A joint optimisation model for inventory replenishment,product assortment,shelf space and display area allocation decisions

In this paper, we propose an optimisation model to determine the product assortment, inventory replenishment, display area and shelf space allocation decisions that jointly maximize the retailer’s profit under shelf space and backroom storage constraints. The variety of products to be displayed in the retail store, their display locations within the store, their ordering quantities, and the allocated shelf space in each display area are considered as decision variables to be determined by the proposed integrated model. In the model formulation, we include the inventory investment costs, which are proportional to the average inventory, and storage and display costs as components of the inventory costs and make a clear distinction between showroom and backroom inventories. We also consider the effect of the display area location on the item demand. The developed model is a mixed integer non-linear program that we solved using LINGO software. Numerical examples are used to illustrate the developed model.     

A piecewise linearization for retail shelf space allocation problem and a local search heuristic

Retail shelf space allocation problem is well known in literature. In this paper, we make three contributions to retail shelf space allocation problem considering space elasticity (SSAPSE). First, we reformulate an existing nonlinear model for SSAPSE to an integer programming (IP) model using piecewise linearization. Second, we show that the linear programming relaxation of the proposed IP model produces tight upper bound. Third, we develop a heuristic that consistently produces near optimal solutions for randomly generated instances of problems with size (products, shelves) varying from (25, 5) to (200, 50) within a minute of CPU time.     

Promoting impulse buying by allocating retail shelf space to grouped product categories

This paper addresses a problem where a retailer seeks to optimize store-wide shelf-space allocation in order to maximize the visibility of products to consumers and consequently stimulate impulse buying. We consider a setting where the retailer, because of product affinities or the retailer’s historical practice, has pre-clustered product categories into groups each of which must be assigned to a shelf. On the basis of its location in the store layout, each shelf is partitioned into contiguous shelf segments having different anticipated customer traffic densities. The retailer seeks to assign each group of product categories to a shelf, to determine the relative location of product categories within their assigned shelf, and to specify their allocated total shelf space within given lower/upper bounds. We propose a 0–1 integer programme that takes into account expected customer traffic densities within the store, groups of product categories, their relative profitability, and the desirability to keep certain product groups in the same aisle, with the objective of maximizing the impulse buying profit. The proposed model is grounded in a preprocessing scheme that explores feasible assignments of subsets of product groups to available aisles by iteratively solving an Open image in new window -hard subproblem and is numerically observed to greatly outperform an alternative mixed-integer programming formulation. We demonstrate the usefulness of and the enhanced tractability achieved by the proposed approach using a case study motivated by a grocery store in New England and a variety of simulated problem instances.     

A Dynamic Model for Strategically Allocating Retail Space

The allocation of shelf space is a major determinent of a retailer's sales and operating costs. All the existing models of this problem focus on static optimization. But to the retailer, anticipating and adapting to new tastes and changing product life cycles is the central strategic problem. This paper shows how the static model can be extented to incorporate such market dynamics. The new model is more plausible than earlier static models in encouraging the retailer to allocate more space to new products and divest earlier from declining ones.     

Heuristic and meta-heuristic approaches for multi-period shelf-space optimization: the case of motion picture retailing

The retail industry is in a highly competitive situation currently. The success of the industry depends upon the efficient allocation of products in the shelf space. Several previous authors have developed mathematical models for optimal shelf-space allocation. We extend the prior research in the direction of the multi-period problem and introduce more realistic characteristics, such as product demand perishability, pricing contract and cross-elasticity. The new characteristics help us address the case of the real-life movie allocation problem in multiplexes. We formulate a linear integer programming model to represent the problem. The proposed model shows a potential benefit of at least 11% increase in revenue for a multiplex theatre situation as compared to the existing methods. We also propose two greedy heuristics and a genetic algorithm to solve the same problem. A computational study shows that the genetic algorithm performs better than the existing method.     

Buffer sizing in multi-product multi-reactor batch processes: Impact of allocation and campaign sizing policies

This paper studies the impact of management policies, such as product allocation and campaign sizing, on the required size of the finished goods inventories in a multi-product multi-reactor batch process. Demand, setup and batch processing times for these products are assumed to be stochastic, and the inventory buffer for every product type needs to be such that target customer service levels are met. To perform this analysis, we develop a queueing model that allows us to explicitly estimate service levels as a function of the buffer size, and the allocation/campaign sizing policies. This model can be used to evaluate the service level given an existing buffer configuration, as well as to determine the buffer sizes required across products to meet a pre-specified service level. It also allows us to formulate a number of insights into how product allocation decisions and campaign planning policies affect buffer sizing decisions in symmetric production systems.     

The location and allocation of products and product families on retail shelves

In this paper, we model a shelf-management problem in which individual products are categorized as part of a product family. It is well known that a product’s shelf location has a significant impact on sales for many retail items. We develop a continuous as well as a discrete model with postprocessing to optimize product placement with consideration given to maintaining the grouping of product families. Computational results are reported on test problems as well as real-world beverage placement problems.     

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.     

A hierarchical decomposition approach to retail shelf space management and assortment decisions

Shelf management is a crucial task in retailing. Because of the large number of products found in most retail stores (sometimes more than 60?000), current shelf space management models can only solve sub-problems of the overall store optimization problem, since the size of the complete optimization problem would be prohibitively large. Consequently, an optimal allocation of store shelf space to products has not yet been achieved. We show that a hierarchical decomposition technique, consisting of two interwoven models, is suitable to overcome this limitation and, thus, is capable of finding accurate solutions to very large and complex shelf space management problems. We further conclude that other important variables (such as product-price) can be included into the methodology and their optimal values can be determined using the same solution technique. Our methodology is illustrated on a real-life application where we predict a 22.33% increase in store profits if our model's solution is implemented.     

A piecewise linearization framework for retail shelf space management models

Managing shelf space is critical for retailers to attract customers and optimize profits. This article develops a shelf-space allocation optimization model that explicitly incorporates essential in-store costs and considers space- and cross-elasticities. A piecewise linearization technique is used to approximate the complicated nonlinear space-allocation model. The approximation reformulates the non-convex optimization problem into a linear mixed integer programming (MIP) problem. The MIP solution not only generates near-optimal solutions for large scale optimization problems, but also provides an error bound to evaluate the solution quality. Consequently, the proposed approach can solve single category-shelf space management problems with as many products as are typically encountered in practice and with more complicated cost and profit structures than currently possible by existing methods. Numerical experiments show the competitive accuracy of the proposed method compared with the mixed integer nonlinear programming shelf-space model. Several extensions of the main model are discussed to illustrate the flexibility of the proposed methodology.     

A Dynamic Programming Approach for Product Selection and Supermarket Shelf-Space Allocation

A dynamic programming approach is proposed to select optimally among a given set of products and allocate integer shelf-space units to the selected products in supermarkets. The approach is designed to consider general objective-function specifications that account for space elasticity, costs of sales, and potential demand-related marketing variables. The optimization is subject to constraints due to product supply availability, 'block' product allocation and operational requirements. A primary focus is on the development of a tractable model approach that can effectively be implemented on a microcomputer. A discussion of applications and computational experience on a microcomputer is provided to support the practical applicability of the optimization approach.     

基于“进场费+收益共享”契约的供应链协调策略研究

在超市等自助零售环境下,影响产品需求的往往是产品的感知质量,而产品感知质量不仅取决于产品质量水平,还受货架空间展示量的影响。本文基于价格和感知质量依赖的需求函数,分别建立了一体化供应链集中决策模型以及考虑是否存在进场费的寄售契约下零售商主导的Stackelberg博弈模型,研究了制造商和零售商的产品定价和货架空间展示策略,并给出了进场费+收益共享的供应链协调策略。研究结果表明分散供应链环境下产品的最优零售价格并不总高于集中决策下产品的最优定价,也就是说提升感知质量在一定程度上可以缓解双重边际效应。另外,收取进场费的收益共享模式可以实现供应链的完美协调,这在理论上说明了进场费模式在一定的市场环境下是合理的。     

The role of store brand positioning for appropriating supply chain profit under shelf space allocation

We consider a retailer’s decision of developing a store brand (SB) version of a national brand (NB) and the role that its positioning strategy plays in appropriating the supply chain profit. Since the business of the retailer can be regarded as selling to NB manufacturers the shelf space at its disposal, we formulate a game-theoretical model of a single-retailer, single-manufacturer supply chain, where the retailer can decide whether to launch its own SB product and sells scarce shelf-space to a competing NB in a consumer good category. As a result, the most likely equilibrium outcome is that the available selling amount of each brand is constrained by the shelf-space available for its products and both brands coexist in the category. In this paper, we conceptualize the SB positioning that involves both product quality and product features. Our analysis shows that when the NB cross-price effect is not too large, the retailer should position its SB’s quality closer to the NB, more emphasize its SB’s differences in features facing a weaker NB, and less emphasize its SB’s differences in features facing a stronger NB. Our results stress the importance of SB positioning under the shelf-space allocation, in order to maximize the retailer’s value appropriation across the supply chain.     

Optimizing product assortment under customer-driven demand substitution

The problem of product assortment and inventory planning under customer-driven demand substitution is analyzed and a mathematical model for this problem is provided in this paper. Realistic issues in a retail context such as supplier selection, shelf space constraints, and poor quality procurement are also taken into account. The performance of three modified models, one that neglects customers’ substitution behavior, another that excludes supplier selection decision, and one that ignores shelf space limitations, are analyzed separately with computational experiments. The results of the analysis demonstrate that neglecting customer-driven substitution or excluding supplier selection or ignoring shelf space limitations may lead to significantly inefficient assortments. The effects of demand variability and substitution cost on optimal assortment and supplier selection decisions as well as on the optimal revenue are also investigated. The main contribution of this paper is the development of a practical and flexible model to aid retailers in finding optimal assortments to maximize the expected profit.     

Shelf-space allocation of national and private brands

We propose a game-theoretic model in which one national-brand manufacturer, acting as a leader, maximizes her own profit and one retailer, selling the national brand and her private label and acting as a follower, maximizes her category profit. We characterize the resulting Stackelberg equilibrium in terms of the amount of shelf space allocated to these brands as well as their prices. The results suggest that the allocation of the shelf space depends on the quality of the private label. In our framework, quality is measured by the baseline sales (or brand equity), the degree of brand substitution and the price positioning.     

Last time buy decisions for products sold under warranty

Manufacturers supplying products under warranty need a strategy to deal with failures during the warranty period: repair the product or replace it by a new one, depending on e.g. age and/or usage of the failed product. An (implicit) assumption in virtually all models is that new products to replace the failed ones are immediately available at given replacement costs. Because of the short life cycles of many products, manufacturing may be discontinued before the end of the warranty period. At that point in time, the supplier has to decide how many products to put on the shelf to replace failed products under warranty that will be returned from the field (the last time buy decision). This is a trade-off between product availability for replacement and costs of product obsolescence. In this paper, we consider the joint optimization of repair-replacement decisions and the last time buy quantity for products sold under warranty. We develop approximations to estimate the total relevant costs and service levels for this problem, and show that we can easily find near-optimal last time buy quantities using a numerical search. Comparison to discrete event simulation results shows an excellent performance of our methods.     

Heuristic,meta-heuristic and hyper-heuristic approaches for fresh produce inventory control and shelf space allocation

The allocation of fresh produce to shelf space represents a new decision support research area which is motivated by the desire of many retailers to improve their service due to the increasing demand for fresh food. However, automated decision making for fresh produce allocation is challenging because of the very short lifetime of fresh products. This paper considers a recently proposed practical model for the problem which is motivated by our collaboration with Tesco. Moreover, the paper investigates heuristic and meta-heuristic approaches as alternatives for the generalized reduced gradient algorithm, which becomes inefficient when the problem size becomes larger. A simpler single-item inventory problem is firstly studied and solved by a polynomial time bounded procedure. Several dynamic greedy heuristics are then developed for the multi-item problem based on the procedure for the single-item inventory problem. Experimental results show that these greedy heuristics are much more efficient and provide competitive results when compared to those of a multi-start generalized reduced gradient algorithm. In order to further improve the solution, we investigated simulated annealing, a greedy randomized adaptive search procedure and three types of hyper-heuristics. Their performance is tested and compared on a set of problem instances which are made publicly available for the research community.     

Synchronized routing of seasonal products through a production/distribution network

This paper presents a multi-period vehicle routing problem for a large-scale production and distribution network. The vehicles must be routed in such a way as to minimize travel and inventory costs over a multi-period horizon, while also taking retailer demands and the availability of products at a central production facility into account. The network is composed of one distribution center and hundreds of retailers. Each retailer has its demand schedule representing the total number of units of a given product that should have been received on a given day. Many high value products are distributed. Product availability is determined by the production facility, whose production schedule determines how many units of each product must be available on a given day. To distribute these products, the routes of a heterogeneous fleet must be determined for a multiple period horizon. The objective of our research is to minimize the cost of distributing products to the retailers and the cost of maintaining inventory at the facility. In addition to considering product availability, the routing schedule must respect many constraints, such as capacity restrictions on the routes and the possibility of multiple vehicle trips over the time horizon. In the situation studied, no more than 20 product units could be carried by a single vehicle, which generally limited the number of retailers that could be supplied to one or two per route. This article proposes a mathematical formulation, as well as some heuristics, for solving this single-retailer-route vehicle routing problem. Extensions are then proposed to deal with the multiple-retailer-route situation.     

An efficient algorithm to allocate shelf space

Shelf space is one of the most important resources of a retail firm. This paper formulates a model and proposes an approach which is similar to the algorithm used for solving a knapsack problem. Subject to given constraints, the proposed heuristic allocates shelf space item by item according to a descending order of sales profit for each item per display area or length. Through the use of simulations, the performances of objective value and the computational efficiency of this method are evaluated. Three options are also proposed for improving the heuristics. Compared to an optimal method, the improved heuristic is shown to be a very efficient algorithm which allocates shelf space at near-optimal levels.     

Dynamic Slotting and Pricing Decisions in a Durable Product Supply Chain

We consider a supply chain in which a manufacturer sells an innovative durable product to an independent retailer over its life cycle. We assume that the product demand follows a Bass-type diffusion process and that it is determined by the market influences, retail price of the product, and shelf space allocated to it. We consider the following retailer profit optimization strategies: (i) the myopic strategy of maximizing the current-period profit and (ii) the far-sighted strategy of maximizing the life-cycle profit. We characterize the optimal dynamic shelf-space allocation and retail pricing policies for the retailer and wholesale pricing policies for the manufacturer. We compute also these policies numerically. Surprisingly, we find that the manufacturer, and sometimes even the retailer, is better off with a myopic retailer strategy in some cases.