Barter exchange as the way to deal with excess inventory: newsvendor problem with multiplicative demand case

Barter exchange has been growing in popularity during the coronavirus pandemic. In this article we consider bartering introduced to the newsvendor model with multiplicative demand. The objective of the model is to specify the order quantity and retail price to maximize the expected profit. We distinguish cases with the prices' co-movement of exchanged products and without it. In the first case, we calculate a precise optimal solution to the problem. In the latter case, we prove the existence of an optimal solution and give the conditions under which it is unique. We examine the sensitivity analysis of the results which is illustrated in numerical examples. The analysis revealed that the greater the commission, the lower the optimal profit is. We make a conclusion that in the model without the prices' co-movement, a greater expected profit can be obtained than in the model with the prices' co-movement.