The Assortment Packing Problem: Multiperiod Assortment Planning for Short-Lived Products

Felipe Caro (), Victor Martínez- de-Albéniz () and Paat Rusmevichientong ()
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Felipe Caro: UCLA Anderson School of Management, University of California, Los Angeles, Los Angeles, California 90095
Victor Martínez- de-Albéniz: IESE Business School, University of Navarra, 08034 Barcelona, Spain
Paat Rusmevichientong: USC Marshall School of Business, University of Southern California, Los Angeles, California 90089

Management Science, 2014, vol. 60, issue 11, 2701-2721

Abstract: Motivated by retailers' frequent introduction of new items to refresh product lines and maintain their market shares, we present the assortment packing problem in which a firm must decide, in advance, the release date of each product in a given collection over a selling season. Our formulation models the trade-offs among profit margins, preference weights, and limited life cycles. A key aspect of the problem is that each product is short-lived in the sense that, once introduced, its attractiveness lasts only a few periods and vanishes over time. The objective is to determine when to introduce each product to maximize the total profit over the selling season. Even for two periods, the corresponding optimization problem is shown to be NP-complete. As a result, we study a continuous relaxation of the problem that approximates the problem well, when the number of products is large. When margins are identical and product preferences decay exponentially, its solution can be characterized: it is optimal to introduce products with slower decays earlier. The structural properties of the relaxation also help us to develop several heuristics, for which we establish performance guarantees. We test our heuristics with data on sales and release dates of women’s handbags from an accessories retailer. The numerical experiments show that the heuristics perform very well and can yield significant improvements in profitability. This paper was accepted by Yossi Aviv, operations management .

Keywords: analysis of algorithms; suboptimal algorithms; marketing; product policy; fractional programming; attraction model; assortment optimization (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (11)

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