Multi-objective production scheduling with controllable processing times and sequence-dependent setups for deteriorating items

• Published in: International journal of production research Vol. 50; no. 24; pp. 7378 - 7400
• Main Authors: Karimi-Nasab, M., Ghomi, S.M.T. Fatemi
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 15.12.2012; Taylor & Francis; Taylor & Francis LLC
• Subjects: Applied sciences; controllable processing time; Decision theory. Utility theory; deteriorating items; Exact sciences and technology; Heuristic; Integer programming; Inventory control, production control. Distribution; Mathematical problems; Mathematical programming; multi-objective; Operational research and scientific management; Operational research. Management science; Pareto optimum; Pareto-optimal solutions; Production scheduling; Scheduling, sequencing; sequence-dependent setups; Studies; Costs; Worst case method; Multiobjective programming; Total variation; Lot sizing; production scheduling; sequence-dependent setups; Pareto-optimal solutions; Time dependence; Production planning; deteriorating items; Setup time; Controllability; controllable processing time; multi-objective; Execution time; Pareto optimum; Mixed integer programming; Scheduling; Experimental study; Global solution; Integer programming; Production management; Small series production; Perishable item; Genetic algorithm; Optimal solution; Heuristic method; NP hard problem; Non linear effect
• ISSN: 0020-7543; 1366-588X
• DOI: 10.1080/00207543.2011.649800

The production scheduling problem is to find simultaneously the lot sizes and their sequence over a finite set of planning periods. This paper studies a single-stage production scheduling problem subject to controllable process times and sequence-dependent setups for deteriorating items. The paper formulates the problem by minimising two objectives of total costs and total variations in production volumes simultaneously. The problem is modelled and analysed as a mixed integer nonlinear program. Since it is proved that the problem is NP-hard, a problem-specific heuristic is proposed to generate a set of Pareto-optimal solutions. The heuristic is investigated analytically and experimentally. Computational experiences of running the heuristic and non-dominated sorting genetic algorithm-I over a set of randomly generated test problems are reported. The heuristic possesses at least 56.5% (in the worst case) and at most 94.7% (in the best case) of total global Pareto-optimal solutions in ordinary-size instances.