The purpose of this study is to determine the optimal special order quantity by
maximizing the total cost saving between special and regular orders during the
length of depletion time for the special order quantity. When the supplier offers a
temporary price discount, the retailer may order a quantity greater than Q* to take
advantage of the discount price. Alternatively, the retailer may ignore this
discount and adopt a regular order policy. Here, we formulate the corresponding
total cost saving function when the special order time occurs at the retailer’s
replenishment time.