A fuzzy goal programming approach to integrated loading and scheduling of a batch processing machine

This paper concerns a real–life problem of loading and scheduling a batch–processing machine. The integrated loading and scheduling problem is stated as a multicriteria optimization problem where different types of objectives are included: (1) short–term objectives of relevance to the shop floor, such as throughput maximization and work–in–process inventory minimization, and (2) long–term objectives such as balancing of end product inventory levels and meeting financial targets imposed by the higher production planning level. Two types of uncertainty are considered: (1) uncertainty inherent in loading and scheduling objective targets (goals) such as the allocated budget and end product demand, and (2) uncertainty in importance relations among the objectives. These two types of uncertainty are modelled using fuzzy sets and fuzzy relations, respectively. A fuzzy goal programming model and the corresponding method are developed which handle both fuzzy and crisp goals and fuzzy importance relations among the goals. Numerical examples are given to illustrate the effectiveness of the developed model.