A Stochastic Approach to Interactive Fuzzy Multi-Objective Linear Programming for Aggregate Production Planning

This study aims to combine probability theory and fuzzy set theory for solving multi-objective aggregate production planning (APP) problems. Herein, a multi-objective APP model is developed and an approach based on the interactive fuzzy linear programming is introduced to solve the APP problems that have fuzzy coefficients, random demands and crisp variables. Applying the model, a decision maker can represent his/her human resources policies regarding the overtime and subcontract production. In the following, initially, the stochastic aspect of the model is worked out. Next, the optimal solution is found by using an interactive method that decides the best compromised solution among the nondominated solution sets at each step. Finally, a numerical example is presented to clarify the features of the proposed approach.