This study aims at optimally coordinating inventory 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. In order to solve this problem, we explore the optimality structure of the optimal objective value curve and derive several interesting properties for the mathematical model. 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.