Coordination of Transportation and Quantity Discount Decisions, with Coalition Formation

Although it is an essential link in any supply chain, transportation is often neglected in inventory decisions. In reordering decisions, for example, this omission may well result in unexpected losses, as transportation and quantity discounts can be tricky. In this paper, we study the problem of optimal coordination of these discounts from the perspectives of the parties who offer them, rather than of those who take them. Using a noncooperative model of a three-party supply chain, we show that cooperation can benefit each member individually, and the supply chain overall. In fact, cooperation can generate a non-empty core - that is, there may be a surplus that can be allocated so that all parties, and all coalitions of parties, are induced to continue to cooperate. We provide a detailed algorithm, based on the Shapley value, to allocate the surplus fairly, and illustrate it with numerical examples