Single-machine lot scheduling problem for deteriorating items with negative exponential deterioration rate

Determining production-inventory level is one of the most important and challenging problems in a manufacturing system. Economic Batch Quantity (EBQ) is the simplest and the most employed inventory model in this field. Here, a single-source production lot-sizing model for deteriorating products with negative exponential deterioration rate is developed. In this manufacturing system, we assume that all items are manufactured using a single source. In this paper the optimal values for cycle length and lot size are derived in a way that the total cost (consists of machine setup cost, manufacturing cost, carrying and disposal costs of the deteriorating items) is minimized. Consequently, the developed model for the proposed problem is formulated. According to the derived mathematical model, we could not provide a closed form optimal solution, but we show that there is a unique optimal solution for the cycle length. At first, the upper and lower bounds of the optimal solution are determined, then using a Bi-section method (root-finding method) the problem is solved. To demonstrate the applicability of this method, we solve a simple example for a manufacturing system with three products. Finally, results of ten experiment that obtain from this method compare to answers from Newton-Raphson method, then it has been shown that this method has great effectiveness and less calculation efforts for the single-machine problem with deteriorating items.