An optimal batch size for integrated productioninventory policy in a supply chain
This study presents a new integrated productioninventory policy under a finite planning horizon and a linear trend in demand. We assume that the vendor makes a single product and supplies it to a buyer with a non-periodic and just-in-time (JIT) replenishment policy in a supply chain environment. The objective is to minimize the joint total costs incurred by the vendor and the buyer. In this study, first, we develop a mathematical model and prove that it has the optimal solution. Then, we describe an explicit solution procedure for obtaining the optimal solution. Finally, we provide two numerical examples to illustrate both increasing and decreasing demands in our proposed model, and we show that the performance of the integrated consideration is better than the performance of any independent decision from either the buyer or the vendor.
supply chain linear trend in demand productioninventory model