Study of stochastic sequence-dependent flexible flow shop via developing a dispatching rule and a hybrid GA

Abstract

A flexible flow shop is a generalized flow shop with multiple machines in some stages. This system is fairly common in flexible manufacturing and in process industry. In most practical environments, scheduling is an ongoing reactive process where the presence of real time information continually forces reconsideration of pre-established schedules. This paper studies a flexible flow shop system considering non-deterministic and dynamic arrival of jobs and also sequence dependent setup times. The problem objective is to determine a schedule that minimizes average tardiness of jobs. Since the problem class is NP-hard, a novel dispatching rule and hybrid genetic algorithm have been developed to solve the problem approximately. Moreover, a discrete event simulation model of the problem is developed for the purpose of experimentation. The most commonly used dispatching rules from the literature and two new methods presented in this paper are incorporated in the simulation model. Simulation experiments have been conducted under various experimental conditions characterized by factors such as shop utilization, setup time level and number of stages. The results indicate that methods proposed in this study are much better than the traditional dispatching rules.

Introduction

Scheduling in manufacturing systems is typically associated with allocating a set of jobs on a set of machines in order to achieve some objectives. It is an important decision making process in the operation level. Manufacturing environments in the real world are subject to many sources of change which are typically treated as random occurrences, such as new job releases, machine breakdowns, etc.

In this paper, we will focus on Flexible Flow shop Scheduling system with Sequence Dependent Setup Times (SDST/FFS). In the considered problem, jobs arrive dynamically over the scheduling period and the objective is to find a schedule that minimizes average tardiness of jobs. Following gives a review of the literature relevant to this problem.

Dispatching rules are very common techniques to deal with dynamic scheduling problems and especially flow shops. Hunsucker and Shah (1992) examined the performance of six different dispatching rules to minimize two tardiness-based criteria in a dynamic flow shop. Lodree et al. (2004) suggested a new rule to minimize the number of tardy jobs, while Branke and Mattfeld (2005) demonstrated that avoiding early idle times helps in minimizing total tardiness in a dynamic flow shop. More recently, Swaminathan et al. (2007) examined minimization of total weighted tardiness in a dynamic flow shop where new jobs arrive at every shift change, while Alfieri (2007) studied the interaction between a number of dispatching rules and due-date quoting policies in a simple dynamic flow shop. Rajendran and Alicke (2007) developed dispatching rules to take into account the presence of bottleneck machines in a flow shop system. Another work that deals specifically with the mean flow time criterion in a dynamic flow shop is that of Rajendran and Holthaus (1999). They compared 13 existing and proposed dispatching rules in a 10-machine flow shop and also concluded that the SPT dispatching rule gives the lowest mean flow times for all the machine utilization levels examined. Kianfar et al. (2009) proposed four dispatching rules to minimize the sum of tardiness and rejection costs and through a statistical simulation model showed the performance of their new methods.

Jayamohan and Rajendran (2000) provide a set of new dispatching rules to minimize various performance measures such as mean, maximum and variance of flow time and tardiness in dynamic shops. A static rule which minimizes the number of tardy jobs is also proposed. To evaluate these proposed rules, their relative performance is analyzed in open job shops and reported in comparison with the standard benchmark rules such as the SPT and EDD, popular rules like ATC and MOD, and the best performing rules in literature such as RR, PT+WINQ, PT+WINQ+SL and AT+RPT. When job arrivals are dynamic, the use of dispatching rules has to be resorted to Hunsucker and Shah, 1992, Hunsucker and Shah, 1994. Their studies were limited by the selection of dispatching rules such as FIFO, SPT and LPT, and efficient rules such as MOD (Baker and Kanet, 1983) and ATC (Vepsalainen and Morton, 1987) were not included. Moreover, a comprehensive set of measures involving mean and variance of flow time, and mean and variance of tardiness of jobs was not considered. In comparison to these studies, the study by Rajendran and Holthaus (1999) appears more complete with respect to many dispatching rules such as COVERT (Russell et al.,1987), RR (Raghu and Rajendran, 1993) and PT+WINQ (Holthaus and Rajendran, 1997). From a relative evaluation of many dispatching rules from the literature survey, it appears that there is a scope to develop efficient dispatching rules that could address a number of performance measures such as the minimization of mean, maximum and variance of flow time and tardiness of jobs, and also minimizing the percentage of tardy jobs.

Heuristic and meta-heuristic algorithms are also widely used in the area of dynamic scheduling. Hmida et al. (2006) presented a heuristic for hybrid flow shop to minimize makespan. They present a climbing discrepancy search that is an adaptation of the depth-bounded discrepancy search method to obtain near-optimal solutions. Fattahi and Fallahi (2010) consider dynamic scheduling in flexible job shop systems by considering simultaneously efficiency and stability. They develop a meta-heuristic algorithm based on GA and state that the proposed algorithm is capable to achieve the optimal solutions for the small size problems and near optimal solutions for the medium size problems.

The studies about flexible flow shops with sequence dependent setup times are really scarce. Kurz and Askin (2003) study dispatching rules for the SDST/FFS. They investigate three classes of heuristics based on simple greedy methods, insertion heuristics and adaptations of Johnson′s rule. Later, Kurz and Askin (2004) formulate the SDST/HFFS as an Integer Programming (IP) model. Because of the difficulty in solving the IP model directly, they develop a random keys genetic algorithm. Zandieh et al. (2006) propose an immune algorithm, and compare it against the random keys genetic algorithm of Kurz and Askin (2004). Naderi et al. (2009) study a hybrid flexible flow shop with respect to sequence dependent setups. They propose a dynamic dispatching rule and an iterated local search algorithm. The new algorithms are evaluated by comparison against 7 other high performing algorithms from the literature. Statistical experiments show that the proposed algorithms are very competitive for the studied problem. Kia et al. (2010) suppose the same problem and present a discrete-event simulation model as well as eleven heuristic algorithms, including 9 dispatching rules and two constructive heuristics. It is notable that all the studies in this paragraph except the paper by Kia et al. (2010) consider the related problems in deterministic conditions in which the arrival times of jobs are known in advance; however, we have defined the proposed problem in stochastic condition in which the jobs information is unknown before they are received.

The paper by Jungwattanakit et al. (2008) considers the flexible flow shop problem with setup times to minimize a convex combination of makespan and the number of tardy jobs. In this study, several basic dispatching rules and constructive heuristics are generalized to the considered problem and a genetic algorithm is developed as well. In 2003, Reddy and Narendran (2003) studied a five machine permutation flow shop problem with dynamically arriving jobs belonging to different families in a stochastic environment where both the process times and the inter-arrival times are assumed to be exponential random variables. Sequence dependent setup times occur between the jobs of distinct families. Reddy and Narendran compared the quality of 9 heuristics with regard to the objectives of minimizing the average job flow time, the average job tardiness and the percentage of tardy jobs.

Vinod and Sridharan (2009) conduct a simulation study that investigates several performance measures in the dynamic job shop scheduling with sequence dependent setup times. They also proposed five setup-oriented scheduling rules that one of them performs better for the mean flow and mean tardiness measures.

The rest of the paper is organized as follows. Section 2 deals with the problem definition. The Neighborhood Search-based Dispatching Rule (NSDR) for the flexible flow shop problem under consideration is introduced in Section 3. In Section 4, a hybrid genetic algorithm for the problem is proposed; and the important aspects of the developed simulation model are described in Section 5. Section 6 presents the details of the experimentation and the results and analysis of different scenarios. Finally, Section 7 is devoted to conclusions and recommendations for future studies.