Shelf Space Allocation Problem Research Articles

A linearization approach in solving a non-linear shelf space allocation problem with vertical categorisation of sales potential levels

Retail is a profit-driven, highly competitive industry. Customers expect retailers to provide appropriate assortment sets and excellent product visibility. The aim of this study was to develop and examine two models for optimising category-level shelf space management that maximise a retailer’s profit. The authors developed two shelf space allocation problem models. The first model combines three sets of constraints: shelf, product, and product group constraints, while the second model enlarges the first with the multi-shelves constraints. The study showed that this approach gives an optimal solution in a very short time (approximately 3 seconds on average and less than a second in 93 of the 134 instances for the first, and in 84 of the 146 instances in the second problem) for large-scale instances, which in most of the test cases is even less than a second. First, non-linear formulations of both problems were presented. Next, the authors proposed to use and adjust linearization techniques which allow transforming both problems into linear ones, thus obtaining the optimal solutions. Finally, both problems were solved using the CPLEX solver, the computational results were provided.

Heuristics for the shelf space allocation problem

The retailers’ goals to maximize the profit of the products in stores are realized on the planogram shelves. In this paper, we investigated a practical shelf space allocation model with a visible horizontal and vertical grouping of products into categories, which takes into account the number of facings, capping and nesting of a product. The result is four groups of constraints, such as shelf constraints, product constraints, multi-shelves constraints, and category constraints that are used in the model. We proposed 6 heuristics to solve the planogram profit maximization problem. The developed techniques on which heuristics are based may be applied to other category of management shelf space allocation problems because all of them share the same nature of the problem, i.e., the initial step of creating the allocation of products on the shelf and steps in which shelves are combined. Experiments were based on data sets generated according to contemporary real retail conditions. The efficiency of the designed heuristics has been estimated using the CPLEX solver.

Decision support for managing assortments, shelf space, and replenishment in retail

Efficiently managing retail space is critical as the increase in product variety is in conflict with limited shelf space and instore replenishment constraints. This paper develops a general framework for retail space management and presents a decision support model with the related problems within the framework of optimizing assortment, shelf space assignment and replenishment. An integrative approach to these planning problems becomes particularly relevant for fast-moving consumer goods and groceries, where stores are regularly replenished from distribution centers. The planning problem at hand is a multi-product shelf space allocation problem where demand is a composite function of the shelf space allocated and assortment-related demand substitution, and actual replenishment practices from retail are incorporated. The model developed extends existing models of shelf space management by jointly considering space-elastic demand and assortment-based substitution and integrating restocking constraints. For the latter, we consider real-world replenishment processes of retailers that distinguish between period-based and ad-hoc replenishment from the backroom. We develop three solution approaches that are based on efficient pre-processing and a nonlinear binary integer programming formulation of the problem. The computation tests based on retail data show the efficiency of the solution approaches in terms of computation time and solution quality. We reveal the improvement in profit levels that can be achieved from integrating assortments, shelf space planning and replenishment where challenges arise in obtaining feasible solutions with limited shelf space and replenishment constraints. We also use sensitivity analyses to demonstrate the high impact of replenishment constraints on profits and solution structures.

A data-driven model assisted hybrid genetic algorithm for a two-dimensional shelf space allocation problem

A data-driven model assisted hybrid genetic algorithm for a two-dimensional shelf space allocation problem

Strategic rearrangement of retail shelf space allocations: Using data insights to encourage impulse buying

Brick-and-mortar retailers are struggling to compete with online retailers, who increasingly use customer-generated data to provide highly customized experiences for their patrons to drive impulse purchases. Although brick-and-mortar retailers cannot offer such customization, they must identify innovative ways to transform their own point-of-sale transaction data into increased customer impulse buying. We propose a shelf allocation-relocation scheme for rearranging storewide product allocations over time to maximize impulse buying behavior. The proposed method provides a roadmap for optimally allocating shelf space when routine rearrangements of a retail store take place per store policy. To the best of our knowledge, this represents one of the first periodic storewide rearrangement studies to use customer tendencies with the current shelf arrangement as the basis for the subsequent one. We also introduce a novel approach for incorporating past transaction data insights of cross-selling elasticity into the Shelf Space Allocation Problem (SSAP) to encourage long-term new business creation through impulse purchases. The method applies insights from association rule mining to group highly affine and profitable product pairs, optimize the assignment of departments to store aisles, and determine the optimal within-aisle space allocations for the products of each department. Our major finding is that, based on the potential of generating multiple forms of impulse purchasing (visibility-driven purchasing, present-shelf impulse, and past-aisle impulse), our strategic rearrangement technique consistently outperforms visually rearranging shelf space allocations and several existing allocation techniques that utilize multi-level association rule mining, while, in many instances, exceeding the profit potential of a more traditional unchanged (one-time optimal) shelf space arrangement, depending on the nature of a retailer’s target market. Our results also highlight the importance of a retailer selecting the most appropriate shelf space rearrangement strategy that fits the characteristics of its customers, especially their discretionary income level and their familiarity with the store layout.

Raf Atama Yönetimi için Tamsayılı Programlama Destekli Meta-Sezgisel Algoritmalar

Retail shelf space management, which is one of the most complex aspects of retailing, can be defined as determining when, where and in what quantities products will be displayed and dynamically updating the display considering changing market conditions. Although it is an important problem, research papers that study rectangular arrangement of products to optimize profit are limited. In this paper, we determine rectangular facing units of products to maximize profit for shelf space allocation and the display problem. To solve our two-dimensional shelf space allocation problem, we develop two matheuristic algorithms by using integer programming and genetic algorithm (TP-GA) and integer programming and firefly algorithm (TP-ABA) meta-heuristics together. The performances of the mathheuristics were compared with a real-world dataset from a bookstore. TP-GA and TP-ABA methods were able to generate near-optimal solutions with an average of 4.47% and 4.57% GAPs, respectively. We can also solve instances up to 900 products. These matheuristic algorithms, which are successful in the two-dimensional shelf assignment problem, can also be used to solve similar problems such as allocation of books in a bookstore, allocation of product families in a grocery store, or display of advertisements on websites.

An integrated optimization model and metaheuristics for assortment planning, shelf space allocation, and inventory management of perishable products: A real application.

Product category management (PCM) plays a pivotal role in today's large stores. PCM manages to answer questions such as assortment planning (AP) and shelf space allocation (SSA). AP problem seeks to determine a list of products and suppliers, while SSA problem tries to design the layout of the selected products in the available shelf space. These problems aim to maximize the retailer sales under different constraints, such as limited purchasing budget, limited space of classes for displaying the products, and having at least a certain number of suppliers. This paper makes an attempt to develop an integrated mathematical model to optimize integrated AP, SSA, and inventory control problem for the perishable products. The objective of the model is to maximize the sales and retail profit, considering the costs of supplier contracting/selecting and ordering, assortment planning, holding, and procurement cost. GAMS BARON solver is hired to solve the proposed model in small and medium scales. However, because the problem is NP-hard, an evolutionary genetic algorithm (GA), and an efficient local search vibration damping optimization (VDO) algorithm are proposed. A real case study is considered to evaluate the effectiveness and capabilities of the model. Besides, some test problems of different sizes are generated and solved by the proposed metaheuristic solvers to confirm the efficient performance of proposed algorithms in solving large-scale instances.

Joint shelf design and shelf space allocation problem for retailers

Effective design of planograms in a retail store can improve the visual representation of products on shelves. Existing approaches, however, assume that the shelf length and height are fixed, which can result in unused space on the planogram and suboptimal assignment of product facings, both resulting in reduced revenue for the retailer. To address this real-world challenge, we introduce the joint shelf design and shelf space allocation (JSD-SSA) problem, which determines the optimal shelf design along with product placement considering product family constraints. We propose a decomposition-based approach, which first partitions the planogram area considering product families and then allocates products in that family to the partitioned area. Our novel hybrid approach relies on Particle Swarm Optimization for partitioning and Constraint Programming for product assignment. We also propose two metrics; one to measure variation in product shapes within and between product families, and another to measure the space tightness of a planogram. Experiments indicate that shorter shelf lengths can increase retailers’ profit by up to 37% depending on the product-family shape variation. Higher within-family shape variation can result in higher revenue. Additionally, if product and planogram dimensions share a common factor or multiple, then more compact planograms can be designed, in turn reducing unused space and increasing a retailer's profit. Our approach is general enough to handle gondola, peg, bin, and mixed type of shelving typically found in retail stores.

Linearization technique for transformation non-linear shelf space allocation problem into a linear one

Currently, the retail sector is quite competitive. The proper placement of products and giving them shelf space is crucial to the industry's success. On planogram, in order to achieve better visibility, the products may be placed on multiple shelves on multiple orientations. The main purpose of this work is to develop and solve a shelf space allocation problem that takes into account shelf, product, orientation, multi-shelves allocation factors. These reflect the realistic conditions of the retail environment. In this paper, a new approach has been used to transform a non-linear shelf space allocation problem into a linear one. We explore how to adopt a more strategic approach of replacing the product of two binary variables and a product of binary and continuous variables in the constraints imposed by the retailer. This allows achieving the optimal solution of product on shelves allocation with the goal of profit maximization. The experiments were performed with the help of a commercial CPLEX solver.

Linear and nonlinear shelf space allocation problemswith vertical and horizontal bands

Aim/purpose – Shelf space is one of the most important tools for attracting customers’ attention in a retail store. This paper aims to develop a practical shelf space allocation model with visible vertical and horizontal categories. and formulate it in linear and non- -linear forms. Design/methodology/approach – The research is mainly based on operational research. Simulation, mathematical optimization, and linear and nonlinear programming methods are mainly used. Special attention is given to the decision variables and constraints. Changing the dimensioning of the decision variables results in an improvement in the formulation of the problem, which in turn allows for obtaining an optimal solution. Findings – A comparison of the developed shelf space allocation models with visible vertical and horizontal categories in linear and nonlinear forms is presented. The compu- tational experiments were performed with the help of CPLEX solver, which shows that the optimal solution of the linear problem formulation was obtained within a couple of seconds. However, a nonlinear form of this problem found the optimal solution only in 19 out of 45 instances. An increase in the time limits slightly improves the performance of the solutions of the nonlinear form. Research implications/limitations – The main implication of research results for sci- ence is related to the possibility of determining an optimal solution to the initially formu- lated nonlinear shelf space allocation problem. The main implication for practice is to take into consideration the practical constraints based on customers’ requirements. The main limitations are the lack of storage conditions and holding time constraints. Originality/value/contribution – The main contribution is related to developing math- ematical models that consider simultaneous categorization of products vertically, based on one characteristic, and horizontally, based on another characteristic. Contribution is also related to extending the shelf space allocation theory with the shelf space allocation problem model in relation to four sets of constraints: shelf constraints, product con- straints, orientation constraints, and band constraints. Keywords: Retailing, decision making/process, merchandising, shelf space allocation, planogram. JEL Classification: C61, L81.

Heuristics for shelf space allocation problem with vertical and horizontal product categorization

In this research, we proposed a practical shelf space allocation model with the vertical and horizontal categorization of products. Five groups of constraints, such as shelf, product, multi-shelves, orientation and band constraints, are implemented in the model. We proposed two heuristics to solve the retailer's profit maximization problem. The experiments were performed on small instances, and the solution was compared to the optimal solution found by the CPLEX solver. The experiments proved that heuristics could find the optimal solution in most cases (14/20 for heuristics H1 and 16/20 for heuristics H2) without checking the whole solutions space. The lowest solution quality is 97.68% which shows that the heuristics allow finding high-quality near-optimal solutions. Therefore the steps implemented in the proposed heuristics should be used in more complicated shelf space allocation problems for which it is impossible to find a solution by the solvers.

A linearisation approach to solving a non-linear shelf space allocation problem with multi-oriented capping in retail store and distribution centre

Shelf space is one of the essential resources in logistic decisions. Order picking is the most time-consuming and labour-intensive of the distribution processes in distribution centres. Current research investigates the allocation of shelf space on a rack in a distribution centre and a retail store. The retail store, as well as the distribution centre, offers a large number of shelf storage locations. In this research, multi-orientated capping as a product of the rack allocation method is investigated. Capping allows additional product items to be placed on the rack. We show the linearisation technique with the help of which the models with capping could be linearised and, therefore, an optimal solution could be obtained. The computational experiments compare the quality of results obtained by non-linear and linear models. The proposed technique does not increase the complexity of the initial non-linear problem.

Exact optimization and decomposition approaches for shelf space allocation

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.

A genetic algorithm for the retail shelf space allocation problem with virtual segments

A genetic algorithm for the retail shelf space allocation problem with virtual segments

Shelf Space Allocation for Specific Products on Shelves Selected in Advance

Purpose: The aim of the research is to develop the shelf space allocation model for specific products on shelves selected in advance, based on the practical retail requirements. Retailers and manufacturers may impose particular conditions for the appearance of products on the shelf based on its package type, brand, price, form and size. Shelf space allocation must be in line with the store positioning strategy of the retailer. Design/Methodology/Approach: This paper proposed dynamic programming to solve the profit maximization problem on small problem sizes considering extra allocation parameters such as capping and nesting. The distribution of shelf space to products has a direct effect on the competitiveness of the retail store. Findings: The paper presented major profit differences between shelf space allocation without capping and nesting parameters and including them. The computational experiments were performed to test the additional gains received with the usage of capping and nesting parameters. Practical Implications: This research provided qualitative insights for the retailers by comparing the profit gained with and without the capping and nesting allocation possibilities proposed in the model. Originality/Value: In this paper the basic shelf space allocation problem was simplified with selection of the shelf to place the products in advance, next the basic shelf space allocation model was extended with capping and nesting on-shelf allocation methods.

Genetic Algorithm for the Retailers’ Shelf Space Allocation Profit Maximization Problem

This paper discusses the problem of retailers’ profit maximization regarding displaying products on the planogram shelves, which may have different dimensions in each store but allocate the same product sets. We develop a mathematical model and a genetic algorithm for solving the shelf space allocation problem with the criteria of retailers’ profit maximization. The implemented program executes in a reasonable time. The quality of the genetic algorithm has been evaluated using the CPLEX solver. We determine four groups of constraints for the products that should be allocated on a shelf: shelf constraints, shelf type constraints, product constraints, and virtual segment constraints. The validity of the developed genetic algorithm has been checked on 25 retailing test cases. Computational results prove that the proposed approach allows for obtaining efficient results in short running time, and the developed complex shelf space allocation model, which considers multiple attributes of a shelf, segment, and product, as well as product capping and nesting allocation rule, is of high practical relevance. The proposed approach allows retailers to receive higher store profits with regard to the actual merchandising rules.

Dynamic programming approach for solving the retail shelf-space allocation problem

The retail sector is an extremely competitive area. One of the most important facets of retailing is managing retail shelf space. In a market place, retailers should offer customers an option of selecting not only the product but also the packaging size and purchasing quantity. In such instances, product prices often differ.This paper investigates a retail shelf-space allocation problem that maximizes the overall planogram profit. The common shelf-space allocation problem was simplified in this research by selecting the shelf on which the items would be placed in advance. This is explained by practical reasons as sometimes retailers assign the products of the specific package, type, brand, price, form or size, weight to the specific shelf. The problem has been formulated as a 0-1 bounded knapsack problem. Exact methods for solving such kinds of a problem include dynamic programming algorithm. We proposed dynamic programming, which could solve the problem using less time and computational resources.The developed dynamic programming could be applied for solving shelf-space allocation problem subproblems or as being a part of other heuristics and metaheuristics approaches. The results of the research are important for the retailers, category managers, and scientists focused on shelf-space allocation or shelf-space optimization problems.

A New Hybrid Optimization Algorithm for the Optimal Allocation of Goods in Shop Shelves

In retail operation management, shelf space allocation problem is an important problem that affects profitability. Various researches have demonstrated that the shelf space allocation of a product affects that product's sales. The decision that how much of which product, where and when should be placed on shelves is a critical issue in retail operation management. In this paper a new hybrid meta-heuristic algorithm based on forest optimization algorithm (FOA) and simulated annulling (SA) is presented to address the shop shelf allocation problem. To apply FOA for shelf space allocation problem, the basic arithmetic operators of FOA have been modified regarding the characteristics of this problem and FOA is improved by SA. Results obtained from an expensive experimental phase show the better performance of the proposed algorithm in comparison with other presented algorithm from the literature. Also, results show the suitability and benefits of the proposed algorithm in finding high-quality solutions and robustness.

Shelf space allocation problem with horizontal shelf division

The retailers are interested in different profit maximization approaches, which help them to perform daily shelf arrangement tasks, improve customers’ satisfaction and avoid out of stocks on the shelves. Most of the retail literature proposes basic models which don’t reflect complicated merchandising rules. The aim of the paper is to develop a shelf space allocation model which investigates vertical shelf levels, horizontal shelf division into segments, and product item allocation rules such as cappings and nestings. A genetic algorithm has been developed to implement the model. The efficiency was estimated with the help of CPLEX solver. The computational experiments show that the proposed approach allows getting the results of sufficient quality for different problem sizes in a short running time without requiring large computing resources. GA and CPLEX found statistically the same profitable solution within the same computational time. However, GA found a better solution in situations where the commercial solver can’t perform calculations during the increased computational time and stopped after a couple of minutes. This proves the reason for GA implementation for shelf space allocation problems.

Exact Optimization and Decomposition Approaches for 2D Shelf Space Allocation

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.