Optimal Air-Cargo Allotment Contract with Multiple Freight Forwarders

  • Kannapha AmaruchkulEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 966)


Consider the air-cargo service chain which comprises a carrier and multiple forwarders. The carrier and each of the forwarders may establish an allotment contract at the start of the season. We formulate the contract design problem as a Stackelberg game, in which the carrier is the leader and offers a contract to a forwarder. The contract parameters may include the discount contract price and the penalty cost for the unused allotment as well as the minimum allotment utilization. The carrier’s contract is accepted, if the forwarder earns at least its reservation profit. Given the carrier’s offer, the forwarder decides how much to book as an allotment, in order to maximize its own expected profit. We show that the two-parameter contract suffices to coordinate the service chain, and the carrier earns the maximum chain’s expected profit less the total reservation profits of all forwarders. If the penalty cost is not imposed, then the minimum allotment utilization is needed to construct an efficient contract. On the other hand, if the penalty cost is strictly positive, then there is no need to impose the minimum allotment requirement.


Air-cargo Capacity management Stochastic model applications 



This research was supported in part by the Thailand Research Fund and Office of the Higher Education Commission, Thailand (Grant RSA58- Kannapha-Amaruchkul). The views expressed in this paper are that of the author and do not necessarily reflect the views of the Thailand Research Fund and Office of the Higher Education Commission, Thailand. Data collection and in-depth interviews were partially conducted by the Ms. Apinya Theppanomrat, one of the full-time master students in the logistics management (LM) program at NIDA, and Ms. Narisara Lueang-orn, one of the part-time master LM students, who has been working at the freight forwarder company (in the numerical example) for several years.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graduate School of Applied Statistics, National Institute of Development Administration (NIDA)BangkokThailand

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