Robust Optimization of the 0-1 Knapsack Problem - Balancing Risk and Return in Assortment Optimization

Forthcoming at the European Journal of Operational Research

42 Pages Posted: 13 Oct 2015

See all articles by Robert P. Rooderkerk

Robert P. Rooderkerk

Rotterdam School of Management, Erasmus University

Harald J. van Heerde

Massey University - Dept of Communication, Journalism & Marketing

Date Written: October 11, 2015

Abstract

Retailers face the important but challenging task of optimizing their product assortments. The challenge is to find, for every category in every store, the assortment that maximizes (expected) category profit. Adding to the complexity of this 0-1 knapsack problem, retailers should also consider the risk associated with every assortment. While every product in the assortment offers an expected return, there is also uncertainty around its expected demand and profit contribution. Therefore, retailers face the difficult task of designing a portfolio of products that balances risk and return. In this paper, we develop a robust approach to optimize retail assortments that offers this balance. Since the dimensionality of this robust 0-1 knapsack problem in practice often precludes full enumeration, we propose a novel, efficient and real-time heuristic that solves this problem. The heuristic constructs an approximation of the risk-return Efficient Frontier of assortments. We find that the robust solutions offer the retailer a considerable reduction in risk (variance), yet only imply a small reduction in expected return. The constructed approximations contain assortments that are optimal solutions to the robust assortment optimization problem. Moreover, they represent insightful visualizations of the solution space, allowing for interactivity (“what risk premium should the retailer pay?”) in real-time (matter of seconds).

Keywords: Retailing, Assortments, Risk-Return, Efficient Frontier, Robust Optimization, Knapsack Problem

JEL Classification: M31, C11, G11, L81

Suggested Citation

Rooderkerk, Robert P. and van Heerde, Harald J., Robust Optimization of the 0-1 Knapsack Problem - Balancing Risk and Return in Assortment Optimization (October 11, 2015). Forthcoming at the European Journal of Operational Research, Available at SSRN: https://ssrn.com/abstract=2672569

Robert P. Rooderkerk (Contact Author)

Rotterdam School of Management, Erasmus University ( email )

P.O. Box 1738
Room T08-21
3000 DR Rotterdam, 3000 DR
Netherlands

HOME PAGE: http://www.rsm.nl/people/robert-rooderkerk/

Harald J. Van Heerde

Massey University - Dept of Communication, Journalism & Marketing ( email )

Dept of Communication, Journalism & Marketing
Private Box 756
Wellington, 6140
New Zealand

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