New Optimization Model for Multi-Period Multi-Product Production Planning System with Uncertainty

Abstract

The focus of this study is to develop a multi-period multi-product (MPMP) production planning system with uncertainty, and products demand (seasonal demand) uncertainty. Mainly, the problem aims reach the production levels of each product according to the uncertain demand for various periods, which depend on constraints of capacity, inventory, and resources. An analytical model proposed for this problem that can be categorized into two classes: non-linear and stochastic. The objective is to minimize the summation of variable production costs. As uncertain demand is a dynamic stochastic data process in the planning horizon, it is considered as a tree model. Each stage in the demand tree model is related to a cluster of a period time. Hence, depending on the tree model for the fluctuation demand; Two-Stage Stochastic Programming (TSP) model is presented as an alternative for all demand scenarios. In some of the reviewed articles validation of the analytical model were missing, while other studies were missing either manufacturing set up costs or assumptions of seasonal demand. Therefore, this study proposes TSP model using Sampling Average Approximation method (SAA) that is suitable for a production planning system in any manufacturing environment considering seasonal demand using optimization program (Lingo 16) to solve the mathematical model. Further, investigation of seasonal demand is performed using the multiplicative seasonal method, and the model validation was checked using Mathworks Matlab R2015a (64-Bit) considering manufacturing set up costs. Finally, some recommendations for future research are suggested.