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Regionalized Assortment Planning for Multiple Chain Stores: Complexity, Approximability, and Solution Methods

  • In retail, assortment planning refers to selecting a subset of products to offer that maximizes profit. Assortments can be planned for a single store or a retailer with multiple chain stores where demand varies between stores. In this paper, we assume that a retailer with a multitude of stores wants to specify her offered assortment. To suit all local preferences, regionalization and store-level assortment optimization are widely used in practice and lead to competitive advantages. When selecting regionalized assortments, a tradeoff between expensive, customized assortments in every store and inexpensive, identical assortments in all stores that neglect demand variation is preferable. We formulate a stylized model for the regionalized assortment planning problem (APP) with capacity constraints and given demand. In our approach, a 'common assortment' that is supplemented by regionalized products is selected. While products in the common assortment are offered in all stores, products in the local assortments are customized and vary from store to store. Concerning the computational complexity, we show that the APP is strongly NP-complete. The core of this hardness result lies in the selection of the common assortment. We formulate the APP as an integer program and provide algorithms and methods for obtaining approximate solutions and solving large-scale instances. Lastly, we perform computational experiments to analyze the benefits of regionalized assortment planning depending on the variation in customer demands between stores.
Author:Michael Hopf, Clemens Thielen, Benedikt Kasper, Hans Corsten
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (162)
Document Type:Working Paper
Language of publication:English
Publication Date:2016/08/08
Year of Publication:2016
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2016/08/09
Tag:Approximation Algorithms; Combinatorial Optimization; Cutting and Packing
Number of page:13
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 30.07.2015