A two-product, multi-period nonstationary newsvendor problem with budget constraint

This paper concerns a two-product, multi-period nonstationary newsvendor model in which the inventory is not allowed to be carried between periods and each period the newsvendor is subject to a budget constraint and has to decide his order quantities on each product. The Weak Aggregating Algorithm (WAA) developed in computer science is an online learning method of prediction with expert advice; it makes decisions by considering all the experts advice, and each expert’s weight is updated according to his performance in previous periods. Without making statistical assumption on future demand sequence, we propose newsvendor ordering policy by applying WAA to nonstationary ordering policy that can switch between different order quantities in all trading periods. Theoretically, we prove that the proposed ordering policy preserves great competitiveness when compared with the best nonstationary ordering policy with not too many switches. We consider both real-valued and integer-valued ordering policies. Numerical examples with different nonstationary demand types of product 1 illustrate the great competitive performance of the proposed ordering policy. It is found that as the budget increases, the order quantities on the two products and the ordering policy’s cumulative gains increase.