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.