Ann Oper Res (2010) 179: 149–167
DOI 10.1007/s10479-008-0455-6
A piecewise linearization for retail shelf space allocation
problem and a local search heuristic
Hasmukh K. Gajjar · Gajendra K. Adil
Published online: 13 November 2008
© Springer Science+Business Media, LLC 2008
Abstract Retail shelf space allocation problem is well known in literature. In this paper, we
make three contributions to retail shelf space allocation problem considering space elasticity
(SSAPSE). First, we reformulate an existing nonlinear model for SSAPSE to an integer
programming (IP) model using piecewise linearization. Second, we show that the linear
programming relaxation of the proposed IP model produces tight upper bound. Third, we
develop a heuristic that consistently produces near optimal solutions for randomly generated
instances of problems with size (products, shelves) varying from (25, 5) to (200, 50) within
aminuteofCPUtime.
Keywords Retail · Shelf space allocation · Piecewise linearization · Upper bound ·
Heuristics
Introduction
Shelf space allocation problem arises when retailer has large number of products to display
on limited shelf space available at disposal (Bai 2005). Efficient shelf space allocation is one
of the key determinants to gain an edge in the highly competitive retail industry (Lim et al.
2004). Yang and Chen (1999) emphasize the importance of store space allocation decisions
and their powerful incentives to the researchers to make such decisions correctly. Decisions
involved in shelf space allocation can be viewed at two levels: (1) how much shelf space to
allocate to a particular product category and (2) how much shelf space to allocate to each
different product within a product category (Reyes and Frazier 2007).
A number of experiments (Kotzan and Evanson 1969; Curhan 1972 and Cox 1970) found
positive relationship between shelf space allocated to a product and its sales indicating the
H.K. Gajjar · G.K. Adil (
)
Shailesh J. Mehta School of Management, Indian Institute of Technology-Bombay, Powai, Mumbai,
India 400076
e-mail: adil@iitb.ac.in
H.K. Gajjar
e-mail: hasmukh.gajjar@iitb.ac.in