Applied Mathematics & Information Sciences

A newsboy model in which a vendor has a limited budget to procure the required items is developed. It is assumed that the manufacturer will either sell the items to the vendor outright or offer the items to the vendor with return policy. In the latter case, the manufacturer buys back from the vendor the unsold items at the end of the selling season. This study considers one item with budget constraints. The vendor has the option of purchasing the goods outright, obtaining the goods with return policy, or a combination of both. By using Kuhn-Tucker Conditions and inductive method, our analysis proposes an optimal inventory policy theorem. The purpose of this study is to investigate how the vendor should replenish the items with return policy under limited budget and changing prices. We show that there exists a set of conditions under which the vendor’s optimal strategy will change based on the amount of available budget for product procurement. If the purchase price with return policy is greater than the price of outright purchase and the vendor has a small amount of available budget, only outright purchase will be optimal. However, if the budget reaches a certain threshold amount, mixed strategies where items are obtained by outright purchase and with return policy are used. We also show that when the purchase price with return policy is not greater than the outright purchase, the vendor will only obtain the items with return policy.