Analytical approach for optimal solution of inventory model with constrained production capacity

Fluid inventory operation is always considered as an essential condition when assessing the managerial performance of an enterprise. Deciding the lot size of an inventory operation is also a very important problem because it directly influences production planning. Thus, many scholars focus their attention on finding the optimal lot size. In this research, we consider Choi and Enns’ article of single-machine processing single-product type in lots under generalized interarrival time assumptions. It was found that the heuristic method proposed by Choi and Enns does not always ensure the location of the optimal solution. For their minimum cost model, we proved the uniqueness of the optimal solution. From their maximum profit model, we found that there is a relation between the optimal demand and the optimal lot size, thus converting it into a one-parameter problem to reduce the burden of their heuristic method. The same examples from Choi and Enns are utilized to illustrate our approach.