Scandinavian Working Papers in Economics
Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science
No 2016/6: Channel Coordination in a Multi-period Newsvendor Model with Dynamic, Price-dependent Stochastic Demand
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: In this study, we extend the single-period newsvendor problem with stochastic demand into a multi-period and time-dependent one and find a solution for it. We analyze the multi-period newsvendor problem with stochastic demand in a Stackelberg framework where the wholesaler is the leader and the retailer (newsvendor) is the follower. We use an additive-multiplicative structure for the demand so that both its mean and variance are considered as functions of the current retail price. Moreover, in our model, the demand mean and variance can be either time-dependent or autonomous with respect to time. A price-dependent memory function is also embedded in this representation of demand that carries the effect of demand level at present over to the demand in future. This leads to a strategic game in which the players must balance immediate high profits with reduced future earnings. We propose a complete solution to this stochastic multi-period Stackelberg game, covering cases with finite and infinite horizons. The theory is illustrated by using Cobb-Douglas demand functions as the deterministic part, while a random variable brings in stochasticity into the model. Because our theory is very flexible with respect to the assumptions made about the demand, market memory, and the behavior of the two agents, it is applicable to a wide variety of functional forms and capable to model many different economic contexts.
Keywords: Stochastic games; multi-period newsvendor problem; stochastic demand; price-dependent demand; time-dependent demand; pricing theory; market engineering
34 pages, March 17, 2016
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