Profit division in newsvendor situations with delivery restrictions

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization, which means that they give a joint order and allocate this quantity among themselves to maximize the total profit after the demands are realized. Furthermore, we assume that the retailers pose some restrictions on the number of items that should be delivered to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where the retailers change their delivery restrictions. We investigate how the profit division might be affected by these changes. We define four new monotonicity properties, which we think are interesting in general, and we derive necessary and sufficient conditions for pairs of totally balanced TU-games to satisfy these properties. We also show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general. Finally, we define a class of games with retailers having a normally distributed demand where one of the monotonicity properties holds