Mathematical Model with Simulation to Find the Optimal Batch Size for a Supply Chain System

Batch size is an important issue in a supply chain system. It affects stock, cost, and service quality. This paper presents a batch-size decision method to determine the optimal batch size for a supply chain system. The goal of this method is to minimize the total cost of a supply chain at a reasonable service level. The proposed method first applies a mathematical model to finding the possible solutions and then uses a simulation tool to model the real-world situation. Three major research variables are involved in the mathematical model: (1) materials ordering batch size, (2) production batch size, and (3) product distribution batch size. At the simulation phase, three performance indicators -operational cost, system total cost, and service level -are used to evaluate whether the tuned variables fit the best solution. A real case of a garment supply chain is presented to evaluate the performance of the method. The results show the effectiveness of our method.