Computational method for the profit bounds of inventory model with interval demand and unit cost

Changing economic conditions make the selling price and demand quantity more and more uncertain in the market. The conventional inventory models determine the selling price and order quantity for a retailer’s maximal profit with exactly known parameters. This paper develops a solution method to derive the imprecise profit of the inventory model when the demand quantity and unit cost are imprecise. Since imprecise parameters contained in the inventory model lie in intervals, the profit value calculated from the model should be in a range as well. We formulate a pair of two-level mathematical programming model to derive the upper bound and lower bound of the profit. Based on the duality theorem of geometric programming, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs. Solving the corresponding pair of geometric programs produces the interval of profit. An example illustrates the idea in this paper. That example also shows that the interval profit contains more information for determining inventory policy.