Process Planning and Due-date Assignment with ATC ...Process Planning and Due-date Assignment with ATC Dispatching where Earliness, Tardiness and Due-dates are Punished Halil Ibrahim

Process Planning and Due-date Assignment with

ATC Dispatching where Earliness, Tardiness and

Due-dates are Punished

Halil Ibrahim Demir, Tarık Cakar, Mumtaz Ipek, Ozer Uygun, and Murat Sari Industrial Engineering Department, Sakarya University, Sakarya, Turkey

Email: {hidemir, tcakar, ipek, ouygun, muratsari}@sakarya.edu.tr

Abstract—Conventionally process planning, scheduling

and due-date assignment are performed independently. But

treating these three functions simultaneously improves

global performance. In literature there are numerous works

on process planning and scheduling and on scheduling with

due-date assignment. But integrating these three functions

are not treated much. In this study, process planning and

due-date assignment are simultaneously treated with ATC

dispatching using genetic algorithm (genetic search) and

random search. Three shop floors are tested in this study.

One is small shop floor with 50 jobs and the other is

medium shop floor with 100 jobs and the third one is the

largest shop floor with 200 jobs. In this study Earliness and

Tardiness symmetrically and quadratically penalized and

length of due-date is linearly punished. Results of Genetic

search and Random search are compared with each other

and with random solution and with unintegrated solution.

Results are summarized and compared with each other.

According to results Genetic search-integrated solution is

the best, Random search-integrated solution is the second,

Random-integrated solution is the third and Unintegrated-

random solution is the poorest.1

Index Terms—Due-date assignment, Process planning, Job

shop scheduling, Genetic Algorithm

I. INTRODUCTION

When we look at the literature we can see many works

on integrated process planning and scheduling and

numerous work on scheduling with due-date assignment.

Traditionally these three functions were being done

sequentially and separately. Unintegrated solutions

become poor inputs to the downstream functions and

global performance can be poor. For example if process

plans are made independently then process planner can

choose same desired machines repeatedly and they don’t

care about scheduling and due-date assignment

performance. Because they can select same machines

repeatedly some machines can become bottleneck and

some machines can be starving and this cause

unbalanced machine loading. When some unexpected

things occur such as machine breakdowns then it

becomes hard to react these occurrences. If we integrate

process plans with other functions then in case of need

Manuscript received July 1, 2014; revised November 1, 2014.

we can react to the unexpected situation and we can

improve shop floor balance. Good and flexible inputs for

scheduling and due-date assignment provide us to make

better scheduling and better due-date assignment.

The scheduling problems involving due dates are of

permanent interest. In a traditional production

environment, a job is expected to be completed before its

due date. In a just-in-time environment, a job is expected

to be completed exactly at its due date…The problems

with due-date determination have received considerable

attention in the last 15 years due to the introduction of

new methods of inventory management such as just-in-

time (JIT) concepts. In JIT systems jobs are to be

completed neither too early nor too late which leads to

the scheduling problems with both earliness and

tardiness costs and assigning due dates. T.C.E. Cheng,

who contributed a lot to the due date assignment and the

related scheduling approaches, remarks that “completing

a job early means to bear the costs of holding

unnecessary inventories, while finishing a job late results

in contractual penalty and loss of customer good-will”

Gordon et al. [1].

II. LITERATURE SURVEY

For integrated process planning and scheduling

problem, Tan and Khosnevis [2] presented a good

literature survey. For scheduling with common due-date

assignment problem, it will be useful to see Gordon et al.

[1] as a state-of-the-art survey about this topic.

Following study uses multiple process plans in contrast

to traditional way.

Chen and Khoshnevis [3] investigated the problem of

integrating the process planning and scheduling functions

as a scheduling problem with flexible process plans.

They developed a concurrent assignment algorithm based

on the added flexibilities introduced by the integration

Above study used multiple process plans and

following study, Jiang and Chen [4], investigated the

influence of alternate process planning on the scheduling

performance according to three criteria, which are mean

tardiness, mean work-in-process and mean machine

utilization.

Integration can be done with manual process plans or

computer aided process plans. Computer advantage is

very important to develop alternative process plans and

2015 Engineering and Technology Publishing 197doi: 10.12720/jiii.3.3.197-204

Journal of Industrial and Intelligent Information Vol. 3, No. 3, September 2015

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integrating process plans with scheduling. Following

studies dealt with process plan or computer aided process

plan integration with the scheduling.

In their paper, Lim and Zhang [5] introduced a multi-

agent based framework in which process planning and

production scheduling are integrated, as a preliminary

step towards agile manufacturing. Kumar and Rajotia [6]

studied integration of scheduling with computer aided

process planning.

Since integrated process planning and scheduling

problems are NP-hard problems, proposed mathematical

solutions are only possible for small sized problems. We

used genetic algorithm in this study, because problem in

this study is more complex than sub integration problems.

Jiang and Hsiao [7] developed an analytic solution to

the problem but their 0-1 integer programming is only

applicable to small sized problems. Hutchison et al. [8]

developed two off-line and one real time scheduling

scheme. The first of the off-line schemes gives an overall

optimal solution to the problem but again it is only

applicable to the small sized problems in terms of

computational time requirements.

Since applying mathematical techniques is not

practical for large-scale problems artificial intelligent

techniques such as neural network, genetic algorithms,

multi-agents and evolutionary algorithms are used and

recommended for many problems.

The integration of process planning and scheduling is

important for an efficient utilization of manufacturing

resources. Kim et al. [9] presented a new method, an

artificial intelligent search technique, called symbiotic

evolutionary algorithm, was presented to handle the two

functions at the same time. Zhao and Wu [10] suggested

a genetic algorithm (GA) to solve the job-sequencing

problem for a production shop that is characterized by

flexible routing and flexible machines. Lee and Kim [11]

proposed a new approach to the integration of process

planning and scheduling using simulation based genetic

algorithms. In their paper, Ming and Mak [12]

formulated the problem of selecting exactly one

representative from a set of alternative process plans…

The techniques of Hopfield neural network and genetic

algorithm are introduced as possible approaches to solve

such a problem.

When we look at these types of problems, objective

functions are not always the same but generally,

objectives are minimizing the cost. Below studies are

given to show what kinds of objectives are used in the

literature.

Thomalla [13] investigated an optimization

methodology for scheduling jobs in a just-in-time

environment. He considered the non-preemptive case

where each job consists of a distinct number of

operations to be processed in a specified order. Each

operation has to be processed on one of a set of resources

(e.g. machines) with possibly different efficiency and

hence processing time. The objective was to minimize

the sum of the weighted quadratic tardiness of the jobs.

Most of the work done on integrated process planning

and scheduling consider only time aspects but Morad and

Zalzala [14] used a formulation based on multi objective

weighted-sums optimization, which are to minimize

makespan, to minimize total rejects produced and to

minimize the total cost of production. Weintraub et al.

[15] presented a procedure for scheduling jobs with

alternative process in a general N-job, M-machine job

shop. The objective of this procedure is to minimize

manufacturing costs while satisfying job due dates.

Usher [16] addressed the benefit of alternative process

plans and worked on the number of alternative process

plans. Jain et al [17] introduced a scheme for integration

of process planning and scheduling. In a job shop kind of

flexible manufacturing environment Wong et al [18]

presented the development of an agent-based negotiation

approach to integrate process planning and scheduling

(IPPS). Kumar and Rajotia [19] proposed a framework

for integration of process planning with production

scheduling. A new simultaneous process planning and

scheduling method is proposed by Ueda et al [20]. In a

supply chain, Moon et al [21] studied integrated process

planning and scheduling (IPPS).

Chan et al. [22] proposed an integrated process

planning and scheduling model inheriting the salient

features of outsourcing and leagile principles to compete

in the existing market scenario. Guo et al [23] developed

a unified representation model for integrated process

planning and scheduling (IPPS).

Li et al [24] presented a review on integrated process

planning and scheduling. A mathematical model of

integrated process planning and scheduling developed by

them and they developed evolutionary algorithm based

approach to facilitate the integration and optimization of

process planning and scheduling. In order to integrate

process planning and shop floor scheduling (IPPS)

Leung et al [25] presented an ant colony optimization

(ACO) algorithm in an agent-based system. Phanden et

al [26] presented a state-of-the-art review of IPPS

(Integration of process planning and scheduling). Due dates sometimes dictated by customer but most of

the time due dates are determined after the negotiation

with the customer. In latter case it is desired to find the

best due date that satisfy both customer and the company.

Recent years numerous works have been done on

concurrent scheduling and due date assignment. If

literature survey is done for the last decade about

concurrent scheduling and due-date assignment

numerous works can be found. Since to be a survivor in

the market, firms should be as strong as possible and

make use of every new ideas and technological

developments that is why determining a reasonable due-

date is very important. According to classical approach,

only tardiness is punished but according to just in time

philosophy earliness is also punished as well. Earliness

means inventory holding cost and costs related with

stock keeping. To be realistic these costs should be

considered too. Studies shows that tardiness is still the

major component in due-date related costs. Tardiness

causes some fixed and variable costs. These costs are

price reduction and loss of customer good will and worst

2015 Engineering and Technology Publishing 198


losing good reputation and the customer. Therefore,

earliness should be punished as tardiness.

While some researches are conducted on single

machine environments, some other researches are done

on multiple machine environments. Multiple machine

environments could be job shop, flow shop, two

machines, n machines, identical or different machine etc.

Whether single or multiple machine environments

most of the studies tries to assign common due-date for

the jobs. This is because in many cases job should be

delivered to the customer at the same time or in some

cases finished parts or semi-assembled parts should be

ready at the same due-date for final assembly. Gordon et

al. [1] presented a state-of-the-art survey about

scheduling with common due-date assignment.

Ng et al [27], Cheng et al. [28], Qi et al. [29], Biskup

and Jahnke [30], Gordon and Strusevich [31], Gordon

and Kubiak [32] Ying [33], Li et al. [34], Nearchou [35],

Xia et al. [36], Lin [37], Panwalker [38], Wang [39],

Cheng et al. [40], and Ventura and Radhakrishnan [41]

studied scheduling with due-date assignment on single

machine environments.

Birman and Mosheiov [42], Mosheiov [43], Cheng

and Kovalyev [44], Adamapolous and Pappis [45], and

Lauf and Werner [46] studied multiple machine

problems.

Birman and Mosheiov [42] addressed a due-date

assignment and scheduling problem in a two-machine

flow-shop setting. Their objective was to find both job

schedule and common due-date that minimize maximum

earliness, tardiness, and due-date costs. Mosheiov [43]

addressed a job scheduling and due-date assignment

problem on parallel identical machines. All jobs share a

common due-date, which is to be determined. The cost of

a given schedule is a function of the maximum earliness

cost, the maximum tardiness cost, and the due-date cost.

Cheng and Kovalyev [44] tried to schedule n jobs on

parallel identical machines. They aimed to make

optimum scheduling while trying to assign best due-dates

to the jobs using PPW (Process plus wait) method.

Adamapolous and Pappis [45] tried to assign common

due dates to some jobs and schedule them on parallel and

unrelated machines. Min and Cheng [47] used genetic algorithm to

determine the optimal due date and optimal scheduling

policy for determining the job number and their

processing order on each machine. Lin et al [37] studied

single machine scheduling involving a common due date.

They minimized total job earliness and tardiness

penalties.

Nearchou [35] studied scheduling multiple jobs on a

single machine for common specified due date where

earliness and tardiness are punished..

Ying [33] studied scheduling jobs on a single machine

against common due dates with respect to earliness and

tardiness penalties.

Gordon and Strusevich [31] studied single machine

scheduling and due date assignment problems in which

the processing time of a job depends on its position in a

processing sequence. Vinod and Sridharan [48]

investigated the interaction between due-date assignment

methos and scheduling rules in a typical dynamic jop

shop production system.

Steiner and Zhang [49] studied a supply chain problem

where a common due date is assigned to all jobs and

number of jobs in delivery batches is constrained by

batch size. Li et al. [34] used CON/SLK (Common Due

Date/ Equal Slack) due date assignment rules with

scheduling deteriorating jobs on a single machine.

Most research on scheduling with due-date assignment

is focused on optimal sequencing of independent jobs.

But in practice some products are manufactured under

precedence constraints that reflects technological,

marketing or assembly requirements Gordon et al. [50].

III. DEFINITION OF THE PROBLEM

In this study integration of process planning,

scheduling and due-date assignment problem is studied.

There are alternative routes in order to improve inputs to

downstream (Scheduling and due-date assignment), to

provide flexibility in case of unexpected occurrences. We

have five alternative routes in case of small and medium

shop floor and we have three alternative routes in case of

big shop floor. One of these alternatives is going to be

selected to improve global (integrated solution)

performance. In case of scheduling we used ATC

(Apparent Tardiness Cost) dispatching rule to improve

global performance. We compared ATC with SIRO

(Service in random order) to see contribution of ATC

heuristic to the problem. We used different due-date

assignment rule at the related gene in a chromosome

(solution).These due-date assignment rules are used for

internal due-date assignment and we used RDM

(Random) due date assignment for external due-date

assignment. By comparing internal due date assignment

rules and external due date assignment we observed the

benefit of due-date determination and integration with

the problem. We compared seven different solutions each

has different level of integration and either makes genetic

or random search or ordinary solutions. These solutions

are explained in detail at section five.

Three shop floors are tested. First is small shop floor

with 50 jobs and 20 machines. At small shop floor there

are five alternative routes of each job and every job has

10 operations and operation time changes in between 10

and 19 minutes ( Processing times = ⌊(10 + |z| ∗ 3)⌋ =

nearest small integer. |z| is absolute value of standard

normal numbers). Processing times are randomly

produced.

Second shop floor is mid-sized shop floor with 100

jobs and 30 machines. At this shop floor again we have 5

alternative routes for each job and one is going to be

selected and each job has 10 different operations to be

performed. Operation times change in between 10 and 19

according to the same formula (Processing times

= ⌊(10 + |z| ∗ 3)⌋ = nearest small integer. |z| is absolute

value of standard normal numbers) with other shop floors.

Third shop floor is large sized shop floor with 200

jobs and 40 machines. At this shop 3 alternative routes

are used for each job and one of these routes is going to



be selected for global (integrated) performance. Each job

has 10 operations in every route and operation times

changes according to following formula (Processing

times = ⌊(10 + |z| ∗ 3)⌋ = nearest small integer in

between 10 and 19. |z| is absolute value of standard

normal numbers). Features of shop floors are given at

Table I.

TABLE I. SHOP FLOORS

Shop floor Shop floor 1 Shop floor 2 Shop floor 3

# of machines 20 30 40

# of Jobs 50 100 200

# of Routes 5 5 3

Processing Times ⌊(10 + |z| ∗ 3)⌋ ⌊(10 + |z| ∗ 3)⌋ ⌊(10 + |z| ∗ 3)⌋ # of op. per job 10 10 10

In this study we penalized earliness, tardiness and due

date. We assumed one shift per day and 8 hours * 60

minutes = 480 minutes are considered as one day. If jobs

are early and tardy within one day then we punished

earliness and tardiness linearly, and if there are more

than one day earliness and tardiness then we punished

quadratically. This is because completion early or tardy

within one day makes very small quadratic punishment

that’s why we used in this range linear punishment. Due

dates are punished linearly. Punishment functions are

given below where PD is penalty for due-date, PE is

penalty for earliness and PT is penalty for tardiness;

IV. SOLUTION TECHNIQUES

In this search following solutions techniques are used

and compared with each other.

Random search: In this search, solutions are produced

randomly. Best of these solutions is recorded as the next

population. Since this technique produces brand new

solutions randomly in every generations and don’t get the

benefit of earlier generations by using previous solutions

to get better solution, That is why it is an undirected

search technique. Since this is an undirected search, it

scans the solution space randomly.

Genetic search: Genetic algorithm is thought to work

well for the studied problem. That’s why over randomly

produced initial population and over the following

generations genetic operators are applied to get a good

solution in a reasonable amount of time. This search

called genetic, because it uses crossover and mutation

operators and updated best population to get better

solutions. Since it tries to find better solution by using

the final best solution, it is called as directed search in

contrast to the random search.

For every types of shop floor population size is ten, in

each generation (iteration) eight new offspring are

produced using crossover operator, and five new

offspring are produced using mutation operator. From

old population, crossover and mutation populations best

ten distinct chromosomes are selected for the next

generation as the new population. Iteration goes like this

until a predetermined number is reached.

Figure 1. Sample chromosome.

Ordinary solution: We use randomly produced initial

populations as ordinary solutions. Each chromosome is

randomly produced and a valid value is assigned to each

gene in the chromosome and performance of the

chromosome is found. Average of these performance

measures are taken as the ordinary solution.

Due dates were assigned using mainly five different

types of rules. Considering different constants and

multipliers the first gene took one of nineteen values.

These rules are explained below at Table II:

TABLE II: DUE-DATE ASSIGNMENT RULES

Method Multiplier k Constant qx Rule no:

TWK k = 1,2,3 0,1,2

SLK qx = q1,q2,q3 3,4,5

PPW k =1,2,3 qx = q1,q2,q3 6,7,8,9,10,11,12, 13,14

NOP k = 1,2,3 15,16,17

RDM 18

In order to dispatch two different methods were used.

Considering different multipliers, the second gene took

one of four different values. Dispatching rules use are

given and explained at Table III.

TABLE III: DISPATCHING RULES

Method Multiplier Rule no

ATC k x =1,2,3 0,1,2

SIRO 3

V. SOLUTIONS COMPARED

ATC-DUE(Ordinary): Process planning, due date

assignment and ATC dispatching are integrated and

ordinary solution is taken. Ordinary means just one

iteration applied and initial population is taken without

making any directed and undirected search. ATC

dispatching means jobs are sequenced scheduled

according to ATC composite dispatching rule.

Dispatching (Scheduling) is integrated with due-date

assignment and route selection.

PE= 8*(E/480) If E <= 480 8*(E/480)* (E/480) If E > 480

PT= 8*(T/480) If T <= 480 8*(T/480)* (T/480) If T > 480

P.D= 8*(Due-date/480) (1)

(2)

(3)

DD DR R1j R2j . . . R nj

Where

DD: Due date assignment gene DR: Dispatching rule gene

R nj : j’th route of job n


A sample chromosome can be illustrated as in Fig. 1.

There are (n+2) genes in one chromosome. First gene is

for due-date assignment and second gene for dispatching

rule and the rest for the routes of each job sequentially.


SIRO-DUE (Ordinary): Process planning and due date

assignment are integrated, but scheduling is unintegrated

and SIRO dispatching rule is used. Ordinary solution is

taken. No directed or undirected search is applied.

SIRO-RDM (Ordinary): In this solution scheduling

and due-date determinations are unintegrated. One of

alternative routes is selected and SIRO (Service in

random order) dispatching rule is used to represent

unintegrated scheduling and RDM (Random) due-date

determination is used to represent unintegrated due-date

assignment.

ATC-DUE (Random): Above solutions were first

iteration solutions (No directed or undirected search are

applied) but this solutions apply undirected search. For

small shop floor we apply 200 random iterations, for

medium sized shop floor we apply 100 iterations and for

large shop floor we apply 50 random iterations. Here

due-date assignment and ATC scheduling are integrated

with process planning.

ATC-DUE (Genetic): Here due-date assignment and

ATC scheduling are integrated with process planning.

Genetic (Directed) search is applied to the problem. For

small shop we apply 200 genetic iterations, for mid-size

shop floor we apply 100 genetic iterations and for large

shop floor we apply 50 genetic iterations. Since genetic

(directed) search is better than random (undirected)

search we used genetic iterations for the solutions below.

SIRO-DUE (Genetic): Here due-date assignment is

integrated with process planning but scheduling is

performed randomly (SIRO) and genetic search is

applied.

SIRO-RDM (Genetic): In this solution scheduling and

due-date determination are unintegrated with process

planning. SIRO dispatching rule is used and RDM due-

date assignment is used and genetic search is applied.

We compared above seven solutions with each other

to determine whether integration of due-date assignment

with process planning is beneficial and whether

integration of scheduling with process planning and due-

date assignment is beneficial. We also tested directed and

undirected search for three shop floors and genetic search

is found better. Results are given at experimentation part

and interpreted at conclusion part.

VI. EXPERIMENTS AND RESULTS

We studied three shop floors which are small medium

and large shop floors. We produced data for three shop

floors and coded integrated process planning, scheduling

and due-date assignment problem and coded random and

genetic search. We coded integrated problem using C++

language and run the experiments on a Notebook with 2

GHz processor. For different shop floors we applied

given number of random and genetic iterations. For small

shop floor we used 200 iterations and it took

approximately 90 seconds to finish 200 iterations if we

use SIRO dispatching and 150 seconds if we use ATC

dispatching. For medium sized shop floor we applied 100

iterations and it took approximately 250 seconds to finish

100 iterations if we use SIRO dispatching and 450

seconds if we use ATC dispatching. For large shop floor

we applied 50 iterations and it took 520 seconds to finish

50 iterations if we use SIRO dispatching and 850

seconds if we use ATC dispatching.

We tested three shop floors for seven types of

solutions. We first looked at unintegrated process

planning scheduling and due-date assignment as SIRO-

RDM (Genetic) and SIRO-RDM (Ordinary). Later we

integrated due-date assignment with process planning

and used SIRO dispatching rule. At these solutions we

looked at SIRO-DUE (Genetic) and SIRO-

DUE(Ordinary) solutions. Finally we integrated process

planning, Due-date assignment and ATC scheduling and

looked at solutions ATC-DUE (Genetic), ATC-DUE

(Random), ATC-DUE (ordinary). Explanations of these

solutions are given at section 5.

TABLE IV: COMPARISON OF SEVEN TYPES OF SOLUTIONS FOR SMALL

SHOP FLOOR

Worst Avarage Best Cpu time

ATC-DUE (O) 612,1 320,07 251,52

SIRO-DUE(O) 625,47 323,33 254,37

SIRO-RDM(O) 430,92 423,04 413,05

ATC-DUE (R) 236,98 235,42 232,88 153sec

ATC-DUE (G) 226,92 226,22 224,48 148sec

SIRO-DUE(G) 241,62 240,85 237,43 87 sec

SIRO-RDM(G) 399,12 397,64 394,82 89sec

Figure 2. Small shop floor results

We tested three shop floors for seven types of

solutions. First shop floor is small shop floor and there

are 20 machines, 50 jobs with 10 operations each and

each job has 5 alternative process plans and processing

times of each operation changes in between 10 and 19

according to following formula . We

compared seven solutions and three of them are ordinary

solutions and use first step (initial step, can be considered

as first iteration) solutions. One of them use random

search and we make 200 random iterations. Three of the

solutions use genetic search and we apply 200 genetic

search iterations. Results are given below for the small

shop floor. Getting ordinary solution occurs at the very



beginning of the iterations so negligible time required for

ordinary solutions. Applying 200 random or genetic

iterations require approximately 90 seconds (with SIRO)

or 150 seconds (with ATC) (cpu time). Times are given

at Table IV at the last column. Results of small shop

floor are given at Table IV and at Fig. 2. According to

results the more the solutions are integrated the results

are better and the more search iteration applied the

solution is better and directed search outperforms

undirected search.

Similar results are found for the second mid-size shop

floor and these results are given at the following Table V

and Fig. 3.

TABLE V: COMPARISON OF SEVEN TYPES OF SOLUTIONS FOR MEDIUM

SHOP FLOOR

Worst Avarage Best Cpu time

ATC-DUE (O) 1111,35 724,9 594,1

SIRO-DUE(O) 1138,97 746,06 649,05

SIRO-RDM(O) 830,59 806,89 784,22

ATC-DUE (R) 584,63 579,07 570,73 439sec

ATC-DUE (G) 555,73 554,32 551,25 427sec

SIRO-DUE(G) 618,9 615,85 612,07 259sec

SIRO-RDM(G) 774,45 772,71 768,9 250sec

Figure 3. Medium shop floor results

Third shop floor is the biggest shop floor and similar

results are found in this shop floor. Results are

summarized at the following Table VI and Fig. 4.

TABLE VI: COMPARISON OF SEVEN TYPES OF SOLUTIONS FOR LARGE

SHOP FLOOR

WORST AVG. BEST CPU

TIME ATC-DUE (O) 2141,55 1872,42 1690,84

SIRO-DUE(O) 2158,09 1965,85 1814,52

SIRO-RDM(O) 1936,56 1910,79 1886,14

ATC-DUE (R) 1639,88 1622,84 1598,17 855sec

ATC-DUE (G) 1565 1558,62 1539,9 848sec

SIRO-DUE(G) 1757,03 1752,86 1735,41 527sec

SIRO-RDM(G) 1813,14 1808,31 1797,27 515sn

Figure 4. Large shop floor results

VII. CONCLUSION

In this study we tried to integrate due-date assignment

process planning and ATC scheduling. We compared

different integration level. At first we took scheduling

and due-date assignment as unintegrated we solved

problem for SIRO-RDM (Genetic) and SIRO-RDM

(Ordinary). Here we assumed that scheduling is

unintegrated and we used SIRO dispatching. We also

assumed due-date determination is unintegrated and we

used RDM due-date assignment in place of external,

unintegrated due-date determination.

Later we integrated due-date assignment with process

pla selection. At solution, at due-date assignment gene

with multipliers and constants we used nineteen different

due-date assignment rules. These due-date assignment

rules are given at section 4. Here we still scheduled jobs

with SIRO we didn’t integrate scheduling with due date

determination and process plan selection. We solved

problem for SIRO-DUE (Genetic) and for SIRO-DUE

(Ordinary).

Later we integrated three functions (process planning,

scheduling and due-date assignment). At solution, at

scheduling gene with multipliers we used four

dispatching rules (ATC and SIRO heuristics) and at due-

date assignment gene we used 19 types of due-date

assignment rules. Here we solved problem for ATC-DUE

(Genetic), ATC-DUE (Random), and ATC-DUE

(Ordinary) cases. At genetic search we repeated genetic

iterations up to 200, 100 and 50 iterations for small,

medium and large sized shop floors. At Random search

we applied these many random iterations for three

different shop floors. Totally these seven types of

solutions and their explanations are given at section 5.

When we looked at the results as we increased

integration level the solution became better. If we look at

searches we found that search is very useful to find better

solution. When we compare directed (genetic) search and

undirected (random) search, genetic search always found

to be best. We proved that higher integration level is

better and if we don’t integrate these three functions then

each function will try to get local optima. Process

planning will not care about scheduling, shop floor

performance, workload level and balance and also will



not care about due-date performance. If we don’t

integrate scheduling with due-date assignment then

scheduling will not take into account of earliness,

tardiness and length of due-date. So benefit of integration

will be substantial.

APPENDIX A: DUE-DATE ASSIGNMENT RULES

TWK (Total Work) Due =TPT * k

SLK (Slack) Due = TPT + qx

PPW (Processing plus Wait)Due=TPT * k + qx

NOP (Number of operations) Due = NOP * k

RDM (Random due assign.) Due = N ~

(3*Pav,(Pavg/2 )2)

TPT= total processing time

Pavg= mean processing time of all job waiting

APPENDIX B: DISPATCHING RULES

ATC(Apparent Tardiness Cost): This is composite

dispatching rule here and it is a kind of hybrid of MS

(Minimum Slack First) and SPT (Shortest Processing

Time First) dispatching rules. For each job, priority index

is calculated as.

Ij(t) = wj/pj*exp(-max(dj-pj-t,0)/Kpavg) .

Ij(t) is priority index,

pj is j’th job processing time,

max(dj-pj-t,0) is j’th job slack,

K is scaling parameter,

Pavg is avarage processing time of the jobs

SIRO(Service in Random order): A job among waiting

jobs is selected randomly to be processed.

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Halil Ibrahim Demir was born in Sivas, Turkey in 1971. In 1988 he

got full scholarship and entered Bilkent University, Ankara, Turkey to Industrial Engineering Department. He got his Bachelor of Science

degree in Industrial Engineering in 1993.

In 1993 he went to Germany for graduate study. He studied German up to intermediate level. In 1994 he got full scholarship for graduate study

in USA from ministry of Education of Turkey. In 1997 he got Master of

Science degree in Industrial Engineering from Lehigh University, Bethlehem, Pennsylvania, USA. He is accepted to Northeastern

University, Boston, Massachusetts for Ph.D. study. He finished Ph.D.

courses at this university and completed Ph.D. thesis at Sakarya University, Turkey in 2005 and got Ph.D. degree in Industrial

Engineering. He started to his academic position at Sakarya University and works as

an Assistant Professor at this university.

Tarık Cakar is an Associate Professor at Sakarya University

Mumtaz Ipek is an Assistant professor at Sakarya University

Ozer Uygun is an Assistant professor at Sakarya University

Murat Sari is a Research Assistant at Sakarya University


[31] V. S. Gordon and V. A. Strusevich, “Single machine scheduling

and due date assignment with positionally dependent processing

times,” European Journal of Operational Research, vol. 198, pp.

57-62, 2009.


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Process Planning and Due-date Assignment with ATC ...Process Planning and Due-date Assignment with ATC Dispatching where Earliness, Tardiness and Due-dates are Punished Halil Ibrahim