Optimal solution for a two-level inventory system with information exchange leading to a more computationally efficient search

In this paper we consider a two-level inventory system with one warehouse and one retailer with information exchange. The retailer applies fixed order size continuous review policy. The supplier starts with m initial batches of the same order size of the retailer, and places an order to an outside source immediately after the retailer’s inventory position reaches an amount equal to the retailer’s order point plus a fixed value s. Transportation times are constant and the retailer faces independent Poisson demand. In a recent paper it was pointed out that the optimal supplier policy in this inventory system is an open question. To obtain the optimal policy for this system, first we find the optimal solution for the exact value of the expected system costs by using a search method. Second to make the numerical computations required by the search process more efficient, we obtain an upper bound for the value of m; and s. For revealing the computational efficiency of the above suggested upper bounds we resort to solving several numerical examples and compare the general upper bounds for the values of m and s with the modified upper bounds obtained in this paper.