Exact Optimization and Decomposition Approaches for 2D Shelf Space Allocation

33 Pages Posted: 19 May 2021

See all articles by Burcu ÇAĞLAR GENÇOSMAN


Uludag University

Mehmet A. Begen

Ivey Business School, University of Western Ontario

Date Written: May 16, 2021


Shelf space is one of the scarcest resources, and its effective management to maximize profits has become essential to gain a competitive advantage for retailers. We consider the two-dimensional shelf space allocation problem (2DSSAP) with additional features motivated by literature and our interactions with a local bookstore. Two dimensions represent the width and height of rectangular arrangement space of a product. We determine optimal number of facings of all products in both dimensions and allocate them as contiguous rectangles to maximize profit. We first develop a mixed-integer linear mathematical programming model (MIP) for our problem and propose a solution method based on logic-based Benders decomposition (LBBD). Next, we construct an exact 2-stage algorithm (IP1/IP2), inspired by LBBD, which can handle larger and real-world size instances. To compare performances of our methods, we generate 100 test instances inspired by real-world applications and benchmarks from the literature. We observe that IP1/IP2 finds optimal solutions for real-world instances efficiently and can increase the local bookstore's profit up to 16.56\%. IP1/IP2 can provide optimal solutions for instances with 100 products in minutes and optimally solve up to 250 products (assigned to 8 rows x 160 columns) within a time limit of 1800 seconds. This exact 2-stage IP1/IP2 solution approach can be effective in solving similar problems such as display problem of webpage design, allocation of product families in grocery stores, and flyer advertising.

Keywords: Retailing; Two-Dimensional Shelf Space Allocation; Rectangular Display Problem; Mixed-Integer Linear Programming; Logic-Based Benders Decomposition; 2-Stage Algorithm

Suggested Citation

ÇAĞLAR GENÇOSMAN, Burcu and Begen, Mehmet A., Exact Optimization and Decomposition Approaches for 2D Shelf Space Allocation (May 16, 2021). Available at SSRN: https://ssrn.com/abstract=3847516 or http://dx.doi.org/10.2139/ssrn.3847516


Uludag University ( email )

16059 Campus Gorukle Nilüfer

Mehmet A. Begen (Contact Author)

Ivey Business School, University of Western Ontario ( email )

1255 Western Road
London, Ontario N6G 0N1

HOME PAGE: http://www.ivey.uwo.ca/faculty/MBegen

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