Scandinavian Working Papers in Business Administration

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2019/10: Solution Algorithms for Optimal Buy-Back Contracts in Multi-period Channel Equilibria with Stochastic Demand and Delayed Information

Reza Azad Gholami (), Leif K. Sandal () and Jan Ubøe ()
Additional contact information
Reza Azad Gholami: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Leif K. Sandal: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Jan Ubøe: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: We analyze the problem of time-dependent channel coordination in the face of uncertain demand. The channel, composed of a manufacturer and a retailer, is to address a time-varying and uncertain price-dependent demand. The decision variables of the manufacturer are wholesale and (possibly zero) buy-back prices, and those of the retailer are order quantity and retail price. Moreover, at each period, the retailer is allowed to postpone her retail price until demand uncertainty is resolved. In order to place emphasis on the price-decadent nature of demand, we embed a class of memory effects in demand structure, such that current demand at each period demand is affected by pricing history as well as current price. The ensuing equilibria problems, thus, become highly nested in time. We then propose our memory-based solution algorithm which coordinates the channel with optimal buy-back contracts at each period. We show that, contrary to the conventional belief, too generous buy-back prices may not only be suboptimal to the manufacturer, but also decrease the expected profit for the retailer and thus for the whole channel.

Keywords: Stochastic optimization; bilevel programming; game theory; channel coordination; buy-back contracts; price postponement; pricing theory; contract theory

JEL-codes: C61; C73; D47; D81

33 pages, September 9, 2019

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