A fuzzy stochastic programming approach to solve the capacitated lot size problem under uncertainty

This paper develops a fuzzy stochastic multi-objective linear programming (FSMOLP) model for a multi-level, multi item capacitated lot sizing problem (CLSP) in a multi assembly shop. The proposed model attempts to minimize the total cost consisting of total production variation cost, inventory cost, backlog cost and total setup cost while maximizing the resource utilization simultaneously. To cope with the uncertainty associated with the most of the input data, e.g., the demand and process-related parameters they are treated as fuzzy stochastic parameters with identical stochastic membership function during the planning horizon. To show the usefulness of the proposed solution method, a numerical example is first solved. Then, the usefulness of the proposed model is validated over a set of randomly generated test problems.