   
  )     
-. (
  -,   
O.*!
))
𝜖,
/       
 
)),*"
 ,/(
, (*
!(,  * -;9>8. ) ,
*5 
     , ,   
 *)

𝜖
  ),
*
6.3. Managerial insights
! )    
         
   * " )   
   V    
)* , ) )
   )     (   (  )
7() ()
   (   , +,  
*
!+  
* #)/Z5
 (Z
!)+)((
(     
 (V
*
Q-learning (QL) ,     O
   @   (  
) *
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>;
Shortest Path (SP) ,    ,
-, 37 .    
 *$
, 
),*
Myopic Policy (MP) ,   , 
)   ()   )  
)( (
*
Crowded Nodes (CN) ,  2 (
      ( 
 (    * $  
 ,      
  ) ,    (
 *
,(,)),(
   +    ( 
 (  * ! ( )  
'   /
)-
 (  )    
.*! )Arc Distance 
Arc Crowdedness ,*!)+
)( *
! 8    ( (
 *
,2)+
  )   SP  MP  
, (
8;*?98>*8H ,*QL CN
( (  
 H?*?K  HA*HK  ,* !
  , (   
/)    ( 
)A9: 89:SP
 MP* , CN   )  (
,  ) 
(*,QL ,
  (   ) ,
( *
%  ) +
    )  )
    (    
   ,  
/*0)+
(       ( 
  , ;*8K: (   ( HE*>C
  HC*E>* !  ( 
,,C*EE:( 
( >?>A*?A   >KK?*E>* !(  
)      @ 
  / ( 
  (      ( 
*
5,
   ()   
-SP  MP.* " 
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>A
Table 5
   ( 899  (  '  -'. #)  -#. , , -.  O -O. *

,
* )
*[% *[
*
[$
 3
O
>CK>8*HE
H?*?K
8CE*>C
>8?>*E>
 3
'
>C9?>*89
8;*?9
K;?*;>
;;HH*?E
 3
#
>8C?9*8H
HA*HK
8>A*89
>>AE*;C
 3

>K>E8*HK 8>*8H
K>;*K8
;;?E*;A
*
>KKK?*;8 HE*>C
8?A*A?
>?>A*?A
 #)
O
>C>E9*8;
HC*A;
8K;*C>
>HKH*;C
 #)
'
>K8EE*C>
89*AH
8EC*8C
>E;?*9;
 #)
#
>K?KH*EC
H8*;H
8A8*9K
>>?C*?K
 #)

>8>9;*A9
H?*C;
8CE*9;
;9E8*89
*
>KHAE*A? HC*E>
8K?*8E
>KKE*E>
/ig. 9.
"/(  SP  -. CN  -.  QL  -.* - ( (   @ 
 (   )  (  *.
(     /  CN ,
  )   ( 
*0)   , ( 
 7 ,* 5  SP  MP  
CN ,) 
7   * ! QL ,  
     (  
 )(*
         QL
    )    ) 
( ) *   )  
)     (  << (
,==(*B 
+ )    (  
  -.    (+,*
'  QL ,  )    
, ,
 )  + 
)*
!,
 4
 ,*" * E )  / (
(), SPCNQL *
  SP ,( () -
 .     ) * % 
QL ,()
  )    () 
*!CN ,( 
*
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>H
6.4. Robustness of the policies
!   6/, (    
 (  ) 
 / *" /)
  QL ,    
-     
' K*>., 2 3  /
Q
HalfSizeQ!()
( ,*
DoubSizeQ !   (    )
 ,*
HalfOffRateQ!(1
( ,*
DoubOffRateQ !   ( 1  
 ,*
2OrderBatchQ7()
 *
CapacityCartQ !     , 
   *
! K     (  /
  )  QL , )* 
    )  -.  (
 ( 
(( 
  ,    ( 
 ( -.(,
*,
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>8
Table 6
   ( 899  (  O -O. , (   *
'
*
[#*
*
[%
*
[&
*
['
*
[
*
['
*
'




*
'
 *
*
$
 *
*
)

*
Baseline
>H8*9H
HC*9; HC*9;
9*99
88E*9;
8E;>*E?
>>*E>
>9*8E
;*?K ;E*9A
HalfSize >H8*H8
KH*K? KH*K?
9*99
A?K*E>
K8;?*HA >K*99
>K*?C
H*9C ;;*HE
DoubSize
>HH*H8 A>*KK A>*KK
9*99
CK9*9;
8>8>*A;
?*A9
K*C?
;*9?
AH*;A
HalfOffRate C;*8E HC*H8 HC*H8
9*99
8KH*9? 8???*CE
>>*?8
>9*HH
>*H;
A?*8K
DoubOffRate ;E9*>H
HC*C8 HC*C8
9*99
8KE*9; 8??E*AC
>>*?;
>9*A8 8*8E
>>*H;
2OrderBatch >H8*9>
KH*CE
A;*H9
9*99
CH>*CA
89K9*98
A*8A
K*?; ;*98 AH*AE
CapacityCart
>H8*AC
AE*EH AE*EH
>*C>
8;E*9H
KH98*>; A;*CA
>;*>>
;*?E ;K*;9
 ) (   ( 
) (
        ( 
      ) 
*
5  ,    
( *
5(

 HalfSize        
 -KH*K?. ,
    V      
->K*K?.*,  V
))->K*99. 
 1  -H*9C.*    
DoubSize *
5(1  
  HalfOffRate    (  
     (   
    ( -C;*8E.* !   
->*H;.*! 
   )-A?*8K.*
DoubOffRate *
"2OrderBatch )()
 -CH>*CA.
 ()      -K*?;.* 0V 
      (   
-;*98.() -A*8A.*
,)
Capac- ityCart       
   2 ,*5
    (   ) 
 2  , -A;*CA.*
",   (     
  ->;*>>.    ( 
 -;*?E.*
!6/
 * 
, /*
7.
Conclusion
!)
       ( 
*! 
       
 (   / ( ;9;9* '
 , )     
&%''')
(  / ,  * &
, 
  (      
   (    
*,,, 
*!)
)   ,* !, )    
(@     ,* 5
  )  (  
     )  (
*!,   
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>K
  (   
 (    /
),*
%+
  @ (  
       
,  (
(   ) 2   (
 * % ,   
(     (
,  )  * !
 (
    (  
    /*
#/ (,
) ($
 )       
    (* 
        )
 )    , 
+ *
7.1. Managerial implications
&   )  , ) 
     2 
  ()  *  / 
 + () ,   (
)*3 , 
    ) 
   * 0) )  
        
  (  * !   
 (     )
,() ,
  (     *
%    (  )
     ) 
,   /* '  ,
) (@
,(*
!)(/
 )),,
 2(
(12 (
 , ( *"  )
*     ( ) 
(
  (    
*   )  )
   )    
,    (   , 
)2*
    
 
 (*
7.2.
Limitations and future work
,  )     
   ( )   
 *
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>C
Offline customer arrival rate % 3   1
   ()    *
0) )
Appendix. Notation
)(    
(*!)
 *!
  )  ),Q->. 
 (  , )    
, ((F-;.
     
,*
Limited demand context ! )    )
  /) 
 (*
(,     
  )    (,
,) ,
 )      ( 
)(*
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F'(
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
2 )
Policy generalization !  )  /  
 (@),
)* 5/,(/
   ( /(
-.*
Picker and cart decoupling "    
     @ , (
 * !(  ,  
,  )  3
)       *
   , )    
/  )  
*
Evaluating customer satisfaction   
  @    
) (
     ( ( 
*!  )  )
,*
,    (   
*     
 )
   / , (  
( 
 * ,    
      ( /
)) /  ) * 
/ ,+,(
* (
(6 
((-, 
)  (   << ( ,==
 ,   .*,))
     (  
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  (    ) 
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Data availability
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>?
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Acknowledgments
!(
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Q-Learning
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F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>E
References
  0 B, # '  ! 2
# ;9;;*    ( ,   
   )* L 
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 * ' I2  ;9;;* $/  
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&D ;9;;* 5,(, ,   , 
 ,

@,
(
*
L 
QVV)))*(*VV (V;9;;V9KV9?V),(,
,
,,
(,(VZ\H;(;8AAA>;*
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3,   , * $ D* %* * ;9;
->. ?4>8*
& SS %,  ^  ' G2
&S ;9>8*   , (  )=
**%* *;A? ->4;. ;C4H9*
#MD #I*M*;9;9*%  )
Q  , )  (  * "* D*
* $* ;;E >9CC;E* #2  '
 ^" ;9;A*    (  
(  , ,  * "* D*
*$* ;K; >9??EE*
#20#;9>?*/(
  
*$D* %* * ;C9 -;. H>E4H;E*
#I_*BNR2S2G;9;9*!((

* (* '* %* * ;; ->. HC48?*
# !#  #* D+ #`S D]
;9>?* /( 
)*
D*%* * '*KE -?.>;H;4>;8A*
# ! ,  # #*  D+
;9>C* %    ) (,  ,
*"*D** * 88 -;>. KAK>4KACE*
# Y*  M* 0 !* ;9>8* '    
  * "Q ;9>8"$$$V#"' >H
"#( #  "( ' -"#"'.*
* 8;E48AA*
# D  M ' 0 ' ^D / Y
, ;9;>* %1    
*(*'*%* **
# Y  3 I  B 
    ;9;>* "   (
   ,  *"Q %2 3
'Q %3' G #(  >E ;9;9* '
"  # * >?>4>?E*
#S7 B*  D* ( 3* >E?8* !  
 
     ,* *
* AA >4;C*
3 *! 3,"* 2D%*>EE8* 
( +, (  Q '   * D*
* * '* ;H
->. A4>K*
3, " 2 D( ;9;;* #) (@
   * * %* * A> ->>.
H9C84H9EH*
 I S 3!  I D ;99C*3 
 ( )  Q  )* $ D*
%* *>?;-;.
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 * * '* KA -?. ;HC?4;HE;*
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 * (* '* %* * >E ->. ?H4E?*
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Q $ ,    * (*
'* %* * ;> ->. ?K4>9;*
B M I  3 ;99?*   , 
 , (  * ""$ !* H9 ->>. >9C94>9?;*
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,  )b*
0'D*;9;>* (,,
 * #* "* $* >8H >9KE>E*
0N / 0 I 0 5 D ;9>K*
 (@ ,Q
  ()*"Q!)  I20 -$*.
"*D* 3** HH -A.*
0' I*" D*D,0M'D;9>A* !
(   Q 
*
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
 (  (@* (* '* %*
**
I ', $* ;9;A* # ( ,      
L*'* ,   8:   ,* L 
QVV)))*(*VV,V ;9;AV9>V>>V(
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\KCK>??KC;*
I3*#BD#*2D$*
;9;;*
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D,'*&)$!*'*;998*/,

  * "* D* * * ;; -H. AE84H>H*
(  *  ' 3* ! 3 % ;9>A* #
( (       
*$D*%* * ;;? ->. ?A4E;*
 M   0 ## ;9>C*  
  (   * 3* '
',* EH EC4>9?*
 D)  M B 2 # ^  ) '
5 ^ D ;9;>* 3 (  (  
    * "$$$ !*
#,* >4>H*
Y^M50 ;9;>*" ( <<,
 ==+,,*
$D*%* * ;EH -A. E;;4EA8*
 5  3 B G ^ O ;9>K*
   ( ,   ) *
$D*%* * ;H? ->. >9C4>;;*
 B, ;9>E* !  (@ Q 5, 
 (     /* L 
QVV)))**VV )V((
),(
,/V)VCA>HC9HC*ZU\U*
 *  * '22 * ! * ;9>?* %2
' &    $B,Q     # 
&@ G*
;9>?'* * A>?4A;K*
  B # 0* B $ 0* ;9;9* % 
  )Q  ,  )* "* D* *
$* ;;H >9C8KH*
  O & B B ;9>>*  ) 
 ( ,     LI  ,
Q   )*
"Q LI , ( "(
', #(  ;9>>*
G,,II,'3 *G
D & B* B /   7
 I* % B  ' & # '
 " I 0 I 3 5
3  ' 0 3 ;9>8* 0 
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
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9
  ( *  8>?
-C8H9. 8;E48AA*
 # 3 ;9;;* A ),    
     * L 
QVV)))*,*V)VA), 
VK;A;9KV*
2*%7, (', ) G*!  ;9>?*
(  (     * "Q
"'*
, ;9;9*OQ/(
,Q 3, * L 
QVV)))*,*VV+V*
%7 &0 Y$ #* ,2) I*
  # $' Dc;9;>* 
,  Q  ,* #* "* $*
>K9 >9CK9H*
  #  #2 0 ;9>?* $/
(   * #* %* * >99
>>C4>;C*
  % # Y  3 I
    ;9;>* ! ,
  Q % 2  ( 
  *  >H ->;.
A89*
 G B  BS #  S *
;9>A* )
( ,   * $ D*
%* * ;;8 ->. >4>>*
  ' $   ;9;>* '  ,
,
* "* D* * * 8E -A. CC;4CEC*
) 5 &* ;99C* / 3, Q '
 # (
3,-5,','.*
5,"L'* ) 5&*;9>E* (()(
2*$D*
%* *;C8 -A. CE84?;>*
F. Neves-Moreira and P. Amorim
International Journal of Production Economics 267 (2024) 109074
>
>
>
( 0 * 5  I # * ;9>K* 3,

Q !   * ) KC
->. A4A>*
O ' #G I, I* ;9>?* 3 (  
  ,    
* * #*"* (* 89 >A4;E*
0*3  '*>E?A*% 
)Q    (    * %*
* A> -A. 89C48;>*
 D ;9;9* &      ( 
 ((* L 
QVV)))*(*V(),VV
;>>A>H>9V,(
((*
2L D 0  * ;9>K*, 
,    * "* D* * *
8H ->. ;>84;A>*
R2 D 2 $  B &
$+ R2',;9>E*!
 /* $ D* %* * ;C? -;. K>84K;?*
 I D  I S ;99>*     
)
)   * $ D* %* * >AA ->. A;4
HA*
 I D I d ;99>*   (
))
  * "* D* * * AE -E. >?K84
>??A*
I DG "** 3!,D*B*;9>8* '
  ( ) ,   * "* D* *
*8A->>.
AA9K4AA;K*
'(, & ;9;;*   (   Q 0) 
2  &%"' /* L 
QVV)))*(*VV(V ;9;;V9AV9HV(
()2 /VZ
\8HECHAE*
'  G 5 ! ;9>K* 89! , 
P#,
Q #  * !* '*
89 -;. 8CE48E9*
'2 S 0 ' '  5e B
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>>KC98>E8EK*
... The advent of e-commerce presents a significant challenge to traditional offline retail channels in catering to diverse consumer demands (Bell et al., 2014;Neves-Moreira & Amorim, 2024;Rigby, 2011). In response, the retail industry has seen a growing trend towards omnichannel retailing, an approach integrating both online and offline channels for enhanced consumer convenience and competitiveness. ...
Conference Paper
This paper is a systematic literature review on use of the Deep Reinforcement Learning (DRL) and Graph Neural Networks (GNN) in warehouse. We first explore the use of DRL and GNN for optimization of order picking and batching in warehouse. Because of very little results on use of GNNs in optimization of order picking and batching we extended our search to general use of GNNs in warehouse environment. We identified different topics of research using Latent Dirichlet Allocation (LDA) and identified main problems in use of DRL and GNNs in warehouse environment.
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Omnichannel Retailing (OCR) places a strong emphasis on how different channels work together to offer seamless purchasing experiences for customers. Nevertheless, retailers will incur significant costs in implementing it. This study investigates the variables influencing OCR by examining the executive perspectives required by retailers to realize, expand, and improve OCR. To achieve this, system dynamics is employed, and a model is created to determine the factors influencing three stock variables-profitability, delivery time, and customer satisfaction-as well as the degree to which these effects are present and the connections among them. Before designing the model, the influential variables were extracted from the literature by considering the ex-perts' opinions. Then, the optimal values of the variables were evaluated by creating two different scenarios and three policies. The findings showed that utilizing OCR contributes to both the highest possible profit and level of customer satisfaction. Moreover, to achieve the lowest level of delivery time, we proposed three policies: 1) the creation of a distribution center, 2) inventory management and safety stock, and 3) demand management. The results of the implementation of these policies are given at the end of the article.
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Establishing innovative fulfillment options for online orders has become a key challenge for bricks-and-mortar retailers. A mere focus on store sales is no longer affordable due to the competition by pure online players. Retailers are continuously developing new approaches for online order fulfillment and last-mile logistics. Further shortening lead times is becoming even more important in this context. One recently developed concept is the omnichannel approach where existing structures are utilized and distribution centers (DCs) and local stores are integrated into a holistic fulfillment concept. This concept is especially relevant when retailers are providing fast delivery services (e.g., same hour delivery). It resembles a multi-depot vehicle routing problem where all facilities act as depots and orders are assigned based on processing and transportation costs as well as available delivery capacity. We address this new concept and present the novel problem for rapid integrated order fulfillment in grocery retailing. We empirically identify decision-relevant costs for order processing in stores and develop an approach for the evaluation of overall fulfillment costs. Our work considers the order assignment to heterogeneous depots and vehicle routing for each depot depending on depot-specific fulfillment costs using a tailored cluster-first-route-second heuristic. We show that integrated rapid order fulfillment can reduce costs by an average of 7.4% compared to order fulfillment from DCs. However, as order processing costs at stores remain a significant cost factor, DCs will always have some relevance and cannot entirely be replaced by delivery from stores. Our results highlight the importance of modeling order processing costs in stores for actual order fulfillment decisions in a heterogeneous network.
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Customers shifting from stationary to online grocery shopping and the decreasing mobility of an ageing population pose major challenges for the stationary grocery retailing sector. To fulfill the increasing demand for online grocery shopping, traditional bricks-and-mortar retailers use existing store networks to offer customers click-and-collect services. The current COVID-19 pandemic is substantially accelerating the transition to such a mixed offline/online model, and companies like the one behind this study are facing the urgent need of a re-design of their business model to cope with the change. Currently, a majority of the operations to service online demand consists of in-store picker-to-parts order picking systems, where employees go around the shelves of the shop to pick up the articles of online orders. The optimization of such operations is entirely left to the experience of the staff at the moment. Since in-store operations are a major cost-driver in retail supply chains, this paper proposes optimization ideas and solutions for these in-store operations. With experimental simulations run on a real store with real online orders, we show that a simple optimization tool can improve the situation substantially. The method is easy to apply and adaptable to stores with complex topologies.
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Problem definition: Observing the retail industry inevitably evolving into omnichannel, we study an offline-channel planning problem that helps an omnichannel retailer make store location and location-dependent assortment decisions in its offline channel to maximize profit across both online and offline channels, given that customers’ purchase decisions depend on not only their preferences across products but also, their valuation discrepancies across channels, as well as the hassle costs incurred. Academic/practical relevance: The proposed model and the solution approach extend the literature on retail-channel management, omnichannel assortment planning, and the broader field of smart retailing/cities. Methodology: We derive parameterized models to capture customers’ channel choice and product choice behaviors and customize a corresponding parameter estimation approach employing the expectation-maximization method. To solve the proposed optimization model, we develop a tractable mixed integer second-order conic programming reformulation and explore the structural properties of the reformulation to derive strengthening cuts in closed form. Results: We numerically validate the efficacy of the proposed solution approach and demonstrate the parameter estimation approach. We further draw managerial insights from the numerical studies using real data sets. Managerial implications: We verify that omnichannel retailers should provide location-dependent offline assortments. In addition, our benchmark studies reveal the necessity and significance of jointly determining offline store locations and assortments, as well as of incorporating the online channel while making offline-channel planning decisions.
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Technological advances in the last two decades have aroused great interest in the class of dynamic vehicle routing problems (DVRPs), which is reflected in the significant growth of the number of articles published in this period. Our work presents a comprehensive review of the DVRP literature of the last seven years (2015 - 2021) focusing mainly on applications and solution methods. Consequently, we provide a taxonomy of the problem and a taxonomy of the related solution methods. The papers considered for this review are discussed, analyzed in detail and classified according to the proposed taxonomies. The results of the analysis reveal that 65% of the articles deal with dynamic and stochastic problems (DS) and 35% with dynamic and deterministic problems (DD). With respect to applications, 40% of articles correspond to the transportation of goods, 17.5% to services, 17.5% to the transport of people and 25% to generic applications. Among the solution methods, heuristics and metaheuristics stand out. We discussed the application opportunities associated with DVRPs in recent business models and new concepts of logistical operations. An important part of these new applications that we found in our review is in the segment of business-to-consumer crowd-sourced services, such as peer-to-peer ride-sharing and online food ordering services. In our review many of the applications fall into the stochastic and dynamic category. This means that for many of these applications, companies usually possess historical data about the dynamic and uncertainty sources of their routing problems. Finally, we present the main solution streams associated with DVRPs.
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Omni‐channel services, such as buy‐online‐pick‐up‐from‐store, transfer the in‐store logistics once completed by shoppers to retailers. To cost‐effectively meet the high demands for such pickup services, we introduce a crowdsourced order‐fulfillment policy that deploys in‐store customers to pick items for online orders while completing their own personal shopping. As opposed to existing store fulfillment policies, this new concept utilizes in‐store customers to help, not constrain, dedicated pickers. Empirical data indicates that a high percentage of surveyed in‐store shoppers would be willing to occasionally participate in such a program. In‐store customers willing to participate were observed to be heterogeneous in their efforts, with variability in how much extra time they would be willing to provide and would prefer picking tasks that had only a small deviation from their personal shopping. Motivated by these empirical results, the decision problem of how to assign picking tasks for arriving online orders with a given service commitment, to a set of arriving in‐store customers or an abundant set of dedicated pickers, was formalized to capture the uncertainty and heterogeneity of using in‐store customers for in‐store picking tasks. We propose a tractable decision‐making methodology to determine whether an order will meet both service commitment feasibility and in‐store customer availability with a probability at least equal to a target threshold. This method captures dynamic order placements and in‐store customer arrivals and stochasticity in in‐store customers shopping baskets. Extensive computational experiments for varying operational conditions of a grocery store dynamically matching actual online orders to arriving in‐store customers helps answer open questions from practitioners. Compensating in‐store customers based on their additional efforts reduced costs of fulfillment by greater than 30%, on average, compared to a baseline that uses only dedicated pickers for store fulfillment. Using the past five shopping baskets of participating in‐store customers to estimate assignment decisions can achieve both high online order service commitments and in‐store customer availability requirements. Our results suggest that in‐store customers should be assigned smaller orders than dedicated pickers. This article is protected by copyright. All rights reserved
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While click and collect (C&C) is a growing omni-channel grocery shopping model spreading out in Europe and in the US, little attention has been paid to the design of convenience measure in this setting is under researched. In particular the role of the digital feature and its impact on consumer response. We explore the impact of C&C on consumer response through the customer's perception, from his digital to his physical trip. This paper studies customers' behaviors toward their usual retailer and their relationship with them toward the theory of services and more precisely the Service dominant logic (S-D-L). Cconsumers response is analyzed through the prism of convenience, especially by transposing usual measures: access, functional, process, relational to the C&C setting and providing a new one: digital convenience. The conceptual model has been tested empirically on a sample of 1078 consumers and responses are analyzed and decomposed by using Path-PLS structural equation modeling. Our evidence also suggests, that in a whole, each feature of convenience positively influence consumer response with different intensity levels. These findings provide specific recommendations for each C&C system. Thus, functional convenience has the strongest contribution of the model and explains 31.4% of customer response. Further segmented approaches of the causal model prove that fulfillment of C&C has a moderating effect on the relationship between convenience and consumer response. Access convenience remains a prerequisite for C&C in a whole, but somewhat surprisingly our results make evidence that it has a negative impact in a drive-in system. We show that digital convenience is clearly discriminant according the type of C&C.
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Problem definition: Omnichannel retailing has led to the use of traditional stores as fulfillment centers for online orders. Omnichannel fulfillment problems have two components: (1) accepting a certain number of online orders prior to seeing store demands and (2) satisfying (or filling) some of these accepted online demands as efficiently as possible with any leftover inventory after store demands have been met. Hence, there is a fundamental trade-off between store cancellations of accepted online orders and potentially increased profits because of more acceptances of online orders. We study this joint problem of online order acceptance and fulfillment (including cancellations) to minimize total costs, including shipping charges and cancellation penalties in single-period and limited multiperiod settings. Academic/practical relevance: Despite the growing importance of omnichannel fulfillment via online orders, our work provides the first study incorporating cancellation penalties along with fulfillment costs. Methodology: We build a two-stage stochastic model. In the first stage, the retailer sets a policy specifying which online orders it will accept. The second stage represents the process of fulfilling online orders after the uncertain quantities of in-store purchases are revealed. We analyze threshold policies that accept online orders as long as the inventories are above a global threshold, a local threshold per region, or a hybrid. Results: For a single period, total costs are unimodal as a function of the global threshold and unimodal as a function of a single local threshold holding all other local thresholds at constant values, motivating a gradient search algorithm. Reformulating as an appropriate linear program with network flow structure, we estimate the derivative (using infinitesimal perturbation analysis) of the total cost as a function of the thresholds. We validate the performance of the threshold policies empirically using data from a high-end North American retailer. Our two-location experiments demonstrate that local thresholds perform better than global thresholds in a wide variety of settings. Conversely, in a narrow region with negatively correlated online demand between locations and very low shipping costs, global threshold outperforms local thresholds. A hybrid policy only marginally improves on the better of the two. In multiple periods, we study one- and two-location models and provide insights into effective solution methods for the general case. Managerial implications: Our methods provide effective algorithms to manage fulfillment costs for online orders, demonstrating a significant reduction over policies that treat each location separately and reflecting the significant advantage of incorporating shipping in computing thresholds. Numerical studies provide insights as to why local thresholds perform well in a wide variety of situations.