A Fuzzy Stochastic Programming Approach for Multi-level Capacitated Lot-Sizing Problem Under Uncertainty

This chapter develops a fuzzy stochastic multi-objective linear programming model for a multi-level, capacitated lot-sizing problem in a mixed assembly shop. The proposed model aims to minimize the total cost consisting of total variable production cost, inventory cost, backorder cost and setup cost while maximizing the resource utilization rate simultaneously. To cope with inherent mixed fuzzy-stochastic uncertainty associated with objective functions coefficients, e.g., setup, holding, and backorder costs, they are treated as fuzzy stochastic parameters with discrete probability density function. To validate the proposed model and the expediency of the proposed solution method, a number of randomly generated test problems of different sizes are solved. The results demonstrate the usefulness of the proposed model and its solution approach.