Multi-stage multi-objective production planning using linguistic and numeric data-a fuzzy integer programming model

Abstract

This paper introduces a methodology to solve a multi-stage production planning problem having multiple objectives, which are conflicting, non-commensurable and fuzzy in nature. The production process consists of multiple stages having one or more machines in each stage. Every processing stage produces work-in-process, semi-finished items as an output, which becomes an input to the subsequent stage either fully or partially depending on the cycle times of the machines. Events of machine breakdowns and imbalances in input–output relations in one or more stages may affect both work-in-process (WIP) and final production targets. Our paper provides a methodology based on fuzzy logic to maintain the desired balanced input–output relation at each stage and the targeted production output at the final stage. This is done by procurement of work-in-process inventory (WIP) and installation of new machines at appropriate stages. The objectives or goals expressed in linguistic terms are represented as fuzzy sets. The Induced Ordered Weighted Averaging (IOWA) operator is used to aggregate the objectives as per their priorities and finally to formulate the production process as a Mixed Integer Programming (MIP) problem. The solution to MIP shows the degrees of achievements of the production process objectives. The methodology is illustrated with a real life application of crankshaft productions in an automobile industry.