Retail Shelf Space and Location Allocation Problems and Related Optimization Algorithms

Abstract

Shelves are known as the "most expensive resource" for retail stores or platforms. In order to meet the growing demand for consumption, product diversity is fully developed, which intensifies the competition for shelf resources, namely shelf space and location. Although the traditional practice of allocating shelf resources based on product profitability is an effective way to alleviate competition, it may also result in suboptimal solutions and cause retail businesses to lose some profits. Therefore, the decision-making process for shelf resource allocation is a critical issue in retail enterprises. With the emergence of various new retail formats and the explosion of retail product types, competition between products has gradually evolved into a comprehensive competition in terms of multi-combination marketing scenarios, retail display dimensions, and retail display design. This has prompted enterprises to fully understand the interaction between product spatial adjacency and consumption dependence in the process of shelf resource allocation decision-making, pay close attention to the expansion of shelf display dimensions, and carefully examine the impact of product characteristics and display design on retail profits. However, existing literature lacks clear conclusions on how to formulate shelf resource allocation decisions under the environment of comprehensive competition to alleviate the intensification of display resource competition, making it difficult to provide theoretical guidance for the shelf resource allocation decisions of retail stores or platforms.

Regarding the issue of shelf resource allocation, this study first focuses on the relative position of products on the shelf, and constructs a shelf space and location allocation model that considers the interaction between product spatial adjacency and consumption dependence. An improved random key genetic algorithm is developed to solve this model. Then, the influence of the two-dimensional extension of the shelf on shelf space and location decisions is further explored, and a data-driven mixed genetic algorithm is developed to assist in solving the problem. Finally, for adjustable shelves, a joint optimization model is constructed by combining the dependence and sensitivity of products on shelf positions. A mapping evolution-based Jaya algorithm is designed to perform joint optimization of discrete and continuous variables. The main work and contributions of this study include:

1) A shelf space and location allocation model considering product spatial adjacency relationships is proposed, and an improved random key algorithm is designed for solving the model, expanding the research on homogeneous shelf space and location allocation. In the optimization research of homogeneous shelf space and location allocation, existing literature mostly considers the demand stimulation from the product's own spatial elasticity and the cross-space elasticity with other products that have consumption dependency, while neglecting the influence of spatial relative positions among products. This study mathematically characterizes the spatial relative positions of products and defines a spatial adjacency factor. With the objective of maximizing profit, it integrates product spatial adjacency relationships and consumption dependency relationships, establishes a nonlinear integer programming model, and proposes an improved random key genetic algorithm for solving it. The research findings indicate that the shelf space and location allocation decisions considering product spatial adjacency relationships proposed in this study can generate higher profits compared to existing models. Additionally, when there is competition for shelf resources among products, the profit improvement initially increases and then decreases with the number of product categories. Furthermore, by proving the NP-hardness of the problem, this study demonstrates that the improved random key genetic algorithm proposed herein significantly improves efficiency compared to LINGO solver in small-scale instances and consistently outperforms the baseline genetic algorithm in all tested instances. The performance tests of the algorithm indicate superior individual and population evolution capabilities. This research fills the gap in existing studies by addressing the neglect of product spatial relative positions and expands the theory of homogeneous shelf space and location allocation, providing guidance to retail managers in determining the positioning and quantity of products on shelves. These conclusions can also be applied to online store design, brochure layout, online advertising placement, and other related fields.

2) A two-dimensional shelf space and position allocation model was constructed, and a data-driven model-assisted hybrid genetic algorithm was designed to optimize the objective function, advancing the theoretical development of two-dimensional shelf space and location allocation. Existing literature mostly considers the one-dimensional characteristics of shelves, assuming that all shelves are homogeneous and only considering the lateral space capacity restrictions of the shelves while neglecting the potential impacts of vertical space extension. In this study, by exploring the characteristics after the vertical extension of shelves, stacking caused by spatial changes and positional effects caused by location transformations are incorporated. A nonlinear integer programming model is established to optimize retail profit, and a data-driven model-assisted genetic algorithm is developed based on this model. The research findings indicate that the two-dimensional shelf space and location allocation model proposed in this study can effectively enhance product visibility and attractiveness, thereby increasing customer purchasing demands and enhancing profitability. Moreover, when there is competition for shelf resources among products, the lateral and vertical extension of shelves have different trends in promoting retail profit. Additionally, the data-driven model-assisted hybrid genetic algorithm proposed in this study outperforms seven commonly used algorithms in terms of efficiency and effectiveness. This is attributed to the accelerating effect of the data-driven model in the early stage of the algorithm and the filtering effect of taboo search in the later stage. Theoretical analysis demonstrates that the substitution effect of the data-driven model reduces the algorithm complexity from O(f(N²)) to O(f(N)). This research enriches the theoretical research on multi-dimensional shelf space and location allocation problems and provides theoretical guidance for retail managers in utilizing shelf resources in both dimensions. Furthermore, the efficiency and superiority of the proposed algorithm also offer potential for commercial applications.

3) A model for adjustable shelf space and location allocation is proposed, and a mapping-based Jaya algorithm is designed to solve the model, extending the research on fixed shelf space and location allocation. Existing literature rarely focuses on the adjustability of shelf space and mostly assumes that shelves are known and fixed, lacking theoretical support for the impact of adjustable shelf space on retail profit. This study revises the assumption of fixed shelves in the field and investigates the influence of continuous adjustment of shelf height on product display space and location decisions. By considering shelf height settings, product display positions, and inter-product adjacency efficiency, a hybrid integer nonlinear programming model is established, and a mapping-based evolutionary Jaya algorithm is proposed for joint optimization and solution. The research findings indicate that compared to the assumption of fixed shelves, the adjustable shelf strategy can effectively promote diversity in product display combinations, stimulate sales, and increase retail profit. Furthermore, the study reveals that the optimal product selection strategy involves choosing products with a wide range of shelf dependence and a narrow range of shelf sensitivity, rather than pursuing maximum shelf utilization. The mapping-based evolutionary Jaya algorithm proposed in this study jointly encodes continuous and discrete variables in the model. In small-scale instances, it significantly reduces computation time without sacrificing accuracy compared to the LINGO solver. Moreover, in all tested instances, it outperforms the baseline Jaya algorithm and other related algorithms in terms of accuracy and convergence time. This is attributed to the novel mapping evolution rules, which prevent the generation of infeasible solutions and improve evolutionary efficiency. This research fills a research gap in the field by considering the adjustability of shelves and provides a new perspective on shelf resource management for retail managers. Additionally, the findings can be applied to various retail scenarios, such as the design of online page shelves, and provide theoretical support in those contexts.

Date of Award	31 Jul 2023
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Feng Wu (External Supervisor), Zijun ZHANG (Supervisor) & Kwai Sang CHIN (Co-supervisor)