Shelf Space Allocation Models Research Articles

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.

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.

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.

Simulated Annealing Hyper-Heuristic for a Shelf Space Allocation on Symmetrical Planograms Problem

The allocation of products on shelves is an important issue from the point of view of effective decision making by retailers. In this paper, we investigate a practical shelf space allocation model which takes into account the number of facings, capping, and nesting of a product. We divide the shelf into the segments of variable size in which the products of the specific types could be placed. The interconnections between products are modelled with the help of categorizing the products into specific types as well as grouping some of them into clusters. This results in four groups of constraints—shelf constraints, shelf type constraints, product constraints, position allocation constraints—that are used in the model for aesthetic symmetry of a planogram. We propose a simulated annealing algorithm with improvement and reallocation procedures to solve the planogram profit maximization problem. Experiments are based on artificial data sets that have been generated according to real-world conditions. The efficiency of the designed algorithm has been estimated using the CPLEX solver. The computational tests demonstrate that the proposed algorithm gives valuable results in an acceptable time.

A Heuristic Approach to Shelf Space Allocation Decision Support Including Facings, Capping, and Nesting

Shelf space on which products are exhibited is a scarce resource in the retail environment. Retailers regularly make decisions related to allocating products to their outlets’ limited shelf space. The aim of the paper was to develop a practical shelf space allocation model offering the possibility of horizontal and vertical product grouping, representing an item (product) with facings, capping, and nesting, with the objective of maximizing the retailer’s profit. Because real category-management problems address a lot of retailer’s rules, we expanded the basic shelf space allocation model, using shelf constraints, product constraints, multi-shelves constraints, and category constraints. To solve the problem, we proposed two adjustable methods that allowed us to achieve good results within a short time interval. The validity of algorithms was estimated, using the CPLEX solver and illustrated with example problems. Experiments were performed on data generated on the basis of real retail values. To estimate the performance of the proposed approach, 45 cases were tested. Among them, the proposed approach found solutions in 34 cases, while CPLEX found solutions only in 23 cases. The profit ratio of the proposed approach is, on average, 94.57%, with minimal and maximal values of 86.80% and 99.84%, accordingly.

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.

A Genetic Algorithm for the Shelf-Space Allocation Problem with Vertical Position Effects

The shelf-space on which products are displayed is one of the most important resources in the retail environment. Therefore, decisions about shelf-space allocation and optimization are critical in retail operation management. This paper addresses the problem of a retailer who sells various products by displaying them on the shelf at stores. We present a practical shelf-space allocation model, based on a genetic algorithm, with vertical position effects with the objective of maximizing the retailer’s profit. The validity of the model is illustrated with example problems and compared to the CPLEX solver. The results obtained from the experimental phase show the suitability of the proposed approach.

Shelf-space Allocation Model with Demand Learning

Shelf-space Allocation Model with Demand Learning

Retail shelf space allocation considering inventory replenishment

Shelf space allocation to products greatly impacts the profitability in a retail store. This paper makes two contributions to existing retail shelf space allocation problem. First, a nonlinear shelf space allocation model (NLSSAMINV) is developed incorporating inventory replenishment into an existing nonlinear shelf space allocation model (NLSSAM). Second, existing solution methods [dynamic programming algorithm (DPA) and local search heuristic (LSH)] developed to solve NLSSAM are suitably adapted for solving NLSSAMINV. A pre-processing routine is also developed to reduce the search space in DPA and LSH. It is found from experimental studies that due to pre-processing routine, DPA and LSH took less CPU time to solve NLSSAMINV than that required for solving NLSSAM.

A new model and a hyper-heuristic approach for two-dimensional shelf space allocation

In this paper, we propose a two-dimensional shelf space allocation model. The second dimension stems from the height of the shelf. This results in an integer nonlinear programming model with a complex form of objective function. We propose a multiple neighborhood approach which is a hybridization of a simulated annealing algorithm with a hyper-heuristic learning mechanism. Experiments based on empirical data from both real-world and artificial instances show that the shelf space utilization and the resulting sales can be greatly improved when compared with a gradient method. Sensitivity analysis on the input parameters and the shelf space show the benefits of the proposed algorithm both in sales and in robustness.

Joint Optimization of Product Price, Display Orientation and Shelf-Space Allocation in Retail Category Management

We develop a model that jointly optimizes a retailer's decisions for product prices, display facing areas, display orientations and shelf-space locations in a product category. Unlike the existing shelf-space allocation models that typically consider only the width of display shelves, our model considers both the width and height of each shelf, allowing products to be stacked. Furthermore, as demand is influenced by each product's two-dimensional facing area, we consider multiple product orientations that capture three-dimensional product packaging characteristics. That enables our model to not only treat shelf locations as decision variables, but also retailers’ stacking patterns in terms of product display areas and multiple display orientations. Further, unlike the existing studies which consider a retailer's shelf-space allocation decisions independent of its product pricing decisions, our model allows joint decisions on both and captures cross-product interactions in demand through prices. We show how a branch-and-bound based MINLP algorithm can be used to implement our optimization model in a fast and practical way.

A Model for Fresh Produce Shelf-Space Allocation and Inventory Management with Freshness-Condition-Dependent Demand

Asignificant amount of work has investigated inventory control problems associated with fresh produce. Much of this work has considered deteriorating inventory control with many models having been proposed for various situations. However, no researchers have specifically studied fresh produce, which has its own special characteristics. Most research categorizes fresh produce into more general deteriorating categories with random lifetimes and nondecaying utilities. However, this classification is not reasonable or practical because the freshness of an item usually plays an important role in influencing the demand for the produce. In this paper, a single-period inventory and shelf-space allocation model is proposed for fresh produce. These items usually have a very short lifetime. The demand rate is assumed to be deterministic and dependent on both the displayed inventory (the number of facings of items on the shelves) and the items' freshness condition (which decreases over time). Several problem instances of different sizes are provided and solved by a modified generalized reduced gradient algorithm.

An inventory-theoretic approach to product assortment and shelf-space allocation

The purpose of this research is to generalize and integrate existing inventory-control models, product assortment models, and shelf-space allocation models. We first generalize the inventory-level-dependent demand inventory model to explicity model the demand rate as a function of the displayed inventory level. We then investigate the product assortment and shelf-space allocation problems by extending this model into the multi-item, constrained environment. A greedy heuristic and a genetic algorithm are proposed for the solution to the integrated problem.

SH.A.R.P.: Shelf Allocation for Retailers' Profit

Shelf space is the retailer's scarcest resource. Space management tools are thus badly needed. For that purpose, commercial computer packages and optimal allocation models have been developed. Building on the work of Corstjens and Doyle, we elaborate a general, theoretical shelf space allocation model, which focuses on the demand interdependencies prevailing across and within product-groups. Rules of thumb are compared to the derived optimal allocation. The SH.A.R.P. model is introduced as a simplified, yet realistic, variant and validated against data collected in a Dutch supermarket chain. Subsequently, the feasibility of its implementation has been experimented in various Belgian chains. Case studies demonstrate the profit potential of SH.A.R.P.