A capacity game in transportation management

Emerging concerns about competitiveness induce a growing number of firms to outsource their outbound transportation operations to third-party logistics providers. The resulting increase in the number of actors often leads to sub-optimal supply chain actions due to the antagonistic nature of the economic objectives of the partners. With the aim of determining possible deviations from the optimal system performance in such supply chains, this study analyzes the contractual relation between a retailer and a third-party logistics provider (carrier) using game theoretical approaches.
The partners of the studied supply chain play a Stackelberg game in which the retailer is the leader and the carrier is the follower. The retailer faces an uncertain demand and needs to supply his store from his warehouse. he has the option of not meeting all the demand but must satisfy at least a minimum proportion of the fi nall demand. On the other hand, the carrier has to determine the number of trucks needed to satisfy this demand before uncertainty is resolved. Once demand is realized, if the reserved transportation capacity is insufficient, the carrier also has the possibility to requisition trucks at a higher price. We modelise the problem and propose a contract having two parameters : the quantity of transported items and the number of truck used. In our settings, the retailer is the one that submits the contract and the carrier decides if he accepts it or not. We compare this situation with a centralized model where a single decision maker takes all the decisions.