Solution Algorithms for Optimal Buy-Back Contracts in Multi-period Channel Equilibria with Stochastic Demand and Delayed Information

35 Pages Posted: 10 Sep 2019

See all articles by Reza Azad Gholami

Reza Azad Gholami

Norwegian School of Economics (NHH) - Department of Business and Management Science

Leif Kristoffer Sandal

Norwegian School of Economics (NHH) - Department of Business and Management Science

Jan Uboe

Norwegian School of Economics (NHH) - Department of Business and Management Science

Date Written: July 2019

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 Classification: C61, C73, D81, D47

Suggested Citation

Azad Gholami, Reza and Sandal, Leif Kristoffer and Uboe, Jan, Solution Algorithms for Optimal Buy-Back Contracts in Multi-period Channel Equilibria with Stochastic Demand and Delayed Information (July 2019). NHH Dept. of Business and Management Science Discussion Paper No. 2019/10, Available at SSRN: https://ssrn.com/abstract=3450501 or http://dx.doi.org/10.2139/ssrn.3450501

Reza Azad Gholami (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

Leif Kristoffer Sandal

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway
+47 55 95 93 41 (Phone)

Jan Uboe

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

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