A new algorithm for optimally determining lot-sizing policies for a deteriorating item in an integrated production-inventory system

In this study, we focus on optimally determining lot-sizing policies for a deteriorating item among all the partners in a supply chain system with a single-vendor and multiple-buyers so as to minimize the average total costs. We revise Yang and Wee's 1] model using the Fourier series to precisely estimate the vendor's inventory holding costs. Also, we transform our revised model into a more concise version by applying anapproximation to the exponential terms in the objective function. In order to solve this problem, we analyze the optimality structure of our revised model and derive several interesting properties. By utilizing our theoretical results, we propose a search algorithm that can efficiently solve the optimal solution. Based on our numerical experiments, we show that the proposed algorithm outperforms the existing solution approach in the literature, especially when the number of buyers is larger in the supply chain system.