A mixed wholesale-option-contract to fix the demand imbalance between substitutable air cargo routes: A cooperative game approach

In this study, we consider a capacity allocation problem with an airline that sells cargo routes to multiple freight forwarders. The airline faces the problem whereby its fixed capacity from one route cannot cover the sum of freight forwarders’ orders (hot-selling routes), while the freight forwarders’ total orders from the substituting route are much less than its capacity (underutilized routes). To solve this imbalance problem, a sequential cooperative game is performed between the airline and the freight forwarders in which they agree that the airline assigns an amount in the underutilized routes proportional to the forwarder's order from the hot-selling routes. In this game, the players’ payoffs are the expected profit from using a mixed-wholesale-option contract between the airline and the freight forwarders. The model solution shows that the demand in the underutilized routes follows self-replicating distributions. In addition, the mixed wholesale-option model is compared with the pure wholesale and pure option-contract models, and the results reveal that the mixed model provides the highest allocations in the underutilized routes, leading to a better demand balance among the substitutable routes.