Comparative Statics Analysis of Multiproduct Newsvendor Networks Under Responsive Pricing

作     者：Bish, Ebru K. Zeng, Xin Liu, Juqi Bish, Douglas R. 

作者机构：Virginia Tech Grado Dept Ind & Syst Engn Blacksburg VA 24061 USA 

出 版 物：《OPERATIONS RESEARCH》 (运筹学)

年 卷 期：2012年第60卷第5期

页      面：1111-1124页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：comparative statics analysis capacity planning responsive pricing resource flexibility substitutable products stochastic programming with recourse convex orders 

摘      要：We propose a novel analytic approach for the comparative statics analysis of multiproduct multiresource newsvendor networks under responsive pricing. Our approach involves exploiting the properties of the primal mathematical programming formulation and of the dual variables and linking those properties to the concept of convex orders and to properties of the underlying demand function. The use of convex orders allows us to establish our main results without restriction to a specific demand distribution. A major strength of our approach is that it is scalable, i.e., it applies to newsvendor networks with any number of nonindependent (i.e., demand or resource sharing) products and resources, without an exponential increase in effort as problem size increases. This is unlike the current approaches commonly used in the operations management literature, which typically involve a parametric analysis of the recourse problem, followed by the use of Jacobians and the implicit function theorem. Providing a rigorous framework for comparative statics analysis, which can be applied to other problems that are not amenable to traditional parametric analysis, is our main contribution. We demonstrate this approach on the optimal capacity decision problem in multiproduct newsvendor networks under responsive pricing, formulated as a two-stage stochastic programming problem with recourse: The firm determines the resource capacities ex ante, in the first stage, when demand intercepts are uncertain, and makes the pricing and production decisions ex post. in the second stage, when demand intercepts (e.g., market conditions) are fully observed. This particular problem and its variants are well studied in the operations management literature. A comparative statics analysis is integral to the study of the capacity investment decision, as it allows answers to important questions such as the following: Does the firm acquire more or less of the different resources available as demand uncer