OPERATIONS RESEARCH Vol. 60, No. 2, March–April 2012, pp. 351–365 ISSN 0030-364X (print)  ISSN 1526-5463 (online) http://dx.doi.org/10.1287/opre.1110.1023 © 2012 INFORMS Cargo Capacity Management with Allotments and Spot Market Demand Yuri Levin, Mikhail Nediak School of Business, Queen’s University, Kingston, Ontario, K7L 3N6, Canada {ylevin@business.queensu.ca, mnediak@business.queensu.ca} Huseyin Topaloglu School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853, topaloglu@orie.cornell.edu We consider a problem faced by an airline that operates a number of parallel flights to transport cargo between a particular origin to destination pair. The airline can sell its cargo capacity either through allotment contracts or on the spot market, where customers exhibit choice behavior between different flights. The goal is to simultaneously select allotment contracts among available bids and find a booking control policy for the spot market to maximize the sum of the profit from the allotments and the total expected profit from the spot market. We formulate the booking control problem on the spot market as a dynamic program and construct approximations to its value functions, which can be used to estimate the total expected profit from the spot market. We show that our value function approximations provide upper bounds on the optimal total expected profit from the spot market, and they allow us to solve the allotment selection problem through a sequence of linear mixed-integer programs with a special structure. Furthermore, the value function approximations are useful for constructing a booking control policy for the spot market with desirable monotonic properties. Computational experiments show that the proposed approach can be scaled to realistic problems and provides well-performing allotment allocation and booking control decisions. Subject classifications : transportation: freight; dynamic programming: applications; programming: integer/applications. Area of review : Transportation. History : Received August 2008; revisions received January 2010, August 2010, March 2011; accepted August 2011. 1. Introduction A significant portion of revenues in the airline indus- try comes from transporting cargo. Indeed, the Interna- tional Air Transport Association (IATA) estimates that 2008 system-wide global revenues from cargo were 64 billion versus 439 billion from passengers; see IATA (2009). Many airlines face the problem of controlling cargo bookings for both dedicated cargo and mixed passenger/cargo air- craft. For a large airline, management of passenger capacity shares many features with management of cargo capacity. Given a limited amount of cargo capacity, an airline, typi- cally called a carrier, decides whether to commit to a cur- rent booking request or to reserve capacity for a possible future booking request with potentially higher revenue. This basic trade-off is accompanied by some other concerns, such as the existing overbooking policies that deal with the fact that not all the booked requests show up at the departure time, and the allotment contracts that reserve portions of cargo capacity to numerous clients. However, while passen- ger capacity management has received significant attention in the revenue management literature, there is nowhere near a comparable effort on cargo revenue management, despite its evident importance as a potential source of improvement in revenues. In this paper, we consider an airline that operates a num- ber of parallel flights to transport cargo between a particular origin–destination pair. The airline faces two problems that interact tightly with each other. The first problem is to determine what contracts, if any, should be signed with potential allotment customers. The allotment contracts typi- cally fix the shipping rate and the amount of reserved capac- ity, and they have a duration of at least a few months so that many departures are scheduled to occur during the contract period. The customers who opt for such contracts are usually intermediaries called forwarders, who provide the end customers with a door-to-door service by handling and transporting cargo packages. The airline periodically collects bids from forwarders for allotment contracts and simultaneously decides which bids are granted, making this problem akin to combinatorial auctions. After setting up the allotment contracts, the airline faces the second prob- lem that determines which booking requests to accept on the spot market. Because the parallel flights are similar from a customer standpoint, spot market demands exhibit con- sumer choice behavior. The two problems interact because allotment and spot market cargo eventually share the same capacity, and the airline is penalized if this capacity is oversold. 351 INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at http://journals.informs.org/.