Heuristic approaches for scheduling jobs in large-scale flexible job shops
Introduction
Flexible job shop scheduling problems have great practical relevance because parallel machines are typical for many manufacturing environments. Semiconductor wafer fabrication facilities (wafer fabs), for instance, can be modeled as flexible job shops with a number of additional constraints (cf. [35]). A typical wafer fab contains up to 500 machines that are organized in different work centers where a single work center consists of unrelated parallel machines (cf. [36]). At the same time, on-time delivery-related performance measures are important in scheduling approaches because customer satisfaction in essential in the fierce competition. However, very often only the makespan measure is considered for flexible job shops in the literature (cf. [20], [15], [37] amongst others).
We are interested in efficient integrated process planning and scheduling approaches with the TWT measure, where for each order a set of alternative bill of materials (BOM) and for each subpart of the order a set of alternative routes is given. Job shop scheduling problems with alternative BOMs for each product can be found in the food industry, for instance in coffee manufacturing, where often a set of alternative ingredients is possible to produce a specific product. Once a specific BOM and a specific route for each subpart are chosen, the remaining problem is a flexible job shop scheduling problem. Because we intend to use neighborhood search techniques to select BOMs and routes, we have to solve a large number of flexible job shop scheduling problems. Hence an efficient scheduling approach for flexible job shops with TWT measure is highly desirable.
Solution approaches for flexible job shops are typically based on the disjunctive graph model. When neighborhood search-based techniques are applied then the evaluation of moves is costly in case of due date-oriented performance measures because it requires the calculation of longest paths from the source to the nodes that are associated with the last operation of each job (cf. [25]). Recently, Mati et al. [29] have proposed an efficient approach to evaluate moves for job shop scheduling problems with an arbitrary regular criterion. However, to the best of our knowledge no such approach is available for flexible job shops. In the present paper, we will propose an efficient local search approach that extends the local search heuristic by Mati et al. [29] to the case of flexible job shops. The neighborhood structures proposed by Dauzère-Pérès and Paulli [11] are applied in the present situation. An evaluation scheme for moves based on a dynamic topological ordering of the disjunctive graph is proposed. In addition, the well-known SBH is hybridized with our local search approach and a VNS scheme. While it seems that different sets of benchmark instances are publicly available for flexible job shop scheduling problems with makespan criterion (cf. [5]), to the best of our knowledge this is not the situation when the TWT criterion is applied. Therefore, we randomly generate such problem instances and use them in our computational experiments.
The paper is organized as follows. We describe the researched problem in Section 2. Related work is discussed in Section 3. An iterative local search scheme is proposed in Section 4. This includes a novel technique to evaluate moves that is based on a dynamic topological ordering of the disjunctive graph. In addition, hybrid algorithms are proposed that are based on the SBH and the local search scheme. We also discuss a VNS approach to solve subproblems of the SBH. The results of computational experiments on a large set of randomly generated problem instances are presented in Section 5.
Section snippets
Problem setting
We consider jobs that have to be scheduled on a given set of machines. The machines are organized in machine groups. Each machine group consists of parallel machines that are identical or unrelated. Each job has a due date and a weight that models the importance of customers. The completion time of job is , whereas denotes the ready time of job . We are interested in minimizing the TWT measure that is given bywhere we use the abbreviation . We
Related literature
Scheduling problems for flexible job shops have been studied for the first time by Brucker and Schlie [6]. They consider a job shop that consists of multi-purpose machines, i.e., a set of machines is assigned to each operation. A polynomial algorithm is proposed for the special case of two jobs. A tabu search approach for is described by Hurink et al. [20] where is the makespan of the jobs. Brandimarte [7] presents a hierarchical algorithm for the flexible job shop scheduling
Heuristic approaches
We describe heuristic approaches for solving problem (2). We start by discussing list scheduling approaches. We then propose an iterative local search scheme that is based on neighborhood structures proposed by Dauzère-Pérès and Paulli [11]. Finally, several SBH variants, some of them hybridized with the local search scheme, are described.
Results of computational experiments
In this section, the proposed heuristics are assessed. We start by describing the design of experiments. Then the computational results are presented and discussed.
Conclusions and future research
Scheduling problems for flexible job shops with TWT objective were studied in this paper. The main contribution is an iterative LS heuristic that is able to quickly find high-quality solutions. The SBH is hybridized with this heuristic. We also proposed a VNS scheme for solving the subproblems of the SBH and for the overall scheduling problem. Because all the heuristics are fast, they can be applied to large-size problem instances. Several effects have been observed in an extensive
Acknowledgments
We would like to thank Paolo Brandimarte for providing us with the set of benchmark problem instances for flexible job shops with TWT criterion from [7].
References (49)
- et al.
Job shop scheduling with modified due dates
J Oper Manag
(1983) A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem
Comput Oper Res
(2011)- et al.
Tabu search with two approaches to parallel flow shop evaluation on CUDA plattform
J Parallel Distrib Comput
(2011) - et al.
Variable neighborhood search approaches for scheduling jobs on parallel machines with sequence-dependent setup times, precedence constraints, and ready times
Comput Ind Eng
(2011) - et al.
A genetic local search algorithm for minimizing total weighted tardiness in the job-shop scheduling problem
Comput Oper Res
(2008) - et al.
A hybrid genetic and variable neighborhood descent algorithm for flexible job shop scheduling problems
Comput Oper Res
(2008) - et al.
Variable neighborhood search: principles and applications
Eur J Oper Res
(2001) - et al.
An effective architecture for learning and evolving flexible job-shop schedules
Eur J Oper Res
(2007) - et al.
Extending the shifting bottleneck procedure to real-life applications
Eur J Oper Res
(1996) - et al.
Priority dispatching with operation due dates in a job shop
J Oper Manag
(1982)
A general approach for optimizing regular criteria in the job-shop scheduling problem
Eur J Oper Res
A distributed shifting bottleneck heuristic for complex job shops
Comput Ind Eng
Simulation-based assessment of machine criticality measures for a shifting bottleneck heuristic in complex manufacturing systems
Comput Ind
Genetic algorithm-based subproblem solution procedures for a modified shifting bottleneck heuristic for complex job shops
Eur J Oper Res
A genetic algorithm for the flexible job-shop scheduling problem
Comput Oper Res
Effective and efficient scheduling of dynamic job shops-combining the shifting bottleneck procedure with variable neighborhood search
CIRP Ann-Manuf Technol
Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm
Eur J Oper Res
The shifting bottleneck procedure for job shop scheduling
Manag Sci
Measures of subproblem criticality in decomposition algorithms for shop scheduling
Int J Prod Res
Guided local search with shifting bottleneck for job shop scheduling
Manag Sci
Job-shop Scheduling with multi-purpose machines
Computing
Routing and scheduling in a flexible job shop by tabu search
Ann Oper Res
The shifting bottleneck procedure for job-shops with parallel machines
Int J Ind Syst Eng
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2022, Computers and Operations ResearchCitation Excerpt :Fig. 3 presents some typical applications of JSSP models. From the figure, we can find that JSSP is widely applied in semiconductor (Lee and Chen, 2000; Chien and Chen, 2007; Ham, 2016; Mirshekarian and Šormaz, 2016; Sobeyko and Mönch, 2016; Gao and Pan, 2016; Gerstl et al., 2017), machine manufacturing (Naderi and Azab, 2014; Gao et al., 2016c; Salido et al., 2016; Li et al., 2020b; Zhu and Zhou, 2020b;), automobile manufacturing (Zhang et al., 2013; Azzouz et al., 2017; Liu et al., 2017;), supply chain (Noroozi et al., 2018; Mohammadi et al., 2020; Rostami et al., 2020; Mohammadi and Shirazi, 2020), metallurgical (Yang and Gu, 2016), textile (Guo et al., 2006), etc. These models are strongly related to the characteristics of the corresponding application fields.