Solving for an Optimal Batch Size for a Single Machine Using the Closed-form Equations to Minimize Inventory Cost

Abstract

IntroductionIn the manufacturing system, batch sizing strategy has significant impacts on the production performance. The process with large batches usually has long lead time and large amount of finished goods inventory which incurs high inventory cost. Significant costs of inventory model are holding cost and setup cost [1].Numbers of studies in the past offered the approaches to find the optimal batch size that improves manufacturing efficiency such as minimizing costs, minimizing production lead time, and maximizing service quality.The approach to find the optimal batch size that minimized the total costs of raw materials ordering and finished goods inventory was developed by Parija and Sarker [2]. However, the cycle time interval between shipments or time intervals are fixed. Wang and Chen [3] proposed the new approach by modifying the cost function of Parija and Sarker to find the possible solutions. The simulation model in the supply chain system was applied to estimate the optimal batch size. Bertrand [4] published his development by extending the queuing model as well as the economic order quantity (EOQ) to find the optimal batch size in "made-to-stock" manufacturing system. However, the algorithm is an iterative procedure that the batch size is determined by adjusting the parameters for each iteration. The parameters were idle cost, wait time, production rates, in process inventory cost, and work orders. Wang and Sarker [5] published an article in which Abstract: Batch sizing strategy in the manufacturing system has significant impacts on the manufacturing performance. In the previous research studies, researchers proposed complicated techniques such as optimization models, queuing theory, simulation, and complex algorithms to solve for the optimal batch size to increase the production efficiency. Using those techniques are difficult for plant managers to calculate for the optimal batch size. Therefore, the closed-form optimal batch size equations are proposed to minimize inventory cost of 2 models. The first model is illustrated when the inventory cost is associated with holding cost but without setup cost. The second model is illustrated when inventory cost is associated with both holding cost and setup cost. Besides the optimal batch size calculation, the value of λ, which is the shadow price of the available setup time, is also solved for sensitivity analysis purpose. Application of the closed-form equation is provided with various parameters applied to different products. The results show that the proposed closed-form equations approach performs well and verifies the effectiveness of the approach.