Multi-objectives optimization model for flexible job shop scheduling problem (FJSSP) with machines' workload balancing

• Published in: AIP Conference Proceedings
• Main Author: Shuib A.; Gran S.S.A.
• Format: Conference paper
• Language: English
• Published: American Institute of Physics Inc. 2018
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85049809715&doi=10.1063%2f1.5041637&partnerID=40&md5=8567bcf7c752411c6412b24be389d8f7

Flexible Job Shop Scheduling Problem (FJSSP) concerns with production scheduling where each operation of any job is allowed to be processed by any machine from a set of machines, rather than one specified machine. FJSSPs are mainly formulated as Mixed Integer Linear Programming (MILP) models with different objectives. Scheduling FJSSP becomes more complex when multiple objectives are considered. Some of these objectives are to minimize the makespan, to maximize total workload of machines, to minimize weighted tardiness and to minimize jobs flow time. In recent years, the idea of balancing machines' workload in FJSSP and including it as part of the multi-objectives has been given the attention. However, studies concerning it are still lacking. This paper presents the methods and results of our study concerning multi-objectives FJSSP (MOFJSSP). Aims of the study include to formulate an MILP model for FJSSP with machines' workload balancing; and to propose an optimal production job shop scheduling strategies based on the solution obtained. The model formulated has three objective functions, which are to minimize the makespan, to minimize the total machining time and to minimize the Mean Absolute Deviation (MAD) between workload assigned and the average workload of all machines. Since the third objective function is a nonlinear function, transformation is required to ensure all linear functions in the model and thus model stays as MILP. This study incorporates the machines' workload balancing in FJSSP setting to ensure balanced assignment of workloads to available machines. Data from benchmark problem instances for the general FJSSP with total flexibility were used in the computational experiments. The optimal solution was obtained using the priori preemptive goal programming approach. Results based on the first two objectives match the results obtained in other studies using metaheuristic approaches and based on the same instances. © 2018 Author(s).