- Email: [email protected]
Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach
G Model
CIRPJ-313; No. of Pages 10 CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj
Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach Pankaj Sharma a,b,*, Ajai Jain a,1 a b
Department of Mechanical Engineering, National Institute of Technology, Kurukshetra 136119, Haryana, India Department of Mechanical Engineering, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India
A R T I C L E I N F O
A B S T R A C T
Article history: Available online xxx
Stochastic dynamic job shop scheduling problem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under different levels of shop utilization and setup time. The important aspects of the results of the simulation investigation are also discussed in detail. ß 2015 CIRP.
Keywords: Scheduling Stochastic dynamic job shop Sequence-dependent setup times Dispatching rule Simulation
Introduction Production scheduling in a manufacturing system is associated with allocation of set of jobs on a set of production resources over time to achieve some objectives. In a job shop manufacturing system, 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 as well as NP-hard 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 in job shop manufacturing systems. Further, in a stochastic dynamic job shop (SDJS) manufacturing system at least one parameter of the job (release time, processing time/setup time) is probabilistic. In traditional approaches, in order to reduce the complexity of solving job shop scheduling problems, setup time is either neglected or included in the processing time of a job. But this effort does not represent the realistic picture of a manufacturing
* Corresponding author at: Department of Mechanical Engineering, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India. Tel.: +91 9466206231; fax: +91 1662 276240. E-mail addresses: [email protected] (P. Sharma), [email protected] (A. Jain). 1 Tel.: +91 9412558040.
system. Setup time is a time that is required to prepare the necessary resources such as machines to perform an operation [3]. In many real-life situations, a setup operation often occurs while shifting from one operation type to another. Sequencedependent setup time depends on both current and immediately previous operation [3]. Sequence-dependent setup time encounters in many industries such as textile industry, printing industry, paper industry, auto industry, chemical processing and plastic manufacturing industry. In textile industry, during dyeing operation, a very little setup time is required for job changing when dyeing from pale shade to deep shade products. On the contrary, much more setup time is required to clean the dyeing vessel, if otherwise. Even in some cases, setup time becomes equal to or more than operation time. Scheduling problems with sequencedependent setup times are among the most difficult classes of scheduling problems [4]. It has been pointed out by Manikas and Chang [5] and Fantahun and Mingyuan [6] that limited research on job shop scheduling problems considering sequence-dependent setup times is available. A dispatching rule is used to select the next job to be processed from the set of jobs awaiting processing in the input queue of a machine. Dispatching rules are also termed as sequencing rules or scheduling rules. These rules are classified into broad four categories namely as process time based rules, due date based rules, combination rules and rules that are neither process time
http://dx.doi.org/10.1016/j.cirpj.2015.03.003 1755-5817/ß 2015 CIRP.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 2
P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
based nor due date based [7]. In a manufacturing system, dispatching rule is one of the methods that can be used to carry out scheduling. Better the dispatching rule, better will be scheduling of the manufacturing system. Scheduling is a part of production planning. Thus, selecting a better dispatching rule for scheduling helps in carrying out a better production planning. This paper assesses the performance of nine dispatching rules identified from the literature. The remainder of the paper is organized as follows. The review of relevant literature is introduced in the section ‘‘Literature review’’. The section ‘‘Job shop configuration’’ describes salient aspects of configuration of the SDJS scheduling problem. The outline for development of simulation model is explained in the section ‘‘Structure of simulation model’’. The section ‘‘Experimental design for simulation study’’ presents details of simulation experimentations. The section ‘‘Results and discussion’’ provides analysis of experimental results. Finally, the section ‘‘conclusions’’ gives concluding remarks and directions for future research. Literature review Ramasesh [8] provided a review of simulation research in dynamic job shop scheduling problems. Allahverdi et al. [9] provided a comprehensive survey of literature on scheduling problems with setup times (costs). Panwalkar et al. [10] provided a survey of scheduling rules used in manufacturing systems. Blackstone et al. [11] presented a state-of-the-art review of scheduling rules used in job shop scheduling problems. Holthaus and Rajendran [12] proposed two new dispatching rules for dynamic job shop scheduling problems to minimize mean flow time, mean tardiness and percentage of tardy jobs performance measures. These rules combine 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). The authors concluded that Rule1 is quite superior in minimizing mean flow time performance measure. Jayamohan and Rajendran [13] proposed seven dispatching rules for minimization of mean flow time, maximum flow time, variance of flow time and tardiness performance measures in dynamic shops. The proposed rules are found to be very much effective in minimizing different performance measures. Jain et al. [14] proposed and assessed the performance of four new dispatching rules for makespan, mean flow time, maximum flow time and variance of flow time measures in a flexible manufacturing system. The authors found that the proposed dispatching rules provide better performance than the existing rules. Dominic et al. [15] developed two better scheduling rules 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. These rules are tested against six existing scheduling rules i.e. 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. There have been a few attempts to address dynamic job shop scheduling problems with sequence-dependent setup times. To the best of authors’ knowledge, Wilbrecht and Presscott [16] were first among researchers to study the influence of setup times on dynamic job shop manufacturing systems performance. The authors proposed and tested a setup oriented scheduling rule, job with Shortest Setup Time (SIMSET). The authors concluded that SIMSET rule outperforms other six existing scheduling rules i.e. Random, Earliest Due Date, Shortest Run, Longest Run, Shortest Process and Longest Process for value of work-in-progress, number of processes completed in a week, number of jobs sent out of the
shop in one week, number of processes completed late in one week, distribution of completion times, queue wait time of a job in a shop, number of jobs waiting in a shop, shop capacity utilized, number of jobs waiting in a queue for more than one week and size of jobs waiting in a queue for more than one week performance measures. Kim and Bobrowski [17] studied impact of sequencedependent setup times on a dynamic job shop manufacturing system performance. The authors concluded that setup oriented scheduling rules i.e. Shortest Setup Time (SIMSET) and Job with Similar Setup and Critical Ratio (JCR) outperforms ordinary scheduling rules i.e. 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 [18] extended their earlier research [17] to investigate impact of setup times variation on sequencing decisions with normally distributed setup times. The authors concluded that setup times variation has a negative impact on a manufacturing system performance. Recently, Vinod and Sridharan [19] proposed and assessed performance of five setup oriented scheduling rules viz. 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. The authors concluded that proposed rules provides better performance than the existing scheduling rules i.e. First-in-Firstout (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. Literature review clearly reveals that there is a need to evaluate the performance of dispatching rules in a SDJS manufacturing system with sequence-dependent setup times. The present paper is an attempt in this direction. It assesses performance of existing nine best performing dispatching rules identified from literature using simulation modeling for makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures in such shop. Further, the effect of change in setup time and shop utilization levels on system performance is also assessed. Job shop configuration In the present study, a job shop manufacturing system with ten machines is selected. The configuration of the manufacturing system is determined based on configuration of job shop considered by previous researchers [12,19]. It has been pointed out by researchers that six machines are sufficient to represent the complex structure of a job shop manufacturing system [16,20] and variations in job shop size don’t significantly affect the relative performance of dispatching rules [12,20]. For the same reason, most of the researchers addressed a job shop scheduling problem with less than ten machines [15,21,22]. Job data Six different types of jobs i.e. job type A, job type B, job type C, job type D, job type E, and job type F arrive at 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.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx Table 1 Routes of job types.
3
Table 2 Processing times of jobs on machines according to routes.
Job type
Number of operations
Route of the job (machine number)
Job type
Processing times of jobs according to machines
A B C D E F
5 4 4 5 4 5
1-6-10-2-4 8-3-5-10 7-9-3-1 5-7-9-2-4 2-8-1-10 6-9-1-3-5
A B C D E F
U(10, U(17, U(17, U(12, U(13, U(19,
11), 18), 18), 13), 14), 20),
U(14, U(10, U(11, U(19, U(19, U(13,
15), 11), 12), 20), 20), 14),
U(17, U(19, U(16, U(16, U(10, U(15,
18), 20), 17), 17), 11), 16),
U(16, U(13, U(13, U(10, U(16, U(10,
17), U(18, 19) 14) 14) 11), U(17, 18) 17) 11), U(14, 15)
system and processing requirements of the jobs. It is observed in the literature that arrival process of the jobs follows a Poisson distribution [8,19,24]. Thus, inter-arrival time is exponentially distributed. Mean inter-arrival time of the jobs is calculated using the following relationship [19,21].
This is an example case study. Table 1 shows the machines visited by different job types in their routes. In deterministic scheduling problems, processing and setup times of the jobs on the machines are fixed. But the real world problems are stochastic in nature. Thus, in the present work, the processing times and setup times of each job are considered stochastic and assumed to be uniformly distributed on each machine. The uniformly distributed time varies in a range. For example, processing time U (10, 12) means that the processing time of the job on the machine varies from 10 to 12 minutes with the mean of 11 minutes. Processing time changes according to job type and route of the job. The processing times of each job on the machines according to their routes are shown in Table 2. The pattern of processing times on different machines is selected based on research work carried out by previous researcher [23]. In the present study, two levels of setup time are considered i.e. setup time level1 (STL1), and setup time level2 (STL2). STL1 and STL2 represent the cases when ratio of mean of mean setup times to the mean of mean processing times is less than, and equal to one, respectively. Sequence-dependent setup times which encounters while shifting from one job type to another are given in Tables 3 and 4 for STL1, and STL2 respectively.
Here, b is the mean inter-arrival time, l the mean job arrival rate, mp the mean processing time per operation (including setup time), mg the mean number of operations per job, U the shop utilization, and M the number of machines in the shop. In the present work, mp is computed by taking the mean of mean processing times of all operations (from Table 2) plus mean of mean setup times (from Tables 3 and 4). Thus, mp = 19.45, 23.61 for STL1 and STL2 respectively. For the taken input data, mg is 4.5 with M = 10. In the present work, the experiments are carried out at two levels of shop utilization i.e. U = 90%, and 85%. Van Parunak [25] reported that due to stochastic nature of input processes (processing times and setup times) actual shop load is approximated and fall within a range of 1.5% of the target value.
Inter-arrival time
Due date of jobs
It is average time between arrivals of two jobs. Rangsaritratsamee et al. [24] reported that average arrival rate of jobs must be selected to have utilization of the machine less than 100%. Otherwise, the number of jobs in the queues in front of each machine will grow without bound. Thus, inter-arrival time of the jobs is established using percentage utilization of the manufacturing
The due date of a job indicates the time at which job order must be completed. The due date of the arriving job could be either externally or internally determined. In case of externally determined due date, due date is either established 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
b¼
1
l
¼
m p mg
(1)
UM
Table 3 Job types/sequence-dependent setup times data (STL1). Preceding job type
Follower job type
A B C D E F
A
B
0 U(5, U(5, U(5, U(5, U(5,
U(5, 0 U(5, U(5, U(5, U(5,
5.50) 5.25) 5.75) 5.50) 5.25)
C 5.25)
D
U(5, U(5, 0 U(5, U(5, U(5,
5.50) 5.25) 5.75) 5.50)
5.75) 5.25)
E
U(5, U(5, U(5, 0 U(5, U(5,
5.50) 5.25) 5.75)
5.50) 5.75) 5.50)
F
U(5, U(5, U(5, U(5, 0 U(5,
5.50) 5.25)
5.50) 5.25) 5.75) 5.25)
U(5, U(5, U(5, U(5, U(5, 0
5.50)
5.25) 5.50) 5.25) 5.50) 5.25)
Table 4 Job types/sequence-dependent setup times data (STL2). Preceding job type
Follower job type A
B
A B C D E F
0 U(18, U(18, U(18, U(18, U(18,
U(18, 0 U(18, U(18, U(18, U(18,
18.50) 18.25) 18.75) 18.50) 18.25)
C 18.25) 18.50) 18.25) 18.75) 18.50)
U(18, U(18, 0 U(18, U(18, U(18,
D 18.75) 18.25) 18.50) 18.25) 18.75)
U(18, U(18, U(18, 0 U(18, U(18,
E 18.50) 18.75) 18.50) 18.50) 18.25)
U(18, U(18, U(18, U(18, 0 U(18,
F 18.50) 18.25) 18.75) 18.25) 18.50)
U(18, U(18, U(18, U(18, U(18, 0
18.25) 18.50) 18.25) 18.50) 18.25)
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
4
processing times and setup times) of the job or number of operations to be performed on the job. The total work content (TWK) method is used by most of the researchers to assign due date of a job [12,19,21,26]. di ¼ ai þ kð pi þ ni ui Þ
(2)
Here, di is the due date of job i, ai the arrival time of job i, k the due date tightness factor, pi the mean total processing times of all the operations of job i, ni the number of operations of job i, and ui the mean of mean setup times of all the changeover of job i. In the present study, due date tightness factor (k) = 3 is considered. Structure of simulation model The study of large and complex manufacturing systems is possible only with simulation modeling. In the present study, using
PROMODEL software, a discrete event simulation model for the operations of SDJS manufacturing system with each dispatching rule is developed. The job flow in the modeled SDJS manufacturing system is shown in Fig. 1. The assumptions made while developing a simulation model are as follows. Each machine can perform only one operation on any job at a time. An operation cannot be performed until its predecessor operation is completed. The jobs arrival in the system is dynamic. A type of job is unknown until it arrives in the system. Unlimited capacity buffer is considered before and after each machine. Processing times and setup times of each job are stochastic and known in priori with their distribution. For processing of the jobs, alternate routings is not allowed. In the present study, a conceptual model of a job shop manufacturing system is developed. In order to ensure that the simulation model is correctly developed, a multilevel verification exercise is performed. For this, the simulation model is debugged
Start
A job arrives dynamically at the shop floor as per probability
Job goes to machine as per its routing
Job enters into machine queue
No
Is machine idle?
Job remains in machine queue
Yes Selection of job as per dispatching rule
No
Is machine idle?
Yes Processing of job by the machine
Is next operation required on the job?
Yes
No Job is completed
Stop
End Fig. 1. Job flow in a modeled job shop.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
and internal logics are checked. The output obtained from 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. Dispatching rules The dispatching rules are used to select a next job to be processed on the machine from a set of jobs awaiting machining in the input queue of the machine. In the present work, the following dispatching rules as identified from the literature are used to make job sequencing decision [16,19]. (1) First Come First Serve (FCFS): Highest priority is given to job which arrives first in the input queue of the machine. (2) Shortest Processing Time (SPT): Highest priority is given to job having the shortest processing time for the imminent operation. (3) Shortest Setup Time (SIMSET): Highest priority is given to job having the shortest setup time for the imminent operation. (4) Earliest Due Date (EDD): Highest priority is given to job having earliest due date. (5) SSPT: Shortest (Setup Time + Processing Time): Highest priority is given to job having smallest value of the sum of setup time and processing time. (6) JSPT: Job with Similar Setup and Shortest Processing Time: The job identical to the job that just finishes operation on the machine is selected for processing. When there is no identical job, highest priority is given to job having shortest processing time for the imminent operation. (7) JEDD: Job with Similar Setup and Earliest Due Date: The job identical to the job that just finishes operation on the machine is selected for processing. When there is no identical job, highest priority is given to job having earliest due date. (8) JMEDD: Job with Similar Setup and Modified Earliest Due Date: The job identical to the job that just finishes operation on the machine is selected for processing. When there is no identical job, highest priority is given to job having modified earliest due date. (9) JSSPT: Job with Similar Setup and Shortest (Setup Time + Processing Time): The job identical to the job that just finishes operation on the machine is selected for processing. When there is no identical job, highest priority is given to job having smallest value of the sum of setup time and processing time.
Performance measures The performance measures used for evaluation purpose in the experimental investigations are as follows: (1) Makespan (M): It is time of completion of last job in a manufacturing system. ¯ It is average time that a job spends in a (2) Mean flow time (F): manufacturing system during processing. " # n 1 X F¯ ¼ Fi (3) n i¼1 Here, Fi = ci ai, Fi the flow time of job i, ci the completion time of job i, ai the arrival time of job i, and n the number of jobs produced during simulation period (during steady state period).
5
(3) Maximum flow time (Fmax): It is a maximum value of flow time that encounters during processing of jobs in a manufacturing system. F max ¼ maxfF i g;
1in
(4)
¯ It is average tardiness of a job in a (4) Mean tardiness (T): manufacturing system during processing. " # n 1 X T¼ T (5) n i¼1 i Here, Ti = max{0, Li}, Li = ci di, Ti the tardiness of the job i, Li the lateness of job i, di the due date of job i. (5) Maximum tardiness (Tmax): It is a maximum value of tardiness that encounters during processing of jobs in a manufacturing system. T max ¼ maxfT i g;
1in
(6)
(6) Number of tardy jobs (NTJ): It is value of the number of jobs which are completed after their due dates. NTJ ¼
n X
dðJi Þ
(7)
i¼1
Here, d(Ji) = 1 if Ji > 0 and d(Ji) = 0, otherwise. (7) Total setups (TSP): It is value of the number of setups that encounters during processing of jobs in a manufacturing system. TSP ¼
n X
dðPi Þ
(8)
i¼1
Here, d(Pi) = 1 if Pi > 0 and d(Pi) = 0, otherwise. (8) Mean setup time (MST): It is average time that a job spends for the setup during processing in a manufacturing system. " # n 1 X MST ¼ Si (9) n i¼1 Here, Si is the setup time of job i.
Experimental design for simulation study Using simulation modeling, a number of experiments on SDJS scheduling problem have been conducted. The first stage in simulation experimentation is to identify steady state period i.e. end of the initial transient period. The Welch’s procedure as described by Law and Kelton [27] is used for this purpose. A pilot study for SDJS manufacturing system is conducted with FCFS dispatching rule. Thirty replications are considered for simulation experimentation. The simulation for each replication is made to run for 20,000 jobs completion. It is observed that the manufacturing system reaches steady state at the completion of 5000 jobs. Finally, the experimental investigation is carried out to assess the performance of nine dispatching rules identified from literature in a SDJS manufacturing system for 20,000 jobs completion (after warm up period of 5000 jobs). Table 5 shows the layout of the SDJS simulation experiments. Results and discussion In SDJS manufacturing system, the performance of nine dispatching rules identified from the literature is assessed. For each performance measure under each dispatching rule, the simulation output of 30 replications is averaged at STL1 and STL2 with each U = 90% and U = 85%. The average values of various performance measures are shown in Figs. 2–17.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
6
Table 5 Layout of the SDJS simulation experiments. Machine parameters
Number of machines: 10 Shop utilization: 02 levels (90% and 85%)
Job parameters
Simulation of job shop
Dispatching rules: 09 Number of replications: 30 Run length: 20,000 jobs completion (after warm up period of 5000 jobs)
Performance measures
Makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups, and mean setup time
Job types: 06 Number of operations: 04-05 Mean inter-arrival time: Exponential distribution Routing pattern: Fixed Processing times and setup times: Stochastic Setup time: 02 levels (STL1, and STL2) Due date: TWK method
Analysis of means The average value of 30 replication of each performance measure at different dispatching rules is analyzed. The detailed analysis is presented in the following subsections. Makespan It represents completion time of the last job. The makespan values for different dispatching rules at STL1 and STL2 are shown in Figs. 2 and 3 respectively. At STL1, JMEDD rule is best performing dispatching rule. This is followed by other dispatching rules i.e. EDD, JEDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS rules in that order. At SLT2, the order of superiority of dispatching rules is as
JMEDD, JEDD, EDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS. Thus, for makespan, JMEDD rule is best performing dispatching rule at both STL1 and STL2. Mean flow time The performance of different dispatching rules for mean flow time measure at STL1 and STL2 is shown in Figs. 4 and 5 respectively. The figures indicate that at STL1, SIMSET rule is best performing dispatching rule. This is followed by other dispatching rules i.e. SSPT, JMEDD, SPT, JEDD, EDD, JSSPT, JSPT, and FCFS dispatching rules in that order. At STL2, the performance wise order of different dispatching rules is as JMEDD, JEDD, EDD, SIMSET, SSPT, SPT, JSSPT, JSPT, and FCFS. Thus, SIMSET and JMEDD rules are best performing dispatching rules at STL1 and STL2 respectively. Maximum flow time Figs. 6 and 7 depict the performance of various dispatching rules for maximum flow time measure at STL1 and STL2 respectively. At STL1, it is observed that the JMEDD dispatching rule provides the best performance. This is followed by JEDD, EDD, JSSPT, JSPT, SSPT, SIMSET, SPT, and FCFS rules in that order as the next best performing dispatching rules. At STL2, the performance of different dispatching rules is as in this order JEDD, EDD, JMEDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS. Thus, JMEDD and JEDD rules are best performing dispatching rules at STL1 and STL2 respectively. Mean tardiness This is due date based performance measure and related to better customer service and satisfaction. Figs. 8 and 9 show the
Fig. 4. Mean flow time at STL1. Fig. 2. Makespan at STL1.
Fig. 3. Makespan at STL2.
Fig. 5. Mean flow time at STL2.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
Fig. 6. Maximum flow time at STL1.
7
Fig. 9. Mean tardiness at STL2.
Fig. 10. Maximum tardiness at STL1. Fig. 7. Maximum flow time at STL2.
Fig. 11. Maximum tardiness at STL2. Fig. 8. Mean tardiness at STL1.
respect to maximum flow time measure. For this measure, JMEDD at STL1 and JEDD at STL2 are best performing dispatching rules.
performance of various dispatching rules at STL1 and STL2 respectively. The figures indicate that at STL1, JMEDD rule is best performing dispatching rule and it is followed by SPT, SIMSET, SSPT, JEDD, EDD, JSSPT, JSPT, and FCFS dispatching rules in that order. At STL2, the order of performance of different dispatching rules is as JEDD, JMEDD, EDD, JSSPT, SPT, SSPT, SIMSET, JSPT, and FCFS. Thus, JMEDD at STL1 and JEDD at STL2 are best performing dispatching rules.
Number of tardy jobs The performance of different dispatching rules for number of tardy jobs at STL1 and STL2 is shown in Figs. 12 and 13 respectively. The figures indicate that at STL1, SIMSET dispatching rule provides best performance. The other dispatching rules i.e. SPT, SSPT, JSSPT, JSPT, JMEDD, JEDD, EDD, and FCFS rank second to ninth respectively in minimizing number of tardy jobs performance measure. At STL2, the performance of different dispatching rules is in this order as SIMSET, SSPT, SPT, JSSPT, JMEDD, JSPT, JEDD, EDD, and FCFS. Thus, at both STL1 and STL2, SIMSET rule is best performing dispatching rule.
Maximum tardiness Figs. 10 and 11 depict the performance of various dispatching rules for maximum tardiness measure at STL1 and STL2 respectively. These figures indicate that the performance pattern of different dispatching rules for maximum tardiness measure is similar to the performance of different dispatching rules with
Total setups The total setups values for different dispatching rules at STL1 and STL2 are shown in Figs. 14 and 15 respectively. At STL1,
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 8
P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
JMEDD rule is best performing dispatching rule. It is followed by JEDD, EDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS dispatching rules in that order. At STL2, the order of performance of different rules is as JMEDD, JEDD, EDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS. Thus, JMEDD dispatching rule ranks first in minimizing total setups at both STL1 and STL2.
Fig. 12. Number of tardy jobs at STL1.
Mean setup time Figs. 16 and 17 represent mean setup time values for different dispatching rules at STL1 and STL2 respectively. The performance of different dispatching rules for this measure is same as that of total setups. Here also, JMEDD is best performing dispatching rule at both STL1 and STL2. Further, Figs. 2–17 also indicate that the performance of different dispatching rules for all the considered measures at U = 90%, and U = 85% is same. Manufacturing system performance under change in shop environment In the present work, the shop environment is changed in terms of shop utilization and setup time. Two levels of each shop utilization, i.e. U = 90%, 85% and setup time i.e. STL1, STL2 are considered. The detailed analysis is presented in the following subsections.
Fig. 13. Number of tardy jobs at STL2.
The effect of changing shop utilization on system performance Two different shop utilization levels i.e. U = 90%, and U = 85% are considered in order to investigate the effect of change in shop utilization level on manufacturing system performance. Figs. 2 and 3 show that there is increase in makespan values as the shop utilization is decreased. This is due to the fact that as shop utilization decreases, the inter-arrival time of the jobs increases
Fig. 14. Total setups at STL1. Fig. 16. Mean setup time at STL1.
Fig. 15. Total setups at STL2.
Fig. 17. Mean setup time at STL2.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
and hence, makespan increases. Figs. 4 and 5, Figs. 6 and 7, Figs. 8 and 9, Figs. 10 and 11 and Figs. 12 and 13 represent mean flow time, maximum flow time, mean tardiness, maximum tardiness, and number of tardy jobs respectively. These figures indicate that as shop utilization decreases, values of these performance measures decreases. This is due to the fact that at low shop utilization, jobs wait for shorter duration for processing at various machines queues and hence, decrease in values of these performance measures is observed. Figs. 14 and 15 and Figs. 16 and 17 represent total setups and mean setup time performance measures respectively. These figures illustrate that for dispatching rules with similar setup logic i.e. JSPT, JEDD, JMEDD, and JSSPT, the total setups and mean setup time performance measures increases as shop utilization decreases from 90% to 85%. This is due to the fact that at lower shop utilization, the arrival rate of the jobs is less and hence, there will be less number of similar types of jobs at any given time which results in increased performance measures values. Further, for dispatching rules that don’t consider similar setup logic i.e. FCFS, SPT, SIMSET, EDD, and SSPT, the total setups and mean setup time performance measures values are nearly same at all considered shop utilization levels. The above discussion clearly reveals that the shop utilization level is an important parameter and it affects the system performance as measured by makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures. The effect of changing setup time on system performance In order to assess the effect of change in setup time on system performance, the two levels of setup time i.e. STL1 and STL2 are considered. Figs. 2 and 3 indicate that as setup time level changes from STL1 to STL2, makespan increases. This is due to the fact that setup time increases as setup time level changes from STL1 to STL2. Figs. 4 and 5, Figs. 6 and 7, Figs. 8 and 9, and Figs. 10 and 11 represent mean flow time, maximum flow time, mean tardiness, and maximum tardiness respectively. These figures indicate that for dispatching rules that don’t consider similar setup logic, the performance measures values increases with the increase in setup time. Further, for dispatching rules with similar setup logic, the performance measures values decreases with the increase in setup time. This is due to the fact that as setup time increases, the number of similar types of jobs in the machines queues increases. Hence, with the same setup maximum numbers of jobs are processed and performance measures values decreases. Figs. 12 and 13 illustrate that with the increase in setup time the number of tardy jobs decreases. The reason is that at higher setup time, due date assigned to jobs by TWK method drastically increases. Thus, there will be less number of tardy jobs at higher setup times. Figs. 14 and 15 indicate that for dispatching rules with similar setup logic, total setups decreases as the setup time increases from STL1 to STL2. This is due to the fact that as setup time increases, the number of similar types of jobs in the machines queues increases. Hence, with the same setup maximum numbers of jobs are processed and total setups decreases. For other dispatching rules nearly same values of total setups are observed. Figs. 16 and 17 indicate increase in mean setup time values with the increase in setup time, which is expected. Thus, the discussion indicates that a significant impact on system performance can be observed if the setup time required for the jobs is changed. Conclusions The present work addresses a SDJS scheduling problem while considering sequence-dependent setup times. A discrete-event simulation model of the SDJS manufacturing system is developed. The performance of nine dispatching rules taken from literature is
9
assessed. The effect of change in shop utilization and setup time level on manufacturing system performance is also assessed. The results can be summarized as follows: (1) The experimental results indicate that JMEDD rule is best performing dispatching rule for makespan, total setups and mean setup time measures at both STL1 and STL2. SIMSET rule provides best performance for number of tardy jobs at both STL1 and STL2. SIMSET and JMEDD are best performing dispatching rules for mean flow time at STL1 and STL2 respectively. JMEDD and JEDD rules provide best performance for maximum flow time, mean tardiness, and maximum tardiness at STL1 and STL2 respectively. (2) Shop utilization affects the system performance. The simulation analysis indicates that as shop utilization decreases, makespan increases. With the decrease in shop utilization, for dispatching rules considering similar setup logic, total setups and mean setup time performance measures increases while for other rules performance measure values remains the same. Further, mean flow time, maximum flow time, mean tardiness, maximum tardiness, and number of tardy jobs performance measures decreases with the decrease in shop utilization. (3) Setup time of the jobs also affects the system performance. The simulation analysis indicates that the makespan and mean setup time performance measures increases as setup time increases. The number of tardy jobs decreases with the increase in setup time. For dispatching rules with similar setup logic, mean flow time, maximum flow time, mean tardiness, and maximum tardiness performance measures decreases with the increase in setup time. While, for other dispatching rules increase in performance measures values is observed. Further, for dispatching rules with similar setup logic, the total setups decreases with the increase in setup time. While for other rules it remains the same. The present work can be extended in a number of ways. The future research could be directed towards addressing the SDJS scheduling problems with sequence-dependent setup times and involving situations like buffer of limited capacity between machines, machine breakdown, batch mode schedule and external disturbances such as order-cancellation and job pre-emption. The development of better dispatching rules is also required.
References [1] Garey, M.R., Johnson, D.S., Sethi, R., 1976, The complexity of flow shop and job shop scheduling, Math Oper Res, 1/2: 117–129. [2] Xiong, J., Xing, L.N., Chen, Y.W., 2013, Robust scheduling for multi-objective flexible job-shop problems with random machine breakdowns, Int J Prod Econ, 141/1: 112–126. [3] Ali, A., Soroush, H.M., 2008, The significance of reducing setup time/setup costs, Eur J Oper Res, 187/3: 978–984. [4] Pinedo, M., 1995, Scheduling theory, algorithms and systems, Prentice-Hall, Englewood Cliffs. [5] Manikas, A., Chang, Y.L., 2009, Multi-criteria sequence-dependent job shop scheduling using genetic algorithms, Comput Ind Eng, 56/1: 179–185. [6] Fantahun, M.D., Mingyuan, C., 2012, Job shop lot streaming with routing flexibility, sequence-dependent setups, machine release dates and lag time, Int J Prod Res, 50/8: 2331–2352. [7] Haupt, R., 1989, A survey of priority rule-based scheduling, Oper Res Spektrum, 11/1: 3–16. [8] Ramasesh, R., 1990, Dynamic job shop scheduling: a survey of research, Omega: Int J Manage Sci, 18/1: 43–57. [9] Allahverdi, A., Gupta, J.N.D., Aldowaisan, T., 1999, A review of scheduling research involving setup considerations, Omega, 27/2: 219–239. [10] Panwalkar, S.S., Iskander, W., 1977, A survey of scheduling rules, Oper Res, 25/ 1: 45–61. [11] Blackstone, J.H., Philips, D.T., Hogg, G.L., 1982, A state-of-the-art survey of dispatching rules for manufacturing job shop operations, Int J Prod Res, 20/1: 27–45.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 10
P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
[12] Holthaus, O., Rajendran, C., 1997, New dispatching rules for scheduling in a job shop – an experimental study, Int J Adv Manuf Technol, 13/2: 148–153. [13] Jayamohan, M.S., Rajendran, C., 2000, New dispatching rules for shop scheduling: a step forward, Int J Prod Res, 38/3: 563–586. [14] Jain, A., Jain, P.K., Singh, I.P., 2004, An investigation on the performance of dispatching rules in FMS scheduling, Int J Simul Model, 3/2–3: 49–60. [15] Dominic, P.D.D., Kaliyamoorthy, S., Saravana Kumar, M., 2004, Efficient dispatching rules for dynamic job shop scheduling, Int J Adv Manuf Technol, 24/ 1–2: 70–75. [16] Wilbrecht, J.K., Presscott, W.R., 1969, The influence of setup time on job shop performance, Manage Sci, 16/4: 274–280. [17] Kim, S.C., Bobrowski, P.M., 1994, Impact of sequence dependent setup time on job shop scheduling performance, Int J Prod Res, 32/7: 1503–1520. [18] Kim, S.C., Bobrowski, P.M., 1997, Scheduling jobs with uncertain setup times and sequence dependent, Int J Manage Sci, 25/4: 437–447. [19] Vinod, V., Sridharan, R., 2008, Dynamic job shop scheduling with sequencedependent setup times: simulation modelling and analysis, Int J Adv Manuf Technol, 36/3–4: 355–372.
[20] Baker, C.T., Dzielinski, B.P., 1960, Simulation of a simplified job shop, Manage Sci, 6/3: 311–323. [21] Yu, X., Ram, B., 2006, Bio-inspired scheduling for dynamic job shops with flexible routing and sequence dependent setups, Int J Prod Res, 44/22: 4793–4813. [22] Rossi, A., Dini, G., 2007, Flexible job shop scheduling with routing flexibility and separable setup times using ant colony optimisation method, Robot Comput Integr Manuf, 23/5: 503–516. [23] Baykasoglu, A., Go¨c¸ken, M., Unutmaz, Z.D., 2008, New approaches to due date assignment in job shops, Eur J Oper Res, 187/1: 31–45. [24] Rangsaritratsamee, R., Ferrell, W.G., Kurz, M.B., 2004, Dynamic rescheduling that simultaneously considers efficiency and stability, Comput Ind Eng, 46/1: 1–15. [25] Van Parunak, H., 1991, Characterizing the manufacturing scheduling problem, J Manuf Syst, 10/3: 241–259. [26] Baker, K.R., 1984, Sequencing rules and due-date assignments in a job shop, Manage Sci, 30/9: 1093–1104. [27] Law, A.M., Kelton, W.D., 1991, Simulation modeling and analysis, McGrawHill, New York.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
CIRPJ-313; No. of Pages 10 CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj
Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach Pankaj Sharma a,b,*, Ajai Jain a,1 a b
Department of Mechanical Engineering, National Institute of Technology, Kurukshetra 136119, Haryana, India Department of Mechanical Engineering, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India
A R T I C L E I N F O
A B S T R A C T
Article history: Available online xxx
Stochastic dynamic job shop scheduling problem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under different levels of shop utilization and setup time. The important aspects of the results of the simulation investigation are also discussed in detail. ß 2015 CIRP.
Keywords: Scheduling Stochastic dynamic job shop Sequence-dependent setup times Dispatching rule Simulation
Introduction Production scheduling in a manufacturing system is associated with allocation of set of jobs on a set of production resources over time to achieve some objectives. In a job shop manufacturing system, 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 as well as NP-hard 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 in job shop manufacturing systems. Further, in a stochastic dynamic job shop (SDJS) manufacturing system at least one parameter of the job (release time, processing time/setup time) is probabilistic. In traditional approaches, in order to reduce the complexity of solving job shop scheduling problems, setup time is either neglected or included in the processing time of a job. But this effort does not represent the realistic picture of a manufacturing
* Corresponding author at: Department of Mechanical Engineering, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India. Tel.: +91 9466206231; fax: +91 1662 276240. E-mail addresses: [email protected] (P. Sharma), [email protected] (A. Jain). 1 Tel.: +91 9412558040.
system. Setup time is a time that is required to prepare the necessary resources such as machines to perform an operation [3]. In many real-life situations, a setup operation often occurs while shifting from one operation type to another. Sequencedependent setup time depends on both current and immediately previous operation [3]. Sequence-dependent setup time encounters in many industries such as textile industry, printing industry, paper industry, auto industry, chemical processing and plastic manufacturing industry. In textile industry, during dyeing operation, a very little setup time is required for job changing when dyeing from pale shade to deep shade products. On the contrary, much more setup time is required to clean the dyeing vessel, if otherwise. Even in some cases, setup time becomes equal to or more than operation time. Scheduling problems with sequencedependent setup times are among the most difficult classes of scheduling problems [4]. It has been pointed out by Manikas and Chang [5] and Fantahun and Mingyuan [6] that limited research on job shop scheduling problems considering sequence-dependent setup times is available. A dispatching rule is used to select the next job to be processed from the set of jobs awaiting processing in the input queue of a machine. Dispatching rules are also termed as sequencing rules or scheduling rules. These rules are classified into broad four categories namely as process time based rules, due date based rules, combination rules and rules that are neither process time
http://dx.doi.org/10.1016/j.cirpj.2015.03.003 1755-5817/ß 2015 CIRP.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 2
P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
based nor due date based [7]. In a manufacturing system, dispatching rule is one of the methods that can be used to carry out scheduling. Better the dispatching rule, better will be scheduling of the manufacturing system. Scheduling is a part of production planning. Thus, selecting a better dispatching rule for scheduling helps in carrying out a better production planning. This paper assesses the performance of nine dispatching rules identified from the literature. The remainder of the paper is organized as follows. The review of relevant literature is introduced in the section ‘‘Literature review’’. The section ‘‘Job shop configuration’’ describes salient aspects of configuration of the SDJS scheduling problem. The outline for development of simulation model is explained in the section ‘‘Structure of simulation model’’. The section ‘‘Experimental design for simulation study’’ presents details of simulation experimentations. The section ‘‘Results and discussion’’ provides analysis of experimental results. Finally, the section ‘‘conclusions’’ gives concluding remarks and directions for future research. Literature review Ramasesh [8] provided a review of simulation research in dynamic job shop scheduling problems. Allahverdi et al. [9] provided a comprehensive survey of literature on scheduling problems with setup times (costs). Panwalkar et al. [10] provided a survey of scheduling rules used in manufacturing systems. Blackstone et al. [11] presented a state-of-the-art review of scheduling rules used in job shop scheduling problems. Holthaus and Rajendran [12] proposed two new dispatching rules for dynamic job shop scheduling problems to minimize mean flow time, mean tardiness and percentage of tardy jobs performance measures. These rules combine 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). The authors concluded that Rule1 is quite superior in minimizing mean flow time performance measure. Jayamohan and Rajendran [13] proposed seven dispatching rules for minimization of mean flow time, maximum flow time, variance of flow time and tardiness performance measures in dynamic shops. The proposed rules are found to be very much effective in minimizing different performance measures. Jain et al. [14] proposed and assessed the performance of four new dispatching rules for makespan, mean flow time, maximum flow time and variance of flow time measures in a flexible manufacturing system. The authors found that the proposed dispatching rules provide better performance than the existing rules. Dominic et al. [15] developed two better scheduling rules 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. These rules are tested against six existing scheduling rules i.e. 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. There have been a few attempts to address dynamic job shop scheduling problems with sequence-dependent setup times. To the best of authors’ knowledge, Wilbrecht and Presscott [16] were first among researchers to study the influence of setup times on dynamic job shop manufacturing systems performance. The authors proposed and tested a setup oriented scheduling rule, job with Shortest Setup Time (SIMSET). The authors concluded that SIMSET rule outperforms other six existing scheduling rules i.e. Random, Earliest Due Date, Shortest Run, Longest Run, Shortest Process and Longest Process for value of work-in-progress, number of processes completed in a week, number of jobs sent out of the
shop in one week, number of processes completed late in one week, distribution of completion times, queue wait time of a job in a shop, number of jobs waiting in a shop, shop capacity utilized, number of jobs waiting in a queue for more than one week and size of jobs waiting in a queue for more than one week performance measures. Kim and Bobrowski [17] studied impact of sequencedependent setup times on a dynamic job shop manufacturing system performance. The authors concluded that setup oriented scheduling rules i.e. Shortest Setup Time (SIMSET) and Job with Similar Setup and Critical Ratio (JCR) outperforms ordinary scheduling rules i.e. 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 [18] extended their earlier research [17] to investigate impact of setup times variation on sequencing decisions with normally distributed setup times. The authors concluded that setup times variation has a negative impact on a manufacturing system performance. Recently, Vinod and Sridharan [19] proposed and assessed performance of five setup oriented scheduling rules viz. 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. The authors concluded that proposed rules provides better performance than the existing scheduling rules i.e. First-in-Firstout (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. Literature review clearly reveals that there is a need to evaluate the performance of dispatching rules in a SDJS manufacturing system with sequence-dependent setup times. The present paper is an attempt in this direction. It assesses performance of existing nine best performing dispatching rules identified from literature using simulation modeling for makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures in such shop. Further, the effect of change in setup time and shop utilization levels on system performance is also assessed. Job shop configuration In the present study, a job shop manufacturing system with ten machines is selected. The configuration of the manufacturing system is determined based on configuration of job shop considered by previous researchers [12,19]. It has been pointed out by researchers that six machines are sufficient to represent the complex structure of a job shop manufacturing system [16,20] and variations in job shop size don’t significantly affect the relative performance of dispatching rules [12,20]. For the same reason, most of the researchers addressed a job shop scheduling problem with less than ten machines [15,21,22]. Job data Six different types of jobs i.e. job type A, job type B, job type C, job type D, job type E, and job type F arrive at 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.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx Table 1 Routes of job types.
3
Table 2 Processing times of jobs on machines according to routes.
Job type
Number of operations
Route of the job (machine number)
Job type
Processing times of jobs according to machines
A B C D E F
5 4 4 5 4 5
1-6-10-2-4 8-3-5-10 7-9-3-1 5-7-9-2-4 2-8-1-10 6-9-1-3-5
A B C D E F
U(10, U(17, U(17, U(12, U(13, U(19,
11), 18), 18), 13), 14), 20),
U(14, U(10, U(11, U(19, U(19, U(13,
15), 11), 12), 20), 20), 14),
U(17, U(19, U(16, U(16, U(10, U(15,
18), 20), 17), 17), 11), 16),
U(16, U(13, U(13, U(10, U(16, U(10,
17), U(18, 19) 14) 14) 11), U(17, 18) 17) 11), U(14, 15)
system and processing requirements of the jobs. It is observed in the literature that arrival process of the jobs follows a Poisson distribution [8,19,24]. Thus, inter-arrival time is exponentially distributed. Mean inter-arrival time of the jobs is calculated using the following relationship [19,21].
This is an example case study. Table 1 shows the machines visited by different job types in their routes. In deterministic scheduling problems, processing and setup times of the jobs on the machines are fixed. But the real world problems are stochastic in nature. Thus, in the present work, the processing times and setup times of each job are considered stochastic and assumed to be uniformly distributed on each machine. The uniformly distributed time varies in a range. For example, processing time U (10, 12) means that the processing time of the job on the machine varies from 10 to 12 minutes with the mean of 11 minutes. Processing time changes according to job type and route of the job. The processing times of each job on the machines according to their routes are shown in Table 2. The pattern of processing times on different machines is selected based on research work carried out by previous researcher [23]. In the present study, two levels of setup time are considered i.e. setup time level1 (STL1), and setup time level2 (STL2). STL1 and STL2 represent the cases when ratio of mean of mean setup times to the mean of mean processing times is less than, and equal to one, respectively. Sequence-dependent setup times which encounters while shifting from one job type to another are given in Tables 3 and 4 for STL1, and STL2 respectively.
Here, b is the mean inter-arrival time, l the mean job arrival rate, mp the mean processing time per operation (including setup time), mg the mean number of operations per job, U the shop utilization, and M the number of machines in the shop. In the present work, mp is computed by taking the mean of mean processing times of all operations (from Table 2) plus mean of mean setup times (from Tables 3 and 4). Thus, mp = 19.45, 23.61 for STL1 and STL2 respectively. For the taken input data, mg is 4.5 with M = 10. In the present work, the experiments are carried out at two levels of shop utilization i.e. U = 90%, and 85%. Van Parunak [25] reported that due to stochastic nature of input processes (processing times and setup times) actual shop load is approximated and fall within a range of 1.5% of the target value.
Inter-arrival time
Due date of jobs
It is average time between arrivals of two jobs. Rangsaritratsamee et al. [24] reported that average arrival rate of jobs must be selected to have utilization of the machine less than 100%. Otherwise, the number of jobs in the queues in front of each machine will grow without bound. Thus, inter-arrival time of the jobs is established using percentage utilization of the manufacturing
The due date of a job indicates the time at which job order must be completed. The due date of the arriving job could be either externally or internally determined. In case of externally determined due date, due date is either established 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
b¼
1
l
¼
m p mg
(1)
UM
Table 3 Job types/sequence-dependent setup times data (STL1). Preceding job type
Follower job type
A B C D E F
A
B
0 U(5, U(5, U(5, U(5, U(5,
U(5, 0 U(5, U(5, U(5, U(5,
5.50) 5.25) 5.75) 5.50) 5.25)
C 5.25)
D
U(5, U(5, 0 U(5, U(5, U(5,
5.50) 5.25) 5.75) 5.50)
5.75) 5.25)
E
U(5, U(5, U(5, 0 U(5, U(5,
5.50) 5.25) 5.75)
5.50) 5.75) 5.50)
F
U(5, U(5, U(5, U(5, 0 U(5,
5.50) 5.25)
5.50) 5.25) 5.75) 5.25)
U(5, U(5, U(5, U(5, U(5, 0
5.50)
5.25) 5.50) 5.25) 5.50) 5.25)
Table 4 Job types/sequence-dependent setup times data (STL2). Preceding job type
Follower job type A
B
A B C D E F
0 U(18, U(18, U(18, U(18, U(18,
U(18, 0 U(18, U(18, U(18, U(18,
18.50) 18.25) 18.75) 18.50) 18.25)
C 18.25) 18.50) 18.25) 18.75) 18.50)
U(18, U(18, 0 U(18, U(18, U(18,
D 18.75) 18.25) 18.50) 18.25) 18.75)
U(18, U(18, U(18, 0 U(18, U(18,
E 18.50) 18.75) 18.50) 18.50) 18.25)
U(18, U(18, U(18, U(18, 0 U(18,
F 18.50) 18.25) 18.75) 18.25) 18.50)
U(18, U(18, U(18, U(18, U(18, 0
18.25) 18.50) 18.25) 18.50) 18.25)
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
4
processing times and setup times) of the job or number of operations to be performed on the job. The total work content (TWK) method is used by most of the researchers to assign due date of a job [12,19,21,26]. di ¼ ai þ kð pi þ ni ui Þ
(2)
Here, di is the due date of job i, ai the arrival time of job i, k the due date tightness factor, pi the mean total processing times of all the operations of job i, ni the number of operations of job i, and ui the mean of mean setup times of all the changeover of job i. In the present study, due date tightness factor (k) = 3 is considered. Structure of simulation model The study of large and complex manufacturing systems is possible only with simulation modeling. In the present study, using
PROMODEL software, a discrete event simulation model for the operations of SDJS manufacturing system with each dispatching rule is developed. The job flow in the modeled SDJS manufacturing system is shown in Fig. 1. The assumptions made while developing a simulation model are as follows. Each machine can perform only one operation on any job at a time. An operation cannot be performed until its predecessor operation is completed. The jobs arrival in the system is dynamic. A type of job is unknown until it arrives in the system. Unlimited capacity buffer is considered before and after each machine. Processing times and setup times of each job are stochastic and known in priori with their distribution. For processing of the jobs, alternate routings is not allowed. In the present study, a conceptual model of a job shop manufacturing system is developed. In order to ensure that the simulation model is correctly developed, a multilevel verification exercise is performed. For this, the simulation model is debugged
Start
A job arrives dynamically at the shop floor as per probability
Job goes to machine as per its routing
Job enters into machine queue
No
Is machine idle?
Job remains in machine queue
Yes Selection of job as per dispatching rule
No
Is machine idle?
Yes Processing of job by the machine
Is next operation required on the job?
Yes
No Job is completed
Stop
End Fig. 1. Job flow in a modeled job shop.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
and internal logics are checked. The output obtained from 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. Dispatching rules The dispatching rules are used to select a next job to be processed on the machine from a set of jobs awaiting machining in the input queue of the machine. In the present work, the following dispatching rules as identified from the literature are used to make job sequencing decision [16,19]. (1) First Come First Serve (FCFS): Highest priority is given to job which arrives first in the input queue of the machine. (2) Shortest Processing Time (SPT): Highest priority is given to job having the shortest processing time for the imminent operation. (3) Shortest Setup Time (SIMSET): Highest priority is given to job having the shortest setup time for the imminent operation. (4) Earliest Due Date (EDD): Highest priority is given to job having earliest due date. (5) SSPT: Shortest (Setup Time + Processing Time): Highest priority is given to job having smallest value of the sum of setup time and processing time. (6) JSPT: Job with Similar Setup and Shortest Processing Time: The job identical to the job that just finishes operation on the machine is selected for processing. When there is no identical job, highest priority is given to job having shortest processing time for the imminent operation. (7) JEDD: Job with Similar Setup and Earliest Due Date: The job identical to the job that just finishes operation on the machine is selected for processing. When there is no identical job, highest priority is given to job having earliest due date. (8) JMEDD: Job with Similar Setup and Modified Earliest Due Date: The job identical to the job that just finishes operation on the machine is selected for processing. When there is no identical job, highest priority is given to job having modified earliest due date. (9) JSSPT: Job with Similar Setup and Shortest (Setup Time + Processing Time): The job identical to the job that just finishes operation on the machine is selected for processing. When there is no identical job, highest priority is given to job having smallest value of the sum of setup time and processing time.
Performance measures The performance measures used for evaluation purpose in the experimental investigations are as follows: (1) Makespan (M): It is time of completion of last job in a manufacturing system. ¯ It is average time that a job spends in a (2) Mean flow time (F): manufacturing system during processing. " # n 1 X F¯ ¼ Fi (3) n i¼1 Here, Fi = ci ai, Fi the flow time of job i, ci the completion time of job i, ai the arrival time of job i, and n the number of jobs produced during simulation period (during steady state period).
5
(3) Maximum flow time (Fmax): It is a maximum value of flow time that encounters during processing of jobs in a manufacturing system. F max ¼ maxfF i g;
1in
(4)
¯ It is average tardiness of a job in a (4) Mean tardiness (T): manufacturing system during processing. " # n 1 X T¼ T (5) n i¼1 i Here, Ti = max{0, Li}, Li = ci di, Ti the tardiness of the job i, Li the lateness of job i, di the due date of job i. (5) Maximum tardiness (Tmax): It is a maximum value of tardiness that encounters during processing of jobs in a manufacturing system. T max ¼ maxfT i g;
1in
(6)
(6) Number of tardy jobs (NTJ): It is value of the number of jobs which are completed after their due dates. NTJ ¼
n X
dðJi Þ
(7)
i¼1
Here, d(Ji) = 1 if Ji > 0 and d(Ji) = 0, otherwise. (7) Total setups (TSP): It is value of the number of setups that encounters during processing of jobs in a manufacturing system. TSP ¼
n X
dðPi Þ
(8)
i¼1
Here, d(Pi) = 1 if Pi > 0 and d(Pi) = 0, otherwise. (8) Mean setup time (MST): It is average time that a job spends for the setup during processing in a manufacturing system. " # n 1 X MST ¼ Si (9) n i¼1 Here, Si is the setup time of job i.
Experimental design for simulation study Using simulation modeling, a number of experiments on SDJS scheduling problem have been conducted. The first stage in simulation experimentation is to identify steady state period i.e. end of the initial transient period. The Welch’s procedure as described by Law and Kelton [27] is used for this purpose. A pilot study for SDJS manufacturing system is conducted with FCFS dispatching rule. Thirty replications are considered for simulation experimentation. The simulation for each replication is made to run for 20,000 jobs completion. It is observed that the manufacturing system reaches steady state at the completion of 5000 jobs. Finally, the experimental investigation is carried out to assess the performance of nine dispatching rules identified from literature in a SDJS manufacturing system for 20,000 jobs completion (after warm up period of 5000 jobs). Table 5 shows the layout of the SDJS simulation experiments. Results and discussion In SDJS manufacturing system, the performance of nine dispatching rules identified from the literature is assessed. For each performance measure under each dispatching rule, the simulation output of 30 replications is averaged at STL1 and STL2 with each U = 90% and U = 85%. The average values of various performance measures are shown in Figs. 2–17.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
6
Table 5 Layout of the SDJS simulation experiments. Machine parameters
Number of machines: 10 Shop utilization: 02 levels (90% and 85%)
Job parameters
Simulation of job shop
Dispatching rules: 09 Number of replications: 30 Run length: 20,000 jobs completion (after warm up period of 5000 jobs)
Performance measures
Makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups, and mean setup time
Job types: 06 Number of operations: 04-05 Mean inter-arrival time: Exponential distribution Routing pattern: Fixed Processing times and setup times: Stochastic Setup time: 02 levels (STL1, and STL2) Due date: TWK method
Analysis of means The average value of 30 replication of each performance measure at different dispatching rules is analyzed. The detailed analysis is presented in the following subsections. Makespan It represents completion time of the last job. The makespan values for different dispatching rules at STL1 and STL2 are shown in Figs. 2 and 3 respectively. At STL1, JMEDD rule is best performing dispatching rule. This is followed by other dispatching rules i.e. EDD, JEDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS rules in that order. At SLT2, the order of superiority of dispatching rules is as
JMEDD, JEDD, EDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS. Thus, for makespan, JMEDD rule is best performing dispatching rule at both STL1 and STL2. Mean flow time The performance of different dispatching rules for mean flow time measure at STL1 and STL2 is shown in Figs. 4 and 5 respectively. The figures indicate that at STL1, SIMSET rule is best performing dispatching rule. This is followed by other dispatching rules i.e. SSPT, JMEDD, SPT, JEDD, EDD, JSSPT, JSPT, and FCFS dispatching rules in that order. At STL2, the performance wise order of different dispatching rules is as JMEDD, JEDD, EDD, SIMSET, SSPT, SPT, JSSPT, JSPT, and FCFS. Thus, SIMSET and JMEDD rules are best performing dispatching rules at STL1 and STL2 respectively. Maximum flow time Figs. 6 and 7 depict the performance of various dispatching rules for maximum flow time measure at STL1 and STL2 respectively. At STL1, it is observed that the JMEDD dispatching rule provides the best performance. This is followed by JEDD, EDD, JSSPT, JSPT, SSPT, SIMSET, SPT, and FCFS rules in that order as the next best performing dispatching rules. At STL2, the performance of different dispatching rules is as in this order JEDD, EDD, JMEDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS. Thus, JMEDD and JEDD rules are best performing dispatching rules at STL1 and STL2 respectively. Mean tardiness This is due date based performance measure and related to better customer service and satisfaction. Figs. 8 and 9 show the
Fig. 4. Mean flow time at STL1. Fig. 2. Makespan at STL1.
Fig. 3. Makespan at STL2.
Fig. 5. Mean flow time at STL2.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
Fig. 6. Maximum flow time at STL1.
7
Fig. 9. Mean tardiness at STL2.
Fig. 10. Maximum tardiness at STL1. Fig. 7. Maximum flow time at STL2.
Fig. 11. Maximum tardiness at STL2. Fig. 8. Mean tardiness at STL1.
respect to maximum flow time measure. For this measure, JMEDD at STL1 and JEDD at STL2 are best performing dispatching rules.
performance of various dispatching rules at STL1 and STL2 respectively. The figures indicate that at STL1, JMEDD rule is best performing dispatching rule and it is followed by SPT, SIMSET, SSPT, JEDD, EDD, JSSPT, JSPT, and FCFS dispatching rules in that order. At STL2, the order of performance of different dispatching rules is as JEDD, JMEDD, EDD, JSSPT, SPT, SSPT, SIMSET, JSPT, and FCFS. Thus, JMEDD at STL1 and JEDD at STL2 are best performing dispatching rules.
Number of tardy jobs The performance of different dispatching rules for number of tardy jobs at STL1 and STL2 is shown in Figs. 12 and 13 respectively. The figures indicate that at STL1, SIMSET dispatching rule provides best performance. The other dispatching rules i.e. SPT, SSPT, JSSPT, JSPT, JMEDD, JEDD, EDD, and FCFS rank second to ninth respectively in minimizing number of tardy jobs performance measure. At STL2, the performance of different dispatching rules is in this order as SIMSET, SSPT, SPT, JSSPT, JMEDD, JSPT, JEDD, EDD, and FCFS. Thus, at both STL1 and STL2, SIMSET rule is best performing dispatching rule.
Maximum tardiness Figs. 10 and 11 depict the performance of various dispatching rules for maximum tardiness measure at STL1 and STL2 respectively. These figures indicate that the performance pattern of different dispatching rules for maximum tardiness measure is similar to the performance of different dispatching rules with
Total setups The total setups values for different dispatching rules at STL1 and STL2 are shown in Figs. 14 and 15 respectively. At STL1,
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 8
P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
JMEDD rule is best performing dispatching rule. It is followed by JEDD, EDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS dispatching rules in that order. At STL2, the order of performance of different rules is as JMEDD, JEDD, EDD, JSSPT, JSPT, SSPT, SPT, SIMSET, and FCFS. Thus, JMEDD dispatching rule ranks first in minimizing total setups at both STL1 and STL2.
Fig. 12. Number of tardy jobs at STL1.
Mean setup time Figs. 16 and 17 represent mean setup time values for different dispatching rules at STL1 and STL2 respectively. The performance of different dispatching rules for this measure is same as that of total setups. Here also, JMEDD is best performing dispatching rule at both STL1 and STL2. Further, Figs. 2–17 also indicate that the performance of different dispatching rules for all the considered measures at U = 90%, and U = 85% is same. Manufacturing system performance under change in shop environment In the present work, the shop environment is changed in terms of shop utilization and setup time. Two levels of each shop utilization, i.e. U = 90%, 85% and setup time i.e. STL1, STL2 are considered. The detailed analysis is presented in the following subsections.
Fig. 13. Number of tardy jobs at STL2.
The effect of changing shop utilization on system performance Two different shop utilization levels i.e. U = 90%, and U = 85% are considered in order to investigate the effect of change in shop utilization level on manufacturing system performance. Figs. 2 and 3 show that there is increase in makespan values as the shop utilization is decreased. This is due to the fact that as shop utilization decreases, the inter-arrival time of the jobs increases
Fig. 14. Total setups at STL1. Fig. 16. Mean setup time at STL1.
Fig. 15. Total setups at STL2.
Fig. 17. Mean setup time at STL2.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
and hence, makespan increases. Figs. 4 and 5, Figs. 6 and 7, Figs. 8 and 9, Figs. 10 and 11 and Figs. 12 and 13 represent mean flow time, maximum flow time, mean tardiness, maximum tardiness, and number of tardy jobs respectively. These figures indicate that as shop utilization decreases, values of these performance measures decreases. This is due to the fact that at low shop utilization, jobs wait for shorter duration for processing at various machines queues and hence, decrease in values of these performance measures is observed. Figs. 14 and 15 and Figs. 16 and 17 represent total setups and mean setup time performance measures respectively. These figures illustrate that for dispatching rules with similar setup logic i.e. JSPT, JEDD, JMEDD, and JSSPT, the total setups and mean setup time performance measures increases as shop utilization decreases from 90% to 85%. This is due to the fact that at lower shop utilization, the arrival rate of the jobs is less and hence, there will be less number of similar types of jobs at any given time which results in increased performance measures values. Further, for dispatching rules that don’t consider similar setup logic i.e. FCFS, SPT, SIMSET, EDD, and SSPT, the total setups and mean setup time performance measures values are nearly same at all considered shop utilization levels. The above discussion clearly reveals that the shop utilization level is an important parameter and it affects the system performance as measured by makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures. The effect of changing setup time on system performance In order to assess the effect of change in setup time on system performance, the two levels of setup time i.e. STL1 and STL2 are considered. Figs. 2 and 3 indicate that as setup time level changes from STL1 to STL2, makespan increases. This is due to the fact that setup time increases as setup time level changes from STL1 to STL2. Figs. 4 and 5, Figs. 6 and 7, Figs. 8 and 9, and Figs. 10 and 11 represent mean flow time, maximum flow time, mean tardiness, and maximum tardiness respectively. These figures indicate that for dispatching rules that don’t consider similar setup logic, the performance measures values increases with the increase in setup time. Further, for dispatching rules with similar setup logic, the performance measures values decreases with the increase in setup time. This is due to the fact that as setup time increases, the number of similar types of jobs in the machines queues increases. Hence, with the same setup maximum numbers of jobs are processed and performance measures values decreases. Figs. 12 and 13 illustrate that with the increase in setup time the number of tardy jobs decreases. The reason is that at higher setup time, due date assigned to jobs by TWK method drastically increases. Thus, there will be less number of tardy jobs at higher setup times. Figs. 14 and 15 indicate that for dispatching rules with similar setup logic, total setups decreases as the setup time increases from STL1 to STL2. This is due to the fact that as setup time increases, the number of similar types of jobs in the machines queues increases. Hence, with the same setup maximum numbers of jobs are processed and total setups decreases. For other dispatching rules nearly same values of total setups are observed. Figs. 16 and 17 indicate increase in mean setup time values with the increase in setup time, which is expected. Thus, the discussion indicates that a significant impact on system performance can be observed if the setup time required for the jobs is changed. Conclusions The present work addresses a SDJS scheduling problem while considering sequence-dependent setup times. A discrete-event simulation model of the SDJS manufacturing system is developed. The performance of nine dispatching rules taken from literature is
9
assessed. The effect of change in shop utilization and setup time level on manufacturing system performance is also assessed. The results can be summarized as follows: (1) The experimental results indicate that JMEDD rule is best performing dispatching rule for makespan, total setups and mean setup time measures at both STL1 and STL2. SIMSET rule provides best performance for number of tardy jobs at both STL1 and STL2. SIMSET and JMEDD are best performing dispatching rules for mean flow time at STL1 and STL2 respectively. JMEDD and JEDD rules provide best performance for maximum flow time, mean tardiness, and maximum tardiness at STL1 and STL2 respectively. (2) Shop utilization affects the system performance. The simulation analysis indicates that as shop utilization decreases, makespan increases. With the decrease in shop utilization, for dispatching rules considering similar setup logic, total setups and mean setup time performance measures increases while for other rules performance measure values remains the same. Further, mean flow time, maximum flow time, mean tardiness, maximum tardiness, and number of tardy jobs performance measures decreases with the decrease in shop utilization. (3) Setup time of the jobs also affects the system performance. The simulation analysis indicates that the makespan and mean setup time performance measures increases as setup time increases. The number of tardy jobs decreases with the increase in setup time. For dispatching rules with similar setup logic, mean flow time, maximum flow time, mean tardiness, and maximum tardiness performance measures decreases with the increase in setup time. While, for other dispatching rules increase in performance measures values is observed. Further, for dispatching rules with similar setup logic, the total setups decreases with the increase in setup time. While for other rules it remains the same. The present work can be extended in a number of ways. The future research could be directed towards addressing the SDJS scheduling problems with sequence-dependent setup times and involving situations like buffer of limited capacity between machines, machine breakdown, batch mode schedule and external disturbances such as order-cancellation and job pre-emption. The development of better dispatching rules is also required.
References [1] Garey, M.R., Johnson, D.S., Sethi, R., 1976, The complexity of flow shop and job shop scheduling, Math Oper Res, 1/2: 117–129. [2] Xiong, J., Xing, L.N., Chen, Y.W., 2013, Robust scheduling for multi-objective flexible job-shop problems with random machine breakdowns, Int J Prod Econ, 141/1: 112–126. [3] Ali, A., Soroush, H.M., 2008, The significance of reducing setup time/setup costs, Eur J Oper Res, 187/3: 978–984. [4] Pinedo, M., 1995, Scheduling theory, algorithms and systems, Prentice-Hall, Englewood Cliffs. [5] Manikas, A., Chang, Y.L., 2009, Multi-criteria sequence-dependent job shop scheduling using genetic algorithms, Comput Ind Eng, 56/1: 179–185. [6] Fantahun, M.D., Mingyuan, C., 2012, Job shop lot streaming with routing flexibility, sequence-dependent setups, machine release dates and lag time, Int J Prod Res, 50/8: 2331–2352. [7] Haupt, R., 1989, A survey of priority rule-based scheduling, Oper Res Spektrum, 11/1: 3–16. [8] Ramasesh, R., 1990, Dynamic job shop scheduling: a survey of research, Omega: Int J Manage Sci, 18/1: 43–57. [9] Allahverdi, A., Gupta, J.N.D., Aldowaisan, T., 1999, A review of scheduling research involving setup considerations, Omega, 27/2: 219–239. [10] Panwalkar, S.S., Iskander, W., 1977, A survey of scheduling rules, Oper Res, 25/ 1: 45–61. [11] Blackstone, J.H., Philips, D.T., Hogg, G.L., 1982, A state-of-the-art survey of dispatching rules for manufacturing job shop operations, Int J Prod Res, 20/1: 27–45.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003
G Model
CIRPJ-313; No. of Pages 10 10
P. Sharma, A. Jain / CIRP Journal of Manufacturing Science and Technology xxx (2015) xxx–xxx
[12] Holthaus, O., Rajendran, C., 1997, New dispatching rules for scheduling in a job shop – an experimental study, Int J Adv Manuf Technol, 13/2: 148–153. [13] Jayamohan, M.S., Rajendran, C., 2000, New dispatching rules for shop scheduling: a step forward, Int J Prod Res, 38/3: 563–586. [14] Jain, A., Jain, P.K., Singh, I.P., 2004, An investigation on the performance of dispatching rules in FMS scheduling, Int J Simul Model, 3/2–3: 49–60. [15] Dominic, P.D.D., Kaliyamoorthy, S., Saravana Kumar, M., 2004, Efficient dispatching rules for dynamic job shop scheduling, Int J Adv Manuf Technol, 24/ 1–2: 70–75. [16] Wilbrecht, J.K., Presscott, W.R., 1969, The influence of setup time on job shop performance, Manage Sci, 16/4: 274–280. [17] Kim, S.C., Bobrowski, P.M., 1994, Impact of sequence dependent setup time on job shop scheduling performance, Int J Prod Res, 32/7: 1503–1520. [18] Kim, S.C., Bobrowski, P.M., 1997, Scheduling jobs with uncertain setup times and sequence dependent, Int J Manage Sci, 25/4: 437–447. [19] Vinod, V., Sridharan, R., 2008, Dynamic job shop scheduling with sequencedependent setup times: simulation modelling and analysis, Int J Adv Manuf Technol, 36/3–4: 355–372.
[20] Baker, C.T., Dzielinski, B.P., 1960, Simulation of a simplified job shop, Manage Sci, 6/3: 311–323. [21] Yu, X., Ram, B., 2006, Bio-inspired scheduling for dynamic job shops with flexible routing and sequence dependent setups, Int J Prod Res, 44/22: 4793–4813. [22] Rossi, A., Dini, G., 2007, Flexible job shop scheduling with routing flexibility and separable setup times using ant colony optimisation method, Robot Comput Integr Manuf, 23/5: 503–516. [23] Baykasoglu, A., Go¨c¸ken, M., Unutmaz, Z.D., 2008, New approaches to due date assignment in job shops, Eur J Oper Res, 187/1: 31–45. [24] Rangsaritratsamee, R., Ferrell, W.G., Kurz, M.B., 2004, Dynamic rescheduling that simultaneously considers efficiency and stability, Comput Ind Eng, 46/1: 1–15. [25] Van Parunak, H., 1991, Characterizing the manufacturing scheduling problem, J Manuf Syst, 10/3: 241–259. [26] Baker, K.R., 1984, Sequencing rules and due-date assignments in a job shop, Manage Sci, 30/9: 1093–1104. [27] Law, A.M., Kelton, W.D., 1991, Simulation modeling and analysis, McGrawHill, New York.
Please cite this article in press as: Sharma, P., Jain, A., Performance analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times: Simulation approach. CIRP Journal of Manufacturing Science and Technology (2015), http://dx.doi.org/10.1016/j.cirpj.2015.03.003