Makespan Minimization for the Two-Stage Hybrid Flow Shop Problem with Dedicated Machines: A Comprehensive Study of Exact and Heuristic Approaches

This paper presents a comprehensive approach for minimizing makespan in the challenging two-stage hybrid flowshop with dedicated machines, a problem known to be strongly NP-hard. This study proposed a constraint programming approach, a novel heuristic based on a priority rule, and Tabu search procedures to tackle this optimization problem. The constraint programming model, implemented using a commercial solver, serves as the exact resolution method, while the heuristic and Tabu search explore approximate solutions simultaneously. The motivation behind this research is the need to address the complexities of scheduling problems in the context of two-stage hybrid flowshop with dedicated machines. This problem presents significant challenges due to its NP-hard nature and the need for efficient optimization techniques. The contribution of this study lies in the development of an integrated approach that combines constraint programming, a novel heuristic, and Tabu search to provide a comprehensive and efficient solution. The proposed constraint programming model offers exact resolution capabilities, while the heuristic and Tabu search provide approximate solutions, offering a balance between accuracy and efficiency. To enhance the search process, the research introduces effective elimination rules, which reduce the search space and simplify the search effort. This approach improves the overall optimization performance and contributes to finding high-quality solutions. The results demonstrate the effectiveness of the proposed approach. The heuristic approach achieves complete success in solving all instances for specific classes, showcasing its practical applicability. Furthermore, the constraint programming model exhibits exceptional efficiency, successfully solving problems with up to n=500 jobs. This efficiency is noteworthy compared to instances solved by other exact solution approaches, indicating the scalability and effectiveness of the proposed method.

[1]  Nengmin Wang,et al.  Tabu search for proactive project scheduling problem with flexible resources , 2023, Computers & Operations Research.

[2]  Aymen Ben Said,et al.  A Constraint Satisfaction Problem (CSP) Approach for the Nurse Scheduling Problem , 2022, 2022 IEEE Symposium Series on Computational Intelligence (SSCI).

[3]  Yunfeng Ai,et al.  Real-Time Scheduling of Autonomous Mining Trucks via Flow Allocation-Accelerated Tabu Search , 2022, IEEE Transactions on Intelligent Vehicles.

[4]  E. Pesch,et al.  An algorithm selection approach for the flexible job shop scheduling problem: Choosing constraint programming solvers through machine learning , 2022, Eur. J. Oper. Res..

[5]  S. Suryono,et al.  A hybrid genetic algorithm and tabu search for minimizing makespan in flow shop scheduling problem , 2021, J. King Saud Univ. Comput. Inf. Sci..

[6]  Yongwen Hu,et al.  A multi-objective scheduling method for distributed and flexible job shop based on hybrid genetic algorithm and tabu search considering operation outsourcing and carbon emission , 2021, Comput. Ind. Eng..

[7]  Pinar Yunusoglu,et al.  Constraint programming approach for multi-resource-constrained unrelated parallel machine scheduling problem with sequence-dependent setup times , 2021, Int. J. Prod. Res..

[8]  Marcelo Seido Nagano,et al.  A comprehensive review of Branch-and-Bound algorithms: Guidelines and directions for further research on the flowshop scheduling problem , 2020, Expert Syst. Appl..

[9]  Hamed Samarghandi,et al.  Minimizing the makespan in a flow shop environment under minimum and maximum time-lag constraints , 2019, Comput. Ind. Eng..

[10]  Hiroki Nishikawa,et al.  A Constraint Programming Approach to Scheduling of Malleable Tasks , 2019, Int. J. Netw. Comput..

[11]  Hamed Samarghandi,et al.  On the exact solution of the no-wait flow shop problem with due date constraints , 2017, Comput. Oper. Res..

[12]  Deming Lei,et al.  A parallel neighborhood search for order acceptance and scheduling in flow shop environment , 2015 .

[13]  R. Ramezanian,et al.  MILP Formulation and Genetic Algorithm for Non-permutation Flow Shop Scheduling Problem with Availability Constraints , 2014 .

[14]  Hatem Hadda,et al.  Exact resolution of the two-stage hybrid flow shop with dedicated machines , 2014, Optim. Lett..

[15]  S. Hajri-Gabouj,et al.  Exact resolution of the two-stage hybrid flow shop with dedicated machines , 2014, Optimization Letters.

[16]  Bertrand M. T. Lin,et al.  Batch scheduling in differentiation flow shops for makespan minimisation , 2013 .

[17]  P. Castro,et al.  Integrated Constraint Programming Scheduling Approach for Automated Wet-Etch Stations in Semiconductor Manufacturing , 2011 .

[18]  Hatem Hadda,et al.  Méthode heuristique pour le problème de flow shop hybride avec machines dédiées , 2009, RAIRO Oper. Res..

[19]  Salah E. Elmaghraby,et al.  SCHEDULING HYBRID FLOWSHOPS IN PRINTED CIRCUIT BOARD ASSEMBLY LINES , 2009 .

[20]  Lifeng Xi,et al.  A tabu search algorithm for the integrated scheduling problem of container handling systems in a maritime terminal , 2007, Eur. J. Oper. Res..

[21]  Zhihong Jin,et al.  Metaheuristic algorithms for the multistage hybrid flowshop scheduling problem , 2006 .

[22]  Mieczysław Wodecki,et al.  A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion , 2004, Comput. Oper. Res..

[23]  Yahya Fathi,et al.  Abstract Discrete Optimization , 2000 .

[24]  Ching-Jong Liao,et al.  A case study in a two-stage hybrid flow shop with setup time and dedicated machines , 2003 .

[25]  Józef Grabowski,et al.  Sequencing of jobs in some production system , 2000, Eur. J. Oper. Res..

[26]  Wendong Xiao,et al.  Hybrid flow shop scheduling using genetic algorithms , 2000, Proceedings of the 3rd World Congress on Intelligent Control and Automation (Cat. No.00EX393).

[27]  Eugeniusz Nowicki,et al.  The flow shop with parallel machines: A tabu search approach , 1998, Eur. J. Oper. Res..

[28]  Mohamed Haouari,et al.  Heuristic algorithms for the two-stage hybrid flowshop problem , 1997, Oper. Res. Lett..

[29]  E. Ignall,et al.  Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems , 1965 .

[30]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[31]  F. Schultmann,et al.  Scheduling Projects with Converging and Diverging Material Flows Using IBM ILOG CP Optimizer - An Experimental Performance Analysis , 2021, OR.

[32]  Hatem Hadda,et al.  The two-stage hybrid flow shop problem with dedicated machines under release dates and delivery times , 2015, Int. J. Adv. Oper. Manag..

[33]  W. Besbes.  A TWO-STAGE FLOW SHOP WITH PARALLEL DEDICATED MACHINES , 2010 .

[34]  Carl Esswein,et al.  Un apport de flexibilité séquentielle pour l'ordonnancement robuste , 2003 .

[35]  Edward Tsang,et al.  Constraint Based Scheduling: Applying Constraint Programming to Scheduling Problems , 2003, J. Sched..

[36]  Philippe Baptiste,et al.  Constraint - based scheduling : applying constraint programming to scheduling problems , 2001 .

[37]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[38]  Eugene L. Lawler,et al.  Optimal Sequencing of a Single Machine Subject to Precedence Constraints , 1973 .

[39]  William L. Maxwell,et al.  Theory of scheduling , 1967 .