Three-dimensional shelf-space allocation and optimal demand planning

Lonnie Turpin () and Aadel Darrat ()
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Lonnie Turpin: McNeese State University
Aadel Darrat: Louisiana State University Shreveport

OPSEARCH, 2025, vol. 62, issue 1, No 19, 448-459

Abstract: Abstract This short paper presents a two-step theoretical framework for three-dimensional shelf-space allocation and optimal demand planning. Step one involves partitioning m shelves into n contiguous cuboid spaces for n products, and then applying a three-dimensional knapsack problem for determining the packing quantity of each product. Step two then uses this quantity optimization to determine the shelf location and facing quantity of the products focusing on maximizing demand. Thus, unlike previous shelf-space allocation research that utilize heuristic approaches in two dimensions, this paper develops a more valid proof optimization that maximizes demand while incorporating the third dimension. The formulated shelf-space allocation and demand planning model offers a valuable tool for retail managers by (1) providing a robust solution given both shelves and their respective products are three-dimensional, (2) adhering to brevity by modeling the associated shelf-space in a framework with only two steps, and (3) addressing the integration of marketing and operations management/research.

Keywords: Shelf-space allocation; Three-dimensional knapsack problem; Demand planning; Multivariate regression (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12597-024-00802-z

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