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Periodic Route Optimization
for FMCG Distributors
Onur Çopur, Mert Yıldız, Simru Göven, Ali ÖvünçGüneri,
Alper Berke Yavuz, Mahmut Ali Gökçe, and Cansu Yurtseven
(&)
Industrial Engineering, Yaşar University, Bornova, Turkey
onurcopur12@gmail.com, mrtyldz.1909@gmail.com,
simrugoven@gmail.com, alperberkeyavuz@gmail.com,
a.ovuncguneri@yahoo.com, {ali.gokce,
cansu.yurtseven}@yasar.edu.tr
Abstract. Izmir based Information Technology (IT) solution provider develops
supply chain management software tools for many customers from fast moving
consumer goods sector (FMCG). Customers of the FMCG sector needs to be
visited a certain number of times in a given period by sales representatives. The
company must decide which customers must be visited in which sequence by
each sales representative while obeying visit frequency and time windows
requirements. These decisions have significant impact on total cost. For this
reason, finding an optimal route for every sales representative for each day of the
planning horizon is important. This practically challenging and technically
important problem can be described as periodic multiple depot traveling sales-
man problem with time windows (PMDTSPTW). We propose a novel mathe-
matical model for the optimal solution of this problem. The proposed model
minimizes the total distance traveled by sales representatives by deciding which
sales representative will visit which customer on which day while following the
time windows to collect demand data. The proposed model is applicable to any
company from FMCG sector. The solution approach in this study is imple-
mented and tested with real life including coordinates and location data of
customers and sales representatives from Turkey’s largest beer distributor. The
proposed model is solved using IBM ILOG CPLEX Optimization Studio ver-
sion 12.8. The results show significant improvement over the current situation.
To ensure efficient usage of the proposed approach, a user-friendly decision
support system (DSS) is constructed and implemented.
Keywords: Periodicity Travelling salesman problem Time windows
Mathematical programming Decision support system
1 Introduction
The purpose of this study is to propose a novel mathematical model for the solution of
periodic multi-depot traveling salesman problem with time windows (PMDTSPTW)
and to present the implementation of the solution in a real-life case study with the data
provided by one of the biggest beer distributor in Turkey. This work focuses on route
optimization problem of sales representatives in fast moving consumer goods (FMCG)
©Springer Nature Switzerland AG 2020
N. M. Durakbasa and M. G. Gencyilmaz (Eds.): ICPR1 2019, LNME, pp. 748–759, 2020.
https://doi.org/10.1007/978-3-030-31343-2_63
sector. In the FMCG sector, big retailers and manufacturers need sales representatives
(SR) and distribution vehicles to sell and distribute their goods to large number of
customers. Each customer should be visited a certain number of times in during a
planning horizon, within the given time windows by sales representatives. Therefore,
finding routes with minimum cost for the sales representatives is a relevant and fre-
quently studied problem in the FMCG sector.
This problem is practically important, technically challenging and forms a new case
for literature. As the data of the problem gets larger, difficulty of optimization increases
exponentially. Proposing a good solution approach for such a complex case is chal-
lenging. The problem studied belongs to one of the largest Information Technology
(IT) solution provider which is a software company headquartered in Izmir and has
several customers in FMCG sector. The customers’request is a routing module to
optimize the visits of sales representatives from seven starting points (houses of SR’s)
to customers with minimum travelling distance. Sales representatives visit local mar-
kets and supermarkets for collecting the orders. The case study presented with the
proposed solution contains 869 customers and 7 sales representatives, which leads a
complicated and dense problem. This study specifically focuses on routing optimiza-
tion of SR’s and PMDTSPTW is used to apply real world conditions as much as
possible.
2 Problem Definition
The problem can be classified as periodic multi-depot travelling salesman problem with
time windows (PMDTSPTW) and it is a variant of TSP. To clarify, the visit frequency
requirements of customers makes the problem periodic and different starting points of
each route makes the problem multi-depot. In addition to that, each customer has
(a) specific time window(s) for accepting the sales representatives. The company has to
assign each sales representative customers to visit with routing information and collect
demand. After collection of demand, the orders are assigned to the delivery vehicles
which distribute the goods. Currently, the last part of problem, which covers assign-
ment of vehicles and distribution of the orders, can be solved by the company to their
satisfaction. However, route determination for sales representatives is done by intuitive
methods based on experience, which can be quite far from the optimal in complex
cases. There are customers to be visited at certain times for a given number of times in
a week, while each sale representative starts and ends the day at his/her own house.
This makes the problem periodic and multi-depot. The solution proposed in this study
may enable customer visits to be performed with less sales representatives than
appointed. To the best of our knowledge, there are a limited number of studies in the
literature and sources related with this type of problem. Therefore, the two motivations
of this study are satisfying requests of the company and contributing the literature.
In order to solve the problem, following input data are required: number of visits
per period for each customer, time spent at each customer, work shifts of sales rep-
resentatives, earliest and latest possible arrival time for each customer, and a distance
matrix that shows the distances between each pair of node. So far, the company
provided the real coordinates of the customers and sales representatives for testing and
Periodic Route Optimization for FMCG Distributors 749
implementation of the proposed solution method. The data used in the case study
belong to one of the biggest beer distributors in Turkey. This distributor is located in
the center of Izmir and has 869 customers in total. Among the 869 customers, 621 of
them need to be visited twice a week and the rest is needed to be visited only once a
week. There are seven (7) sales representatives employed by this distributor. According
to this data set, a distance matrix will be fetched by using Bing Maps Restful API on
Python 3. The Bing Maps Distance Matrix API provides travel time and distances for a
set of origins and destinations. The distances and times returned are based on the
routes, calculated by the Bing Maps Route API. Distance matrices can be calculated for
driving, walking and public transit routes. For this case, it is assumed that all distances
between customers are driving distances. A distance matrix can be requested that has
up to 2500 origins-destinations pairs which is calculated by multiplying the number of
origins, by the number of destinations. However, in this problem, the distance matrix
size should be 869 * 869. A python code is developed to create the whole distance
matrix by creating a sliding 50 * 50 matrix inside the 869 * 869 size matrix. If a new
customer is added to the system, or if it is desired to remove, updating the data will be
easier with the API code. To fetch the data from Bing Maps API, Json and urllib
libraries are used.
In addition, on average, a sales representative works 10 h a day, spends 10–15 min
at each customer and visits 35–40 customers in a day. Currently, routing operations are
made based on personal experience of the employees. Therefore, total traveled distance
by sales representatives and the workload balance of sales representatives can be
compared with the previous status as a performance measure. In this problem, main
objective is minimizing the total traveled distance by sales representatives within
working hours. They start their routes from different locations (considered as a multi-
depot problem) for collecting orders from different customers who are needed to be
visited according to their visit frequency. This problem is easy to solve for small data
sets. However, with 869 customers mathematical model takes too much time to gen-
erate a solution for large size instances.
3 Literature Review
The problem studied is the combination of three different extensions of vehicle routing
problem (VRP). These are Periodic VRP (PVRP), Multi-depot VRP (MDVRP) and
VRP with time windows (VRPTW). Since, TSP is quite similar to VRP and the
difference between them is that in VRP, vehicles have a limited capacity which pick-up
and deliver the goods to the customers. The extensions of these vehicle routing
problems are frequently studied in FMCG sector and known as challenging problems.
Because of the similarities to our problem, we have reviewed many articles. The
articles are examined in detail below and sorted by the relevance.
Chu et al. [2] proposed a periodic capacitated arc routing problem. This study
contains linear programming model, metaheuristic and lower bounds, also includes task
assignments and determination of vehicle trips while focusing on minimizing the total
cost.
750 O. Çopur et al.
Thangiah [10] represented a study about vehicle routing problems with time win-
dows. This study contains Hybrid Genetic Algorithms, Simulated Annealing and Tabu
Search Heuristic. With similar to our problem, this study focuses on minimizing the
distance traveled to service the customers. In addition this study includes decisions
about the number of vehicles.
Pacheco et al. [7], studied about optimizing vehicle routes in a bakery company. In
this case, delivery dates are flexible. This study is related to our problem with same
objective function; minimizing the total distance travelled for the daily routes over the
week. Unlike our problem, this study has flexibility at delivery dates.
Alinaghian [1] proposed a navel heuristic algorithm for a periodic vehicle routing
problem. This paper also focuses on client visits over a given time horizon. The
represented model also optimizing the routes in each time period. In addition, this paper
represents a new heuristic algorithm based on data mining.
Tan et al. [9] proposed a heuristic method for vehicle routing problem with time
windows. Objective of this article is to achieve the minimum transportation cost
including travelled distance while considering the penalties. Also a novel genetic
algorithm clustering method is proposed in this paper.
Clarke and Wright [3] represented a study about vehicle scheduling. In this case
there is a central depot and delivery points. This study focuses on finding the optimum
routes under the conditions of varying truck capacities. To mention this study finds
optimum or near-optimum routes for the problem.
Paletta [8] developed a new heuristic algorithm for the periodic traveling salesman
problem. This new algorithm has smaller average percentage error than existing
algorithms. This paper is also considered as a traveling salesman problem and objective
is to minimize the total distance traveled.
Coene et al. [4] studied on a periodic vehicle routing problem. This paper is about a
variant of a periodic vehicle routing problem. Objective function of this study is to
minimize the sum of the costs of all routes over the planning horizon.
Mancini [6] proposed a solution approach for a multi depot multi period vehicle
routing problem. In this study there is a heterogeneous fleet. The aim of this study is to
minimize the total delivery cost. This fleet contains vehicles with different capacity.
Similar to our problem, this paper also has mixed integer programming (MIP) solution
approach.
The most relevant article with our study is proposed by Cordeau et al. [5]. They
developed a base mathematical model and suggested minor changes to solve the
periodic vehicle routing problem, the periodic traveling salesman problem, and the
multi-depot vehicle routing problem. Besides the mathematical model, they also pro-
posed a tabu search heuristic. The proposed solution for this study based on compu-
tational experiments carried out on instances taken from the literature indicates that the
proposed method outperforms existing heuristics for all three problems. All relevant
articles are mentioned in Table 1.
There are a number of contributions to literature from this study. To the best
knowledge of the authors, the novel mathematical model is the first of its kind for a
periodic routing problem of multiple sales representatives as described, taking into
account not only time windows but also considers traffic conditions while minimizing
the total distance traveled and ensuring the workload balance. Also, the model is
Periodic Route Optimization for FMCG Distributors 751
verified and validated and tested with real life data, as presented in Sect. 5. In the
literature, there are problems with similar aspects to our study, but there is no problem
that meets our case.
4 Modeling and Solution Methodology
In this section, a novel mixed integer mathematical programming model is proposed for
PMDTSPTW. Indices, sets, parameters and decision variables of the problem are
shown in Table 2.
Table 1. Literature table
Periodic Multi
depot
Time
windows
Vehicle routing
problem
Traveling salesman
problem
Alinaghian, M., 2014 ✓✓
Chu et al., 2004 ✓✓
Clarke, G., Wright,
J.W., 1964
✓
Coene et al., 2010 ✓✓
Cordeau et al., 2010 ✓✓ ✓
Mancini, S., 2015 ✓✓ ✓
Pacheco et al., 2012 ✓
Paletta, G., 2002 ✓✓
Tan, K.C. et al., 2001 ✓✓
Thangiah, S.R., 1999 ✓✓
Our Study ✓✓✓ ✓
Table 2. Indices, sets, parameters and decision variables
Indices, Sets, Parameters
iStarting node index
jDestination node index
kSales representative index
lDay index
rPossible visits index
I;JSet of customers I;J¼Mþ1;...;Nfg
HSet of dummy indices to ensure that a sales representative arrives at a customer on a
given day it also leaves that customer on the same day. H¼Mþ1;...;N
fg
KSet of sales representatives K¼1;...;M
fg
LSet of days of week (period), 1 represents Monday, 6 represents Saturday.
L¼1;...;6
fg
RSet of all possible visit combination
CiSet of allowable visit combination for customer i2I;Ci2R
(continued)
752 O. Çopur et al.
4.1 Mathematical Model
min z¼X
i2I[KX
j2J[KX
k2KX
l2L
dijxijkl ð0Þ
Subject to
X
r2Ci
yir ¼18i2Ið1Þ
X
j2JX
k2K
xijkl ¼X
r2Ci
arlyir 8i2I;8l2Lð2Þ
X
i2I
xihkl ¼X
j2J
xihkl 8h2H;8k2K;8l2Lð3Þ
Table 2. (continued)
MNumber of sales representatives
NNumber of customers
EriEarliest service time for each customer i
LaiLatest service time for each customer i
VAverage Speed of vehicle
dij The distance from node i2Ito j2J
arl 1;iff day l2Lbelongs to visit combination r2Ci
0;otherwise
WE Work ending hour in terms of minutes
MTD Morning traffic duration
ETD Evening traffic duration
SiService duration of customer i2I
Decision Variables
xijkl 1;iff sales representative k2Kvisits customer j2Jimmediately
after visiting customer i2Iduring day l2L
0;otherwise
8
<
:
yir 1;iff visit combination r2Ciis assigned to customer i2I
0;otherwise
wikl Service start time of customer 8i2Iby sales representative 8k2Kon day 8l2L
uikl Sequence index variable defined for subtour elimination 8i2I;8k2K;8l2L
xikl Sequence index variable defined for subtour elimination 8i2I;8k2K;8l2L
yikl Sequence index variable defined for subtour elimination 8i2I;8k2K;8l2L
zikl Sequence index variable defined for subtour elimination 8i2I;8k2K;8l2L
Cf il 0:85;if wikl 90 or wikl 390
1;otherwise
Periodic Route Optimization for FMCG Distributors 753
X
i2IX
k2K
xijkl 18j2J;8l2Lð4Þ
X
j2K
xijkl ¼18j2J;8k2K;8l2Lð5Þ
X
j2K
xijkl ¼18i2I;8k2K;8l2Lð6Þ
wikl þSiþdij
VCfil
60 M1xijkl
wjkl
8i2I[K;8j2J[K;8k2K;8l2L
ð7Þ
Eriwikl Lai8i2I;8k2K;8l2Lð8Þ
wikl MTD þWE ETDðÞxikl ð9Þ
wikl WE ETDðÞ1yikl
ðÞ ð10Þ
wikl MTD 1zikl
ðÞ ð11Þ
wikl WE ETDðÞþMTD zikl
ðÞ ð12Þ
xikl þyikl þzikl ¼2ð13Þ
cfil 0:85 zikl þ1zikl
ðÞ ð14Þ
uikl þ1ujkl þM1xijkl
8i2I;8j2J;8k2K;8l2Lð15Þ
xijkl 20;1
fg 8i2I;8j2J;8k2K;8l2Lð16Þ
yir 20;1
fg 8i2I;8j2J;8k2K;8l2Lð17Þ
uikl 08i2I;8k2K;8l2Lð18Þ
wikl 08i2I;8k2K;8l2Lð19Þ
The objective function minimizes the total distance travelled by sales representa-
tives (0). Constraint (1) ensures that exactly one feasible visit combination must be
assigned to each customer. Constraint (2) indicates that each customer is visited only
on the days corresponding to the assigned combination. Constraint (3) ensures that
when sales representatives arrive at a customer on a given day it also leaves that
customer on the same day. Constraint (4) restricts that each customer must be visited by
at most one sales representative on each day. Constraint (5) indicates that each sales
representative starts the tour from their homes on each day. Constraint (6) ensures that
each sales representative goes back to their homes at the end of every day. Constraints
(7–8) ensures that the arrival time of two consecutive customers does not collide with
754 O. Çopur et al.
each other considering the duration of service and travel between customers and
limiting the sales representatives to arrive at a specific time. Constraints (9–14) ensure
that velocity constant should be 0.85 if wikl is in morning traffic duration or evening
traffic duration. Constraint (15) is for subtour elimination. Constraints (16–19) are sign
restrictions.
5 Computational Results
Due to the size and complexity of the real data received from the company, a general
coordinate scan was performed to test the accuracy of the data. The mathematical
model is solved by IBM ILOG CPLEX version 12.8 optimization software with dif-
ferent sizes of data for the purpose of monitoring performance and accuracy control.
The results of MIP model are shown in Table 3.
Table 3presents the results of the optimization model for varying number of
customers. These cases use the real life data from the case study. The results reported in
Table 3show that the problem a steep increase in solution time as the problem size gets
larger. While for the cases with number of customers 30, 40, 50, 60, 70 have optimal
results, the best results for cases with number of customers 80, 90 and 120 are best
solutions reported by CPLEX after the cutoff point of 4 h applied. Even though
problems larger than 70 customers are run without any time limit, the best computer in
hand, 2.8 GHz Core i7 CPU and 16 GB RAM, turned memory error and stopped
before reaching to an optimum solution. For this reason, we have added cutoff points
for CPLEX and the results returned for this restricted times. It seems that for real large
size problems can only be solved by dividing the problem into the sub-problems and/or
by employing heuristic methods. The mathematical model results prove that the model
runs smoothly. The solution founded by MIP on CPLEX checked manually and the
routes satisfy all constraints which mean the method is verified and considered as valid.
Table 3. Results of MIP by IBM ILOG CPLEX 12.8
Number
of SR
b
Number
of
customers
Number of customers
with single visit
frequency
Number of customers
with double visit
frequency
Objective
function
(Km)
Solution
time
(Min)
2 30 9 21 17.74 10.37
2 40 12 28 19.35 25.48
2 50 15 35 20.32 52.29
2 60 18 42 21.80 92.54
2 70 21 49 34.97 123.45
2 80 24 56 37.65 240.00
a
2 90 27 63 43.85 240.00
a
2 120 36 84 54.12 240.00
a
a
Cut off point (4 h) results.
b
SR = Sales Representatives
Periodic Route Optimization for FMCG Distributors 755
6 Decision Support System
Decision Support System (DSS) is an information system that allows people to get
support from computer technology during decision making. Dense and complex data
used while problem solution phase can be modeled and reduced to understandable
levels. To mention briefly, decision support system is a combination of data, infor-
mation, software, analysis and mathematical model. DSS helps people to understand
the complex systems and solution methodology of these systems. Due to such benefits,
in this study a user-friendly decision support system is constructed.
There are three main parts of DSS; “Main Page”,“Solve”and “PDFPrint”.“Main
Page”screen displays general information and explanations about DSS, what opera-
tions DSS performs and how it performs, and information such as printouts. DSS main
screen is enriched with vehicles and route visuals to better represent the purpose of the
project visually. There are two buttons on the “Main Page”screen; “Start”and “Help”
button, which can be seen in Fig. 1.
Clicking the “Start”button displays the “Solve”page of DSS, see Fig. 2.“Solve”
page is divided into three separate parts. Simply, there are inputs on the left side and the
outputs in the middle of the “Solve”page. There is also “Google Maps”area on the
right side of the page, which visualizes optimal routes found at the end of the solution.
“Add”button adds sales representative or customer to the system. “Remove”button to
removes sales representative or customer from the system. There is one extra button,
“Clear”, which helps user to clear all sales representatives or customers from the
system with just one click.
To see the solution, sales representative name and day are selected from the “Out-
put”screen. The solution is displayed on the screen when “Bring the Result”button is
Fig. 1. DSS Main Page
756 O. Çopur et al.
pressed. The solution screen displays where the sales representative comes from and
where the sales representative goes, the name of the sales representative, the specific day
and arriving and departure time of the customer. When the “Detailed PDF Report”
button is clicked, system generates a detailed PDF report which is visualized in Fig. 3.
Fig. 2. DSS system menu
Fig. 3. DSS report output
Periodic Route Optimization for FMCG Distributors 757
When all transactions are completed, the detailed report is sent to sales represen-
tatives by just clicking on a single button, “Mail to Sales Representatives”, and sending
them as e-mail. In this way, loss of communication and time loss between processes are
prevented.
7 Conclusion and Future Work
In this study, a mathematical model is proposed for periodic multi-depot traveling
salesman problem with time windows (PMDTSPTW). Firstly, a general system anal-
ysis is performed. To explain briefly, the technically challenging and practically very
important problem studied and to mention, given data belongs to one of the biggest
beer distributor in Izmir. Companies associated with FMCG sector needs route opti-
mization to distribute their goods. The coordinate’s data given by company used to find
the distance matrix. Bing Maps Restful API is the tool that found and creates this
matrix on Python 3.6. As it is mentioned before the goal of this study is to minimize the
total traveled distance by sales representatives. According to customers’visit frequency
multiple routes, for multiple sales representatives who start to their routes from dif-
ferent depots (houses) founded for a planning horizon. While these routes founded a
certain time window considered. The mixed integer programming (MIP) method is
used.
There are important contributions both to company and literature from this study.
To the best knowledge of the authors, the novel mathematical model is the first of its
kind for a periodic routing problem of multiple sales representatives as described,
taking into account time windows and also traffic conditions while the aim is mini-
mizing the total distance traveled and ensuring the workload balance. In the literature,
since there are problems with similar aspects to our study but there is no problem that
meets our case, a contribution to the literature is made.
The main contribution to the company by this study can be identified as a solution
method that has been created which increases the efficiency, minimizes the total
traveled distance and ensures the workload balance. In the old system, the routes
created based on the experience of the sales representatives are formed with the help of
scientific methods in the new system. The decision support system is developed for a
routing system based on scientific methods. With this mathematical model and user
friendly decision support system, new system can be adapted to any company from real
life. The decision support system created with the Excel VBA interface enables the
finding, visualization and reporting of optimal routes for sales representatives. The
reporting process is an additional feature of the decision support system that enables the
sales representatives to receive their daily routes by e-mail. The summary report
consists of destination, day, sales representative name, total number of visits and notes.
In accordance with the observed examples, the total distance traveled was reduced to a
minimum as intended.
Finally, as future work; there may be different types of sales representatives such as
pedestrians, motor driver sales representatives. Another possibility is that if a sales
representative finishes his/her route and working hours remain, another route can be
assigned to him/her. In addition, a lunch break constraint can be added to implement
758 O. Çopur et al.
the problem. For the solution method for cases with really large number of customers, a
detailed heuristic approach must be developed, tested and implemented.
Acknowledgement. This study is supported by TUBITAK (The Scientific and Technological
Research Council of Turkey) in the program of “2209-B Undergraduate Research Projects for
Industrial Applications Fellowship Program”. We would like to thank Ege Can Erdoğan,
Doğacan TANIŞand Zafer Yapıcıel for their support and contributions to this study.
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