Exact optimization and decomposition approaches for shelf space allocation


European Journal of Operational Research, vol.299, pp.432-447, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 299
  • Publication Date: 2022
  • Doi Number: 10.1016/j.ejor.2021.08.047
  • Journal Name: European Journal of Operational Research
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, International Bibliography of Social Sciences, ABI/INFORM, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Computer & Applied Sciences, EconLit, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.432-447
  • Keywords: Retailing, Shelf space allocation, Rectangular display problem, Mixed-integer linear programming, Logic-based Benders decomposition, 2-stage algorithm, DATA MINING APPROACH, BENDERS DECOMPOSITION, PRODUCT SELECTION, ASSORTMENT, MODEL, ALGORITHM, SALES, MANAGEMENT, CUTS
  • Bursa Uludag University Affiliated: Yes


© 2021 Elsevier B.V.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 shelf space allocation problem with additional features (e.g., integer facings, rectangular arrangement restrictions) motivated by literature and our interactions with a local bookstore. We determine optimal number of facings of all products in two aspects (width and height of a rectangular arrangement space for each product), 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 s. 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.