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HEURISTICS AND HIPERHEURISTICS FOR SEQUENCING MIXED

MODEL ASSEMBLY LINES MINIMIZING WORK OVERLOAD

Joaquín Bautista Valhondo

NISSAN Chair UPC, – Escuela Técnica Superior de Ingeniería Industrial de Barcelona – Universitat Politècnica de

Catalunya, Barcelona, Spain

joaquin.bautista@upc.edu

Jaime Cano Belmán

Departament d’Estadística i Investigació Operativa – Universitat Politècnica de Catalunya

Barcelona, Spain

jaime.cano-belman@upc.edu

Abstract – There are different approaches for the

mixed model sequencing problem on assembly lines. In

this paper the goal of minimizing work overload is

treated. Since solve this problem optimally is difficult, we

test constructive procedures, local search and a new

hiperheuristic procedure.

Keywords: Sequencing, assembly line, work over-

load, local search, priority rules, JIT.

I. INTRODUCTION

Assembly lines are commonly used in automotive in-

dustry. Two important decisions for managing mixed

model assembly lines are to spread out work in stations

(balancing) and determine the sequence to introduce

cars in to the assembly line (sequencing). When the

medium term decision of balancing has been taken, se-

quencing decision must be considered. Depending on

the manufacturing environment it may be desirable

minimize or maximize some parameters or characteristics

of the line [1]. One of the two main criteria [2] for se-

quencing mixed models on assembly lines considers the

labelling of load on stations. The problem addressed in

this paper considers the objective of minimizing the work

overload.

Since a processing time for a product in a station can

be grater than cycle time, there is a maximum quantity of

those products that can be consecutively introduced in

the line without causing a delay in the finishing of

works. All those jobs with high and low work content

must be under control for avoiding excessive work load

and idle time. Stations are confined by upstream limit

and down stream limit. That implies that products are

mounted on an assembly line that moves at constant

speed and workers can do their job on products only

when they are inside their station. Products get in the

station at constant time intervals. Work overload occurs

when work on a product can not be finished before it

leaves the station.

Initial works on this criterion were carried out by [3]

or [4]. In this paper an extension of a procedure in [3] is

proposed, which considers not only two different

jobs/products (basic product and special product, dif-

ferentiable by their poor and rich work content respec-

tively), but also multiple products. Other literature re-

lated with the problem is [5], [6], [7] and recently [8].

Inspired on procedures from [4] and [9], four proce-

dures are proposed, which also consider multiple prod-

ucts and multiple stations. We use local search with

different neighborhoods for improving the solutions

obtained with constructive procedures. A new hiperheu-

ristic is tested with the sequencing problem.

This paper is organized as follows: section 2 contain

our constructive proposals, in section 3 we apply local

search, section 4 contains a proposal of a new hiperheu-

ristic procedure, section 5 shows computational experi-

ence for constructive procedures, local search and the

hiperheuristic. In section 6 conclusions are mentioned.

II. WORK OVERLOAD MEASUREMENT

In [3] a general formulation for measuring work over-

load is proposed. Work overload is measured in time

units and the time unit is the cycle time c (time between

product arrivals into the station). Let L denote the sta-

tion length (or time window), pik the processing time for

the job on the product i (i=1,…,I) in the station k

(k=1,…,K), st the starting instant of the job in the posi-

tion t (s1=0; st=max(t-1,ft-1)), and ft the finishing instant of

the job in position t (ft=min(st+pi,t-+L)). Given a se-

quence of size T (t=1,…,T), and considering only one

station, wot is the work overload obtained in position t

of the sequence: wot = [pi+st–(t-1+L)]+ where [x]+ =

max(0,x). The total work overload is z = ∑twot. Mathe-

matical programming formulations of the problem can be

found in [3] or [6]. The problem is difficult to solve due

to the lack of structural properties. The problem has a lot

of possible solutions and a big effort to evaluating those

solutions is required. As explained in [3], [6] or [8] the

problem is considered to be NP-hard.

To elucidate the reader on the work overload problem,

a single station illustrative example is shown. Four prod-

ucts are considered: A, B, C, and D, with the following

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235

processing times (0.82, 0.94, 1.19, 1.15), and demands

(3,5,7,1). Station length L=1.2. Processing times and

station length are expressed in cycle time units (c=1).

Let us assume products are going to be introduced into

the assembly line in the following order:

CCCADCCBCABABCBB.

Figure 1- Worker movement diagram

Without loss of generality, the initial worker position

is assumed to be on the upstream limit of the station.

Figure 1 represents the movement of the worker during

his job on the products according to the sequence es-

tablished above. Arrows represent the processing times,

and dotted lines represent the worker displacement from

one finished product to the next product on the line.

Station length is limited by the down stream limit (dsl).

The first job is done on a product kind C, which requires

1.19 time units. When this job is finished, the worker

walks upstream for reaching the product C in position 2

of the sequence. We assume this time is negligible be-

cause the velocity of the worker is greater than the con-

veyor speed. Then, the worker starts the second job 0.19

units away from the upstream station limit and would

finish it 0.19+1.19 units away from the upstream limit.

Nevertheless, the worker can not go beyond the dsl, and

0.18 units of work must be left unfinished (w1). When

the worker reaches the dsl, he leaves his job and walks

upstream, and starts working on the product in position

3 of the sequence 0.20 units away from the upstream

limit. Again, the time allocated is not enough to finish

the job, and 0.19 units of work overload are produced

(w2). The product in position 4 requires 0.84 time units,

and the work on it is finished when the worker is

0.20+0.84 units away from the upstream limit. This time,

the job is completed. Products in positions 6, 7 and 9,

also produce work overload (w3=0.16, w4=0.19,

w5=0.13). The total work overload produced by the se-

quence is 0.85 cycle time units.

III. CONSTRUCTIVE PROCEDURES

In this section, four procedures are proposed inspired

on the works from [3], [4] y [9]. Our proposals assume

multiple products and only one station. Then those one

station procedures are used for determining work over-

load prediction values in a multi station procedure taken

from [3]. An original procedure (Y&R) from literature is

described to make more understandable the proposed

extension.

A. Y&R Procedure

The original procedure from [3] considers single sta-

tion and two kinds of products: products with optional

components and basic products. Let A denote special

products, which have processing time greater that c, and

B denote basic products with processing time smaller

than c. The procedure is based on the repetition of a

stable subsequence composed by ma units A, and mb

units B. Since processing times for special products pa is

greater than c, there is a limit on the number of units A

that can be consecutively sequenced, without causing

work overload. This limit (X) is the maximum integer

satisfying X = (L-c)/(pa-c), and is also the maximum value

ma can take. The procedure tries to regenerate, that is, to

bring the worker back to the beginning of the window

(its assumed original position), after a cycle composed

by ma units A and mb units B.

The subsequence of ma and mb units, can be deter-

mined with the equation ma⋅pa+mb⋅pb=ma+mb, where

ma≤X. Then, assuming there are integer values for ma

and mb, maximum utilization is achieved by solving the

next nonlinear MP model (1).

maximize )/()( babbaa mmmpmp+⋅+⋅ (1)

s.t. ma ≤ X

pa ⋅ ma + pb ⋅ mb = ma + mb

ma , mb ≥ 0, integers

Let ni the quantity to be produced of product i (T=∑ni),

and nc the maximum number of cycles composed by ma

units A, and mb units B. The sequence is built according

to the following steps: 1) assign the nc cycles, 2) assign

xa=min(na-nc⋅ma, ma) products A, 3) assign xb=nb-nc⋅mb

products B, and 4) if necessary assign na-nc⋅ma-xa prod-

ucts A.

B. Y&R Procedure Extension

This extension considers not only two but also multi-

ple products. As in the original procedure, our extension

(YRx) builds sub-sequences composed by mi units of the

product i. While there are enough unscheduled units,

the sub-sequence is repeated. Otherwise, a new subse-

quence is calculated with the remaining products. Let A

the set of products with processing time greater than the

cycle time (pi>1), B the set of products with processing

time smaller than the cycle time (pi ≤ 1), and xi the maxi-

mum consecutive quantity of product i that can be

scheduled without causing overload or idle time.

maximize ∑∑ == ⋅I

ii

I

iii mmp11 (2)

s.t.

C C C A D C C B C A B A B C B B

w1 w2 w3 w4 w5

time

dsl

{

}

integers,0

,min

11

≥≤⋅

≤∑∑ ==

i

I

ii

I

iii

iii

m

mmp

dxm

L

1

0

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236

Model (2) is the extension proposal of the original

model (1), which finds the quantity of each product

contained in the sub-sequence.

In model (2), xi ≤ L-c/pi-c, ∀i∈A, and xi ≤ L-c/c-pi,

∀i∈B. di represents the remaining production of product

i. When t=0, di = ni. To arrange products in the subse-

quence, we consider alternatively the set A, and then the

set B. Let c denote the cycle time. The order in which

units will be incorporated into the sequence is done

according the diminishing value of index ri = mi⋅|c-pi|.

Thus, from the set A, the item with the bigger index ri (let

j) is selected and the mj products j are consecutively

assigned. Then, from the set B, the item with the bigger

index ri is selected (let l), and the ml corresponding

products l are assigned; and so on. Since it is easier to

solve a linear model than a non-linear model, we have

transformed the non-linear model (1) into a linear one.

Then we used the transformed model for finding subse-

quences.

C. Greedy Procedures

The proposed procedures try to favour the movement

of the worker in the station from the lower to the upper

limit of its station (Up-Down) as depicted in figure 2.

Arrows represent the processing times, and dotted lines

represent the worker displacement from one finished

product to the next product on the line. If a long arrow is

scheduled after the unit has been completed (in the

circle of figure 2), work overload is produced, then,

down step is required to avoid it.

With those two up-down cyclic steps, we attempt to

regenerate. Perfect regeneration is reached only for cer-

tain parameters values [3].

Figure 2- Up-down worker movement diagram

During the up step, only products with processing

time greater than c are considered. Products with proc-

essing time smaller than c are considered during the

down step.

For deciding the kind of product to sequence in the

period t, we make use of a dynamic index ri = di ⋅ |c-pi|,

where i belongs to the set A or B considered in the cur-

rent stage t. If t=0, di=ni. Since ri depends on the pend-

ing production of product i, it must be updated in each

phase. The product of the set under analysis with the

bigger index ri is selected to be assigned in period t. s1=0

is assumed.

Following those ideas, three procedures are pro-

posed: Ud, UdC and UdR. Ud allows commit in idle time

only ones in each cycle reaching the complete regenera-

tion; while it is possible; UdC forbids incurring in either

idle time or work overload, putting them off; UdR allows

a maximum quantity of work overload until the position t

of the sequence. This quantity is limited by lbw/T*t. lbw

is a lower bound of work overload considering multiple

stations.

( )

[

]

∑ ∑

=

+

=+−⋅−⋅=K

k

I

ikikiLTcpnlbw 1 1 )1( (3)

Where [x]+ is max(0,x). UdR tries to distribute or regu-

larize work load along the sequence.

D. Multi-station procedure

A multi-station procedure is taken from [3]. This pro-

cedure is based on single station procedures. Single

station procedures are used for determining work over-

load predictions. The sequence is built progressively in

such a way that for each sequencing instant t, the prod-

uct with remaining production and the best overload

predictor is selected and assigned in the tth position of

the sequence.

Let: wpik be the work overload predictor in station k

due to the assignment of product i, wi(k,t) be the work

overload obtained in station k in period t of the se-

quence due to the assignment of product i, skt be the

starting instant of job in station k in period t (or initial

worker position in station k in period t), and sci(t) be the

total work overload prediction produced by product i in

period t.

0. Initialize s=0.

for ( t =1 to T )

for ( i=1 to I )

1. Assume sequence(t) ← i, (di-1).

2. Compute predictor sci(t) for each station.

3. di+1.

end for

4. sequence(t) ←

{

}

)(min)(:**tsctscii

Ii

i∈

=.

5. Update data.

end for

wpik is obtained with single station procedures. The

work overload produced in period t due to the assign-

ment of product i is obtained by (5) and (6).

(

)

∑=⋅+= K

kkiikisctkwwptsc 1),()( (4)

wi(k,t) = [skt+pik - ((t-1)⋅c)-Lk]+ ∀ i ∈ A (5)

wi(k,t) = [(t⋅c)-skt-pik] + ∀ i ∈ B (6)

IV. LOCAL SEARCH

For improving the solutions obtained with the four

constructive procedures described in the previous sec-

tion, local search is applied. Two well known kinds of

neighborhoods had been used in the search: swap and

insertion.

up down

up-down regenated cycle

L

0

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237

A. Swaps

Swaps of two and three elements of the sequence had

been considered. Swap of two elements (2S) is simple.

One solution can just produce a new one. Nevertheless,

swap of three elements have five possible neighbors

solutions. From those five possibilities, only in two of

them the three elements considered take a new position

in the sequence: (b,c,a) and (c,a,b) in figure 3.

Figure 3- 3 swap neighbors

Then, we had used two different 3-swap neighbor-

hoods: 3S(a) and 3S(b). 3S(a) considers the tow changes

where all of the elements considered take a new position

in the sequence. In the other hand, 3S(b) take into ac-

count the five possibilities. We had also considered the

idea of applying 3 swap after no improvement can be

found with 2 swap, we call that 2-3S(b).

B. Insertion

By the insertion, a new neighbor from the current fea-

sible sequence is obtained getting a segment of certain

size from the solution, and then it is inserted in a differ-

ent position of the sequence. Even tough size of seg-

ments (let or) can take the value 1 ≤ or ≤ T, in the com-

putational experience only had been tested 2 ≤ or ≤ 10.

The size of the Insertion neighborhood is smaller than

the Swap neighborhood; therefore, the computational

effort is smaller too.

Figure 4- Insertion neighbors

In all the local search experience, the maximum num-

ber if iterations with out improvement has been estab-

lished to T.

V. PRIORITY RULES

In this section a hiperheuristic is described. The pro-

cedure is inspired on the Scatter Search (SS) Meta heu-

ristic. Instead of using feasible solutions for producing

new ones, our proposal use priority rules chains. The

objective value of a chain is obtained getting the corre-

sponding solution sequence. That is done using a con-

structive procedure of rules combination (PCCR), and

measuring its work overload value.

A. PCCR

PCCR is a greedy constructive procedure based in the

combination of priority rules. The assignation of a prod-

uct in certain position of a sequence depends on the

priority rules. A set of rules R={r1,r2,r3,...,rR} establishes

the order of the products in a sequence. The chain (se-

quence of priority rules) will have the same number of

rules as positions have a product solution sequence (T).

The rule in the position t of the chain, determines from a

set of products, the product i that best satisfies the rule

r. Given a rules chain size T, the determination of the

product that best satisfies the rule r of the position t of

the chain is obtained as follows:

- For each candidate product, compute the value of

the application of the rule r.

- Select the product i with the best value for the rule

r.

- Assign the product i in the position t of the prod-

ucts sequence.

- Update pending demand for product i.

B. Hiperheuristic

Similarly to SS [10], our proposal is an evolutionary

algorithm that creates new elements combining the exis t-

ing ones, improving this way the criterion used to evalu-

ate the elements. Our proposal operates on a Reference

Set (RefSet). But, instead of a reference set of solutions,

we use a reference set of rules chains. Combining those

rules chains, new rules chains are created. A typical

RefSet size in SS is 20 or less, while the size of our RefSet

is in function of the number of rules R considered.

The following is a pseudo code of the proposed pro-

cedure:

start

0.1 Create RefSet static and dynamic.

0.2 Initialize frequency matrix, Fr.

while ( Diversifications < Max Diversifications )

1. Combine rules of the RefSet.

2. Regenerate RefSe.t

if ( RefSet state is not improved )

3. Diversify RefSet.

end if

end while

The RefSet is conformed by two tiers: the static sub-

set (RSs) and the dynamic (operative) subset (RSd). The

size of both RSs and RSd is R.

RSs is called “static”, because it is not modified dur-

ing the search process. In RSs the rules chain 1 contains

only the rule 1, the rules chain 2 contains only the rule 2,

and so on. In this way the procedure ensures the con-

sideration of all the priority rules in the combination

phase.

}:{),...,,,(RrcrRSsrrrrcr rr ∈=→= (7)

a b c

or

=2

T

Knowledge and Decision Technologies

238

The dynamic RefSet changes in each iteration of the

search process. The rules chains of the initial RSd are

generated randomly. RSd contains the elite group of

rules chains. RSd is updated in each iteration of the

process taking into account the new chains with the

best values of work overload obtained by the last com-

bination.

1 ≤ RSdit ≤ R (8)

The work overload value for a chain is obtained ap-

plying the PCCR. In this work, 20 priority rules had been

used. If during the PCCR procedure, one or more prod-

ucts have the best value for the rule in period t of the

sequence, the tie is eliminated taking only the products

in the tie and applying the rules in order (starting with

rule 1), until the tie disappears.

Different criteria are considered in the priority rules

used in the procedure. Rules 1-4 decide which product is

going to be assigned using the processing times data.

Rules 5 and 6 select the product with the bigger and

smaller pending demand respectively. Rules 7,8,14 and

15 differentiate the products making a relation of pend-

ing production and the difference between the process-

ing time and cycle time. The displacement of the workers

in the stations is used for selecting the product in rules 9

and 10. Bottleneck station processing times are consid-

ered in rules 11 and 12. Rules 16 and 18 use the work

overload caused by the assignment of a product. Rules

17 and 19 use idle time. Rule 13 select a product using

the measurement of the regularization of the load along

the sequence. Similarly, rule 20 select according the

regularization of idle time.

In each iteration of the process, a frequency matrix is

obtained Fr(r,t) , which contains the number of times

that a rule r is in the position t of the chains in the RSd.

Since RSs do not change, it is not necessary consider it

for computing Fr. The Fr matrix is used in the combina-

tion of the rules chains in the RefSet. Fr is also used in

the diversification phase.

When two rules chains (parents) are combined, a new

one (son) is obtained.

The element in the position t of the son chain is de-

termined according to the frequency that the rule r has

in the position t in the Fr matrix.

cp(t) if cp(t) = cq(t)

cr(t) = cq(t) if Fr(cp(t),t) ≥ Fr(cq(t),t)

cp(t) otherwise

Once all the son chains had been obtained, the PCCR

is used for getting the work overload value for the new

chains. Those with the best values are considered for

updating the RSd. That is, the RSd is regenerated.

Three regeneration alternatives are analyzed in this

paper:

- The RefSet is regenerated with the best chains,

considering both, the parents set and the sons set.

- The RefSet is regenerated with the R best chains in

the sons set.

- The worst αR chains in the RefSet are regenerated

by the αR best chains in the parents set.

In the regeneration process, duplication must be

avoided. Then, all the chains in the RefSet have different

work overload values.

When the regeneration process does not produce im-

provements, the RefSet must be diversified. Diversifica-

tion is done in two steps: 1) creation of diversified

chains, and 2) selection of those diversified chains

which are the least similar to each other.

Step 1 of diversification is done using the informa-

tion contained in the frequency matrix Fr. When diversi-

fication is necessary, the combination of rules is done in

a different way. Given two parent chains p and q, one

diversified son chain is obtained. The difference in the

way chains are combined in the diversification phase is

the following: in position t of the new diversified son

chain, the rule of the parent chain that has the smaller

value in the frequency matrix Fr is assigned. The idea is

to create chains containing rules with inferior frequency

in the Fr, so the space of solutions explored is changed.

The second step of the diversification process itera-

tively looks for diversified chains that are different with

respect to the chains inside the current RSd. The grade

of differentiation between two chains is measured with

the number of coincidences. A coincidence exists if in

the same position t, both of the chains have the same

rule r.

VI. COMPUTATIONAL EXPERIENCE

The proposed procedures are tested with the battery

of problems designed by [6]. In all the instances c=90

time units. Instances do not consider weight (cost) by

incurring in work overload or idle time in stations. For

measuring the quality of the solutions obtained by the

proposed procedures we use the same global index used

by the battery designers.

Originally, instead of weak lower bounds, the objec-

tive function values wo*h of the best known solution for

an instance h is used when comparing procedures. Since

this measure is not defined for wo*h = 0, the following

aggregated relative deviation is used:

(

)

∑∑ ∑ =∗

= = ∗⋅−100

1

100

1

100

1%100:.hh

h h hh wowowoworel (9)

We have added two more indexes for aggregated rela-

tive deviation. The original index (9) is represented by

rel.wo2. In rel.wo1 the value wo*h is the lower bound

obtained by (3). In rel.wo3 the value wo*h is the best

solution founded considering the results obtained with

CPLEX after 15 minutes of search. Computations are

performed in a Pentium 4 CPU 2.4 GHz, 512 MB RAM

under a system Microsoft windows XP professional

2002. CPLEX 7.5 was used in YR-x procedure, and for

searching the optimum during 15 minutes.

Knowledge and Decision Technologies

239

Table I shows the results for the three indexes evalu-

ated for the four constructive procedures described in

section III. The best indexes are reached by the proce-

dure that tries to spread out the work overload along the

sequence. In the other hand, our extension proposal for

Y&R procedure produces not the expected results.

Table I- Global results for initial procedures

Index Ud UdC UdR YRx

rel.wo1 45.64 41.82 40.97 69.25

rel.wo2 5.49 2.73 2.11 27.90

rel.wo3 6.00 3.22 2.59 28.51

#best 19 42 44 2

Cpu 3.99 4.96 4.56 4276

Local search was also applied on the results of con-

structive procedures. Table II shows the value for the

index rel.wo1 after LS. 2S, 3S(a), 3S(b) and 2-3S(b) corre-

spond to Swap neighborhoods. 2-10 Ins are segment

insertion neighborhoods with segment size from 2 until

10. In the search by three elements sweeping, the com-

putational effort is much bigger than the effort required

in 2 elements sweep due to the size of the neighborhood.

Applying 3 swap elements after 2 swap can improve the

solutions.

Table II- Global results after LS, rel.wo1

Rel.wo1 (%)

Initial Procedure

Ud UdC UdR YRx

Original 45.64 41.82 40.97 69.25

2S

3S(a)

3S(b)

2-3S(B)

24.32

35.16

32.99

23.96

24.30

33.03

31.86

23.88

24.53

34.84

30.55

24.09

24.54

55.39

44.15

24.06

2Ins

3Ins

4Ins

5Ins

6Ins

7Ins

8Ins

9Ins

10Ins

23.88

23.51

23.34

23.15

23.01

22.98

22.82

22.72

22.56

23.64

23.35

23.20

23.00

22.95

22.87

22.71

22.61

22.65

23.80

23.34

23.19

23.00

22.99

22.77

22.63

22.60

22.44

24.38

24.22

24.25

24.02

24.03

23.91

23.34

23.35

23.29

The neighborhood size when segment insertion is

used, is much smaller, and requires less computational

effort than swapping. Furthermore, according to global

indexes, work overload solutions are better. Cpu time

limit was imposed in the search of local optimums. The

limit for LS with Swaps was 3600 seconds, except for 2-

3S(b), which had 3600 for the 2Swap search, and 1800

seconds for the 3S(b) search. In segment insertion

search, time limit was 1800 seconds.

Rel.wo2 index is shown in table III. Since better solu-

tions had been founded during LS, the original rel.wo2

value for some initial procedures is different to those

values in table I. In general, better results are obtained

when LS is applied on the UdR initial procedure, and for

our problem, segment insertion neighborhood over-

whelms swapping neighborhoods.

Table III- Global results after LS, rel.wo2

rel.wo2 (%)

Initial Procedure

Ud UdC UdR YRx

Original

20.12 16.97 16.37 40.16

2S

3S(a)

3S(b)

2-3S(B)

2.53

11.47

9.68

2.23

2.51

9.72

8.75

2.17

2.70

11.1

7.67

2.34

2.71

28.16

18.89

2.32

2Ins

3Ins

4Ins

5Ins

6Ins

7Ins

8Ins

9Ins

10Ins

2.17

1.86

1.73

1.57

1.45

1.43

1.29

1.21

1.08

1.97

1.74

1.61

1.45

1.40

1.34

1.21

1.12

1.16

2.11

1.72

1.60

1.44

1.44

1.26

1.14

1.12

0.98

2.58

2.45

2.48

2.28

2.29

2.20

1.73

1.73

1.69

After LS, all results are better than those obtained 15

minutes of search using the optimization software

CPLEX 7.5, then, the index rel.wo3 loss worth.

Table IV- Results for HH1, rel.wo1

rel.wo1 (%)

Regeneration type

Max

Diversif. Reg1 Reg2 Reg3

D3

D4

D5

D6

42.81

42.72

42.64

42.53

42.79

42.74

42.64

42.55

42.54

42.45

42.47

42.33

A computational experience has also been done for

the hiperheuristic proposed procedure. This experience

is not related with the solutions values from previous

experiences. Our analysis considers the combination of

three kind of regeneration used in the procedure and the

maximum number of diversifications (first column of

tables). Table V- Results for HH1, rel.wo3

rel.wo3 (%)

Regeneration type

Max

Diversif.

Reg1 Reg2 Reg3

D3

D4

D5

D6

1.85

1.78

1.73

1.65

1.84

1.80

1.73

1.66

1.66

1.60

1.54

1.51

Table IV shows the global results for the index

rel.wo1. The performance of the three regeneration

methods is similar. As can be expected, when more di-

versifications are applied, results are improved; never-

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240

theless, this improvement is small. Index rel.wo3, consid-

ers also the CPLEX result after 15 minutes of search.

Work overload solutions are almost as good as the solu-

tions obtained considering CPLEX. In average, 156 sec-

onds are needed by the procedure to finishing the

search.

VII. CONCLUSIONS

This work treats with a variant of the problem of se-

quencing products (mixed models) on a paced assembly

line. We consider the approach in which a product de-

mands a component (attribute), which has different ver-

sions, and requires different processing times in the

application of each. The aim of these procedures is to

minimize work overload (lost work) in all the stations of

the assembly line due to the limited time spared in the

stations and to the work loads along a given sequence.

Both boundaries of stations are closed, and we assume

as in [3], and [6], the displacement time the worker need

to go from one product in to the next, is negligible. We

compiled some procedures founded in literature: [3], [4]

and [9], and we propose greedy procedures inspired on

the previous procedures. Procedures consider more than

two different products and multi stations.

Results obtained for constructive procedures dealing

with the deviation in relation to a bound, are highly

satisfactory, results also show CPU time required for the

greedy proposed procedures is acceptable for big in-

stances, and when work overload is spread our along

the sequence, better results are obtained.

When LS is applied on the constructive procedures

results, index rel.wo1 is improved to almost the half.

Local search with segment insertion outperforms the

elements swap neighborhood, requiring less computa-

tional effort.

The hiperheuristic proposed procedure get good re-

sults which are comparable with those obtained with the

constructive procedures.

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