HAOYA CHEN, affiliation not provided to SSRN
FRANK CHEN, Chinese University of Hong Kong - Department of Systems Engineering & Engineering Management
Email: yhchen@se.cuhk.edu.hk
TSAN-MING CHOI, affiliation not provided to SSRN
Email: tcjason@inet.polyu.edu.hk
SURESH SETHI, University of Texas at Dallas - School of Management
Email: sethi@utdallas.edu

We study a coordination contract for a supplier-retailer channel producing and selling a fashionable product exhibiting a stochastic price-dependent demand. The product's selling season is short, and the supply chain faces great demand uncertainty. We consider a scenario where the supplier reserves production capacity for the retailer in advance, and permits the retailer to place an order not exceeding the reserved capacity after a demand information update during a leadtime. We formulate a two-stage optimization problem in which the supplier decides the amount of capacity reservation in the first stage, and the retailer determines the order quantity and the retail price after observing the demand information in the second stage. We propose a three-parameter risk and profit sharing contract that coordinates the supply chain. The proposed contract is robust which permits any agreed-upon division of the supply chain profit between the channel members.

MING HU, University of Toronto - Operations Management
Email: ming.hu@rotman.utoronto.ca

In many industries, multiple capacity providers compete to sell their own fixed initial inventories of differentiated perishable items over the same finite sales horizon. We formulate this competitive pricing problem as a stochastic control game in continuous time. We distinguish systematically between the case of price and quantity (sales target) competition. In the former, each seller independently chooses his price and in the latter, each of the sellers selects a sales target and the demand rate of each seller depends on the sales volumes targeted by all sellers. The available menu of decision variables is assumed to be pre-determined and each player has full information of other players' remaining capacities. We focus on games with strategic substitutabilities where the revenue function for each player exhibits submodularity property in joint decision variables, specifically, price competition of gross complementary products or quantity competition of gross substitutable products. For games with strategic substitutabilities, we obtain a threshold-type switching policy for each seller that is sustained as a unique Nash equilibrium for the stochastic game. Such a policy is constructed recursively and can be computed in a reasonable effort. Monotonicity properties of equilibrium policies, in time and inventory, may break down for general competition. However, for games under consideration we are still able to retain time monotonicity. We provide numerical examples showing that our algorithm may also work for competition of strategic complementarities such as price competition of substitutable products.

GUILLERMO GALLEGO, Columbia University
Email: gmg2@columbia.edu
MING HU, University of Toronto - Operations Management
Email: ming.hu@rotman.utoronto.ca

Existing revenue management solutions, based on allocating capacity to pre-defined fare classes, are inadequate to compete against low-cost carriers that impose few or no fare restrictions and make their fares widely available through the Internet. To avoid revenue erosion from inadequate solutions, legacy carriers need to develop systems that take into account consumer purchasing behavior which itself depends on the fares available at the time of purchase. This requires a choice-based, multi-player, game theoretic formulation of dynamically pricing perishable capacities over finite-horizons. Here we present such a formulation as a stochastic control problem in continuous time. Since this problem is intractable in general we provide sufficient conditions for the existence and uniqueness of closed-loop Nash equilibria of the corresponding differential game. We show these solutions actually degenerate into open-loop policies and that pricing heuristics based on these open-loop policies are asymptotically Nash equilibria for the original stochastic game. The robust stability of the unique open-loop Nash equilibrium is also studied. Asymptotic results are extended to account for quality attributes, to network models and to sales over different channels.