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Batch sizing strategy in the manufacturing system has significant impacts on the production performance. In the previous research studies, researchers proposed complicated techniques such as optimization models, simulation, queuing theory, and complex algorithms to solve for the optimal batch size. 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.

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