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ARTICLE
Year : 2015  |  Volume : 5  |  Issue : 1  |  Page : 19-25

Stochastic Dynamic Job Shop Scheduling with Sequence-Dependent Setup Times: Simulation Experimentation


Department of Mechanical Engineering, National Institute of Technology, Kurukshetra, Haryana, India

Date of Web Publication16-Jan-2015

Correspondence Address:
Pankaj Sharma
Department of Mechanical Engineering, National Institute of Technology, Kurukshetra, Haryana
India
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/0976-8580.149475

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   Abstract 

Stochastic dynamic job shop (SDJS) scheduling problems with sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of five dispatching rules (DRLs) in such shop from makespan, mean flow time, mean tardiness, number of tardy jobs, total setups, and mean setup time performance measures viewpoint. A discrete event simulation model of a SDJS manufacturing system is developed for investigation purpose. Five DRLs, that is, first come first serve (FCFS), shortest processing time (SPT), shortest setup time (SIMSET), earliest due date (EDD) and shortest sum of setup times and processing time (SSPT) are incorporated in the simulation model. The simulation experiments are conducted under due date tightness factor of 3, shop utilization percentage of 90 and setup time less than processing time. Results indicate that SIMSET rule provides best performance for mean flow time and number of tardy jobs performance measures. The SPT rule provides best performance for mean tardiness measure. The EDD rule is best-performing DRL for makespan, total setups and mean setup time measures.

Keywords: Dispatching rule, scheduling, sequence-dependent setup times, simulation, stochastic dynamic job shop


How to cite this article:
Sharma P, Jain A. Stochastic Dynamic Job Shop Scheduling with Sequence-Dependent Setup Times: Simulation Experimentation. J Eng Technol 2015;5:19-25

How to cite this URL:
Sharma P, Jain A. Stochastic Dynamic Job Shop Scheduling with Sequence-Dependent Setup Times: Simulation Experimentation. J Eng Technol [serial online] 2015 [cited 2017 Oct 22];5:19-25. Available from: http://www.onlinejet.net/text.asp?2015/5/1/19/149475


   1. Introduction Top


The production scheduling is associated with the allocation of the set of jobs on a set of production resources over time to achieve some objectives. In a job shop, a set of jobs are processed on a set of machines and each job has specific operation order. The job shop scheduling problem is a combinatorial optimization problem, and it is one of the most typical and complex among various production scheduling problems [1],[2] . In dynamic job shop scheduling problems jobs arrive continuously over time. Further, in a stochastic dynamic job shop (SDJS) scheduling problems at least one parameter of the job, that is, release time, processing time or setup time is probabilistic [3],[4] .

Setup time is a time that is required to prepare the necessary resources such as machines to perform a task [5] . In many real-life situations, a setup operation often occurs when shifting from one operation to another. Sequence-dependent setup time depends on both current and immediately previous operation [5] . Sequence-dependent setup time encounters in many industries such as printing industry, paper industry, auto industry, chemical processing and plastic manufacturing industry. Scheduling problems with sequence-dependent setup times are among the most difficult classes of scheduling problems [6] . The two papers of Manikas et al. [7] and Fantahun et al. [8] reported that limited research on job shop scheduling problems with sequence-dependent setup times is available.

A dispatching rule (DRL) is used to select the next job to be processed from the set of jobs awaiting processing in the input queue of a machine. DRLs are also called scheduling rules or sequencing rules. Haupt [9] classified DRLs into broad four categories namely as process time based rules, due date based rules, combination rules and rules that are neither process time-based nor due date based. This paper focuses the performance of five DRLs identified from the literature in a SDJS scheduling problem while considering a sequence-dependent setup times.

The remainder of the paper is organized as follows. A review of relevant literature is introduced in section 2. Section 3 describes salient aspects of configuration of the SDJS scheduling problem. The outline for the development of the simulation model is explained in section 4. Section 5 presents details of simulation experimentations. Section 6 provides an analysis of experimental results. Finally, section 7 gives concluding remarks and directions for future work.


   2. Literature Review Top


Ramasesh [10] provided review of simulation research in dynamic job shop scheduling problems. Allahverdi et al. [11] provided a comprehensive survey of the literature on scheduling problems with setup times (costs). Panwalkar et al. [12] provided a survey of DRLs used in manufacturing systems. Blackstone et al. [13] presented a state-of-the-art review of DRLs used in job shop manufacturing system. Holthaus and Rajendran [14] proposed two new scheduling rules for a dynamic job shop scheduling problem to minimize mean flow time, mean tardiness and percentage of tardy jobs performance measures. These rules combined process time and work content in queue for the next operation on a job by making use of additive (Rule 1) and alternative approaches (Rule 2). Jayamohan and Rajendran [15] developed seven DRLs to minimize various performance measures such as mean flow time, maximum flow time, variance of flow time and tardiness in dynamic shops. Jain et al. [16] developed and evaluated the performance of four new DRLs for makespan, mean flow time, maximum flow time and variance of flow time measures in a flexible manufacturing system. They found that the proposed DRLs provide better performance than the existing rules. Dominic et al. [17] developed two DRLs viz. longest sum of Work Remaining and Arrival Time of a job (MWRK_FIFO) and shortest sum of Total Work and Processing Time of a job (TWKR_SPT) for dynamic job shop scheduling problems. They concluded that proposed rules provides better performance than the existing scheduling rules, that is, first in first out (FIFO), last in first out (LIFO), shortest processing time (SPT), longest processing time (LPT), most work remaining (MWRK) and total work (TWKR) for mean flow time, maximum flow time, mean tardiness, tardiness variance and number of tardy jobs performance measures.

A few attempts have been made to address dynamic job shop scheduling problems with sequence-dependent setup times. To the best of authors's knowledge, Wilbrecht and Presscott [18] were first among researchers who studied the influence of setup times on dynamic job shop scheduling problems. They proposed and tested a setup oriented scheduling rule, that is, job with Smallest Setup Time (SIMSET). They concluded that SIMSET rule outperforms other existing scheduling rules. Kim and Bobrowski [3] studied the impact of sequence-dependent setup times on the performance of a dynamic job shop scheduling problem. They concluded that setup oriented scheduling rules, that is, SIMSET and job with similar setup and critical ratio (JCR) outperforms ordinary scheduling rules, that is, Shortest Processing Time (SPT) and critical ratio (CR) for mean flow time, mean work-in-process inventory, mean finished good inventory, mean tardiness, proportion of tardy jobs, mean machine utilization, mean setup time per job, mean number of setups per job and mean total cost per day performance measures when a manufacturing system with sequence-dependent setup times is considered. Kim and Bobrowski [4] extended their previous work [3] to investigate the impact of setup times variation on sequencing decisions with normally distributed setup times. They concluded that setup times variation has a negative impact on system performance. Recently, Vinod and Sridharan [19] proposed and assessed the performance of five setup oriented scheduling rules, that is, shortest sum of setup time and processing time (SSPT), job with similar setup and shortest processing time (JSPT), job with similar setup and earliest due date (JEDD), job with similar setup and modified earliest due date (JMEDD) and job with similar setup and shortest sum of setup time and processing time (JSSPT) for dynamic job shop scheduling problems with sequence-dependent setup times. They concluded that proposed rules provides better performance than the existing scheduling rules, that is, First in First out (FIFO), Shortest Processing Time (SPT), earliest due date (EDD), modified earliest due date (MEDD), Critical Ratio (CR), Smallest Setup Time (SIMSET) and job with similar setup and Critical Ratio (JCR) for mean flow time, mean tardiness, mean setup time and mean number of setups performance measures.

It is clearly evident from the literature review that there is a need to evaluate the performance of DRLs in a SDJS scheduling problems with sequence-dependent setup times. The present paper is an attempt in this direction. It assesses the performance of existing five best performing DRLs identified from the literature using simulation modeling for makespan, mean flow time, mean tardiness, number of tardy jobs, total setups, and mean setup time performance measures in a SDJS scheduling problem with sequence-dependent setup times.


   3. Job Shop Configuration Top


In the present work, a job shop scheduling problem with ten machines is selected. The configuration of the scheduling problem is determined based on configuration of job shop considered by various researchers [14],[ 19] . It has been pointed out by researchers that six machines are sufficient to represent the complex structure of a job shop scheduling problem [18],[20] and job shop size variations don't significantly affect the relative performance of DRLs [14],[20] . For the same reason, most of the researchers addressed a job shop scheduling problems with less than ten machines [17],[ 21],[ 22] .

3.1 Job data

Six different types of jobs, that is, job type A, job type B, job type C, job type D, job type E and job type F arrive in the manufacturing system. All the job types have equal probability of arrival. Job types A, B, C, D, E, and F require 5, 4, 4, 5, 4, and 5 operations respectively. The machines visited by different job types in their routes are shown in [Table 1]. The processing times, and setup times of each job are stochastic. Both are assumed to be uniformly distributed on each machine. Processing time changes according to job type and route of the job. [Table 2] presents processing times of each job on the machines according to their routes. The selection of pattern of processing times on different machines is based on research work carried out by previous researcher [23] . Sequence-dependent setup times which encounters when shifting from one job type to another are given in [Table 3].
Table 1: Routes of job types


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Table 2: Processing times of jobs on machines according to routes

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Table 3: Job types/sequence-dependent setup times data

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3.2 Inter-arrival time

It is average time between arrivals of two jobs. The average arrival rate of jobs is to be selected to have utilization of the machine <100%. Otherwise, the number of jobs in the queues in front of each machine will grow without bound [24] . Thus, inter-arrival time of the jobs is created using percentage utilization of the shop and processing requirements of the jobs. It is observed in the literature that arrival process of the jobs follows a poisson distribution [10],[ 19],[ 24] . Thus, inter-arrival time is exponentially distributed. Mean inter-arrival time of the jobs is calculated using the following relationship [19],[ 21] .



Here

b = Mean inter-arrival time

λ = Mean job arrival rate

μp = Mean processing time per operation (including setup time)

μg = Mean number of operations per job

U = Shop utilization

M = Number of machines in the shop.

In the present work, μp is computed by taking the mean of mean processing times of all operations [Table 2] plus mean of mean setup times [Table 3]. Thus, μp =19.45. For the taken input data, μg is 4.5 with M = 10. In the present work, experiments are carried out at shop utilization (U) = 90%. It is observed by Van Parunak [25] that due to stochastic nature of input processes (processing times and setup times) actual shop load is approximated and fall within the range of ±1.5% of the target value.

3.3 Due date of jobs

It is time at which job order must be completed. When a job enters into manufacturing system, its due date is either externally or internally determined. In case of externally determined due date, due date is either indicated by the customer or set for a specific time in the future. In case of internally determined due date, due date is based on total work content (sum of processing times and setup times) of the job or number of operations to be performed on the job. Most of the researchers used total work content (TWK) method to establish a due date of the job [14],[ 19],[ 21],[ 26] .



Here

di = Due date of job i

ai = Arrival time of job i

k = Due date tightness factor

pi =Mean total processing times of all the operations of job i

ni = Number of operations of job i

u
i = Mean of mean setup times of all the changeover of job i

In the present study, due date tightness factor (k) =3 is considered.


   4. Structure of Simulation Model Top


The simulation modeling is a powerful technique for studying large and complex scheduling problems. In the present work, a discrete event simulation model for the operations of SDJS scheduling problem with each DRL is developed using PROMODEL software. The job flow in the modeled SDJS manufacturing system is shown in [Figure 1]. The following assumptions are made while developing simulation model.
Figure 1: Job flow in a modeled job shop

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  1. Each machine can execute at most one operation at a time on any job
  2. An operation cannot start until its predecessor operation is completed
  3. The arrival of jobs in the shop floor is considered dynamic. The type of job is unknown until it arrives in the shop
  4. Unlimited capacity buffer is considered before and after each machine
  5. Both processing times and setup times are stochastic and known in priori with their distribution.


In the present work, a conceptual model of a job shop scheduling problem is developed. A multilevel verification exercise is performed in order to ensure that the simulation model is correctly developed. For this, the simulation model is debugged, and internal logics are checked. The output obtained from the simulation model is compared with that obtained from a manual exercise by using same input data. Finally, the simulation model is run under different settings in order to check that the model behaves in a logical manner.

4.1 Dispatching rules

A DRL is used to select the next job to be processed on the machine from a set of jobs waiting in the input queue of the machine. In the present study, the following DRLs identified from the literature are used to make job sequencing decision [18],[ 19] .

  1. First come first serve (FCFS): The job arriving first in the input queue of the machine is selected for processing.
  2. Shortest processing time (SPT): The job with shortest processing time for the imminent operation is selected for processing.
  3. Shortest setup time (SIMSET): The job with shortest setup time for the imminent operation is selected for processing.
  4. Earliest due date (EDD): The job with earliest due date is selected for processing.
  5. Shortest sum of setup time and processing time (SSPT): The job with shortest value of the sum of setup time and processing time is selected for processing.


4.2 Performance measures

The following performance measures are used for evaluation purpose in the experimental investigations:

  1. Makespan (M): It is time of completion of last job in a manufacturing system.
  2. Mean flow time (): It is average time that a job spends in the shop floor during processing.




Here

Fi = ci - ai

Fi = Flow time of job i

ci = Completion time of job i

a
i = Arrival time of job i

n
=

Number of jobs produced during the simulation period (during steady state period).

3. Mean tardiness (): It is average tardiness of a job in the shop floor during processing.



Here

Ti = max {0, L i}

Li = ci - di

Ti = Tardiness of job i

Li = Lateness of job i

d
i = Due date of job i.

4. Number of tardy jobs (NTJ): It is the value of the number of jobs that are completed after their due dates.



Here, d (Ji ) = 1 if Ji > 0 and d (Ji ) = 0, otherwise.

5. Total setups (TSP): It is the value of the number of setups that encounters during processing of jobs.



Here, d (Pi ) = 1 if Pi > 0 and d (Pi ) = 0, otherwise.

6. Mean setup time (MST): It is average time that a job spends for the setup during processing.



Here, Si = Setup time of job i


   5. Experimental Design for Simulation Study Top


Using simulation modeling, a number of experiments on SDJS scheduling problem have been conducted. The first stage in simulation experimentation is identification of steady state period, that is, end of the initial transient period. The Welch's procedure described by Law and Kelton [27] is used for this purpose. A pilot study for SDJS scheduling problem is conducted with FCFS DRL, and thirty replications are considered for simulation experimentation. The simulation for each replication is made to run for 20000 jobs completion. It is found that the manufacturing system reaches steady state at the completion of 5000 jobs. Finally, the experimental investigation is carried out to analyze the performance of five DRLs identified from the literature in a SDJS scheduling problem for 20000 jobs completion (after warmup period of 5000 jobs).


   6. Results and Discussion Top


In SDJS scheduling problem, the performance of five DRLs identified from the literature is analyzed. For each performance measure under each DRL, the simulation output of 30 replications is averaged. [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7] indicate the average values of various performance measures.
Figure 2: Performance of dispatching rules for makespan

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Figure 3: Performance of dispatching rules for mean flow time

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Figure 4: Performance of dispatching rules for mean tardiness

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Figure 5: Performance of dispatching rules for number of tardy jobs

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Figure 6: Performance of dispatching rules for total setups

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Figure 7: Performance of dispatching rules for mean setup time

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6.1 Makespan

The performance of different DRLs for makespan is shown in [Figure 2]. It indicates that EDD rule is best-performing DRL for makespan. This is followed by SSPT, SPT, SIMSET, and FCFS DRLs in that order. Thus, EDD rule is best-performing DRL for makespan performance measure.

6.2 Mean flow time

The performance of different DRLs for mean flow time measure is shown in [Figure 3]. It indicates that SIMSET rule is best-performing DRL for mean flow time performance measure. This is followed by SSPT, SPT, EDD, and FCFS DRLs in that order. Thus, SIMSET rule is best-performing DRL for mean flow time performance measure when a SDJS scheduling problem with sequence-dependent setup times is considered.

6.3 Mean tardiness

This performance measure is related to better customer service and satisfaction, and it is the due date based. [Figure 4] shows the performance of various DRLs for mean tardiness measure. It clearly indicates that SPT rule is best-performing DRL, and it is followed by SIMSET, SSPT, EDD, and FCFS DRLs in that order. Thus, SPT DRL outperforms other DRLs for mean tardiness performance measure.

6.4 Number of tardy jobs

The performance of different DRLs for number of tardy jobs measure is shown in [Figure 5]. This figure indicates that SIMSET DRL provides the best performance for number of tardy jobs measure. This is followed by other DRLs, that is, SPT, SSPT, EDD, and FCFS in that order in minimizing number of tardy jobs performance measure.

6.5 Total setups

[Figure 6] shows the performance of various DRLs for total setups measure. It clearly indicates that EDD rule is best-performing DRL, and it is followed by SSPT, SPT, SIMSET, and FCFS DRLs in that order. Thus, EDD DRL outperforms other DRLs for total setups performance measure.

6.6 Mean setup time

It indicates average time that a job spends for the setup during processing. The performance of different DRLs for mean setup time measure is shown in [Figure 7]. This figure indicates that EDD DRL provides the best performance for this performance measure. This is followed by other DRLs, that is, SSPT, SPT, SIMSET and FCFS in that order in minimizing mean setup time performance measure.


   7. Conclusions Top


The present work addresses a SDJS scheduling problem while considering sequence-dependent setup times. The performance of five DRLs taken from literature is assessed. The experimental results indicate that SIMSET rule is best-performing DRL for mean flow time, and number of tardy jobs performance measure. The SPT rule provides the best performance for mean tardiness measure. The EDD rule is best performing DRLs for three performance measures, that is, makespan, total setups and mean setup time.

The present work can be extended in a number of ways. Further experimental work is required to address SDJS scheduling problems with sequence-dependent setup times which involves the situations like limited capacity buffer between machines, machine breakdown, batch mode schedule and external disturbances for example order cancellation and job pre-emption. The development of better DRLs is also recommended.

 
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   Authors Top


Pankaj Sharma passed his B.E. in Mechanical Engineering from Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra. He completed his M.Tech. in Mechanical Engineering from Kurukshetra University, Kurukshetra, Haryana. Currently, he is working as Associate Professor in Department of Mechanical Engineering, Guru Jambheshwar University of Science and Technology, Hisar, Haryana. He is having teaching experience of about 15 years.



Prof. Ajai Jain obtained his B.Sc. in Mechanical Engineering from Dayalbagh Educational Institute, Agra. He completed his M.E. in Production & Industrial System Engineering from University of Roorkee, Roorkee (Now IIT Roorkee) and Ph.D. in Mechanical Engineering from Kurukshetra University, Kurukshetra. He is Fellow of Institution of Engineers (India) and Life Member of Indian Society of Technical Education. Currently, he is working as Professor in Department of Mechanical Engineering, National Institute of Technology, Kurukshetra. His areas of current interest are Design and Operations of Manufacturing Systems, Non-traditional Machining, CAM/CIM. He has published articles in refereed National and International journals .


    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]
 
 
    Tables

  [Table 1], [Table 2], [Table 3]


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1 New setup-oriented dispatching rules for a stochastic dynamic job shop manufacturing system with sequence-dependent setup times
Pankaj Sharma,Ajai Jain
Concurrent Engineering. 2016; 24(1): 58
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