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A Model for Optimizing Retail Space Allocations
Abstract
The allocation of scarce shelf space among competing products is a central problem in retailing. Space allocation affects store profitability through both the demand function, where both main and cross space elasticities have to be considered, and through the cost function (procurement, carrying and out-of-stock costs). A model is developed which uniquely incorporates both effects. A case study is used to estimate the parameters and the problem is solved within a geometrical programming framework. An extensive comparison with alternative procedures suggests this general model leads to significantly different allocation rules and superior profit performance.
... Shelf space allocation problems can be classified according to model structures that consider various factors affecting demand, assortment, and allocating decisions such as space elasticity ( Curhan, 1972;Hansen & Heinsbroek, 1979 ), location elasticity ( Chandon, Hutchinson, Bradlow, & Young, 2009 ), and cross-space elasticity ( Bianchi-Aguiar, 2015;Corstjens & Doyle, 1981 ). Spaceelasticity factor represents the effect of number of facing units (number of products in front of the shelf) on demand. ...
... Cross-elasticity captures how responsive demand for a good is when the position of another good changes. This is positive for substitute goods and negative for complementary goods ( Corstjens & Doyle, 1981;Özcan, 2011 ). In this paper, we assume that demand is only affected by space elasticity and location elasticity, which is common and well justified in the literature ( Table 2 ). ...
... There is substantial literature on shelf space allocation problems started with empirical studies date back to the 1960s ( Cox, 1970;Kotzan & Evanson, 1969 ). Since then, a great deal of research has been carried out, including mathematical models of shelf space planning problems ( Anderson & Amato, 1974;Corstjens & Doyle, 1981;Urban, 1969;Zufryden, 1986 ). However, as mentioned before, we concentrate only on studies that are similar to our problem, such as SA or SAL problems that consider vertical allocation and/or horizontal location with a rectangular assignment. ...
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 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.
... Shelf space allocation problems can be classified according to model structures that consider various factors affecting demand, assortment, and allocating decisions such as space elasticity (Curhan 1972, Hansen & Heinsbroek 1979, location elasticity (Chandon et al. 2009), and cross elasticity (Corstjens & Doyle 1981, Bianchi-Aguiar 2015. Space-elasticity factor represents the effect of number of facing units (number of products in front of the shelf) on demand. ...
... Cross-elasticity captures how responsive demand for a good is when the position of another good changes. This is positive for substitute goods and negative for complementary goods (Corstjens & Doyle 1981,Özcan 2011. Location elasticity represents the effects of products' vertical and horizontal positions on the demand of products. ...
... There is substantial literature on shelf space allocation problems started with empirical studies date back to the 1960s (Kotzan & Evanson 1969, Cox 1970. Since then, a great deal of research has been carried out, including mathematical models of shelf space planning problems (Urban 1969, Anderson & Amato 1974, Corstjens & Doyle 1981, Zufryden 1986). However, as mentioned before, we concentrate only on studies that are similar to our problem, such as SA or SAL problems that consider vertical allocation and/or horizontal location with a rectangular assignment. ...
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.
... Literatürdeki çalışmalar, üst ve orta raf konumları (göz ve el seviyesi) ile koridor başlarında yer alan konumların diğer konumlara göre daha etkin olduğunu göstermektedir (Chandon, Hutchinson, Bradlow ve Young, 2009). Raf alanı tahsisi probleminde önemli bir diğer kavram ise çapraz esneklik katsayısıdır (Bianchi-Aguiar, 2015;Corstjens ve Doyle, 1981). Belirli bir ürünün sergileme alanı değişiminin ikame veya tamamlayıcı ürünün talebi üzerindeki etkisini ölçmeyi esas alan çapraz esneklik katsayısı, ikame mallar için negatif, tamamlayıcı mallar için pozitif değer almaktadır (Corstjens ve Doyle, 1981). ...
... Raf alanı tahsisi probleminde önemli bir diğer kavram ise çapraz esneklik katsayısıdır (Bianchi-Aguiar, 2015;Corstjens ve Doyle, 1981). Belirli bir ürünün sergileme alanı değişiminin ikame veya tamamlayıcı ürünün talebi üzerindeki etkisini ölçmeyi esas alan çapraz esneklik katsayısı, ikame mallar için negatif, tamamlayıcı mallar için pozitif değer almaktadır (Corstjens ve Doyle, 1981). Bu çalışmada ele alınan raf alanı tahsisi probleminde talebin alan esnekliği ve konum esnekliğinden etkilendiği varsayılmıştır. ...
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.
... Several studies mention various formulations for this problem in early studies. Between some of them, Corstjens and Doyle [10], [11] and Zufryden [12] suggested comprehensive models of multiple polynomial powers, which served as valuable benchmarks for many scholars. ...
... Because space is a limited resource, increasing the display space of one product necessitates that the display space of another product on the shelf decreases, or vice versa. Corstjens and Doyle [10] presented a dynamic programming solution based on this aspect, but integer facings for the objects are not mentioned. However, margins, inventory costs, shelf-space elasticity, cross-elasticity are considered. ...
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.
... It could be shown that people change their consumption behavior when their preferred products are not available, or there are other similar products on display (Ehrenberg 1965). In most cases, there is a non-linear relationship between the amount of space allocated to the products and the turnover achieved with the products (Doyle and Corstjens 1981). The space allocation of the products is made more difficult because there is also a so-called cross-elasticity between the products. ...
... In realistic scenarios, usually, more than ten products should be optimized concerning one or more parameters. Especially when cannibalization effects have to be considered (Doyle and Corstjens 1981;Irion et al. 2012), it becomes unrealistic to evaluate all possible combinations and collect sales data. On the other hand, there is an exponential growth in profitability of the optimization result the higher the elasticity of the sales forecast is. ...
Electronic commerce involves data-rich business models that offer many application areas for machine learning. In electronic commerce retailers aim to optimize the product listing on their webpages to increase revenues. This optimization requires sales forecasts. We conceptualize the product listing on webpages as a factorial optimization problem that requires historical data often not available at small and medium retailers. Thus, we apply a design science research approach to implement three methods for systematically generating historic sales data that improve elasticity for product placement involving a genetic algorithm. The problem of non-availability of historic data to train forecast algorithms was exemplified in a case study of a medium-sized German retailer. Simulating these methods for a larger data set revealed that the clustered data generation algorithm performs best in terms of expected profits and computational time. Additionally, we propose an enhanced process for the introduction of data science in electronic commerce.
... In the early work on space modelling, the emphasis was placed on establishing a relation between space and sales. Indeed, the positive impact of space allocation on sales has been documented by several studies (Curhan, 1972;Corstjens and Doyle, 1981;Bultez et al., 1989;Borin et al., 1994;Dreze et al., 1994;Desmet and Renaudin, 1998). In light of research on space modelling, we developed a statistical model to measure the effect of allocated space in a planogram on category sales focusing on the solution of the space management optimisation problem specified in step 2 mentioned above. ...
... In early work, Hansen and Heinsbroek (1979) proposed a generalised Lagrange multiplier technique to solve the problem and implemented it on a large problem instance. Corstjens and Doyle (1981) used geometric programming and Zufryden (1986) developed a dynamic programming framework to tackle the problem on small problem instances. Borin et al. (1994) and Urban (1998) were the first to utilise meta-heuristics. ...
Floor space optimisation (FSO) is a critical revenue management problem commonly encountered by today's retailers. It maximises store revenue by optimally allocating floor space to product categories which are assigned to their most appropriate planograms. We formulate the problem as a connected multi-choice knapsack problem with an additional global constraint and propose a Tabu search-based metaheuristic that exploits the multiple special neighbourhood structures. We also incorporate a mechanism to determine how to combine the multiple neighbourhood moves. A candidate list strategy based on learning from prior search history is also employed to improve the search quality. The results of computational testing with a set of test problems show that our Tabu search heuristic can solve all problems within a reasonable amount of time. Analyses of individual contributions of relevant components of the algorithm were conducted with computational experiments.
... In the early work on space modelling, the emphasis was placed on establishing a relation between space and sales. Indeed, the positive impact of space allocation on sales has been documented by several studies (Curhan, 1972;Corstjens and Doyle, 1981;Bultez et al., 1989;Borin et al., 1994;Dreze et al., 1994;Desmet and Renaudin, 1998). In light of research on space modelling, we developed a statistical model to measure the effect of allocated space in a planogram on category sales focusing on the solution of the space management optimisation problem specified in step 2 mentioned above. ...
... In early work, Hansen and Heinsbroek (1979) proposed a generalised Lagrange multiplier technique to solve the problem and implemented it on a large problem instance. Corstjens and Doyle (1981) used geometric programming and Zufryden (1986) developed a dynamic programming framework to tackle the problem on small problem instances. Borin et al. (1994) and Urban (1998) were the first to utilise meta-heuristics. ...
Floor space optimization is a critical revenue management problem commonly encountered by retailers. It maximizes store revenue by optimally allocating floor space to product categories which are assigned to their most appropriate planograms. We formulate the problem as a connected multi-choice knapsack problem with an additional global constraint and propose a tabu search based meta-heuristic that exploits the multiple special neighborhood structures. We also incorporate a mechanism to determine how to combine the multiple neighborhood moves. A candidate list strategy based on learning from prior search history is also employed to improve the search quality. The results of computational testing with a set of test problems show that our tabu search heuristic can solve all problems within a reasonable amount of time. Analyses of individual contributions of relevant components of the algorithm were conducted with computational experiments.
... A large body of literature points the space elasticity as a measurement of increased responsiveness of sales if more space is given to a product (Curhan, 1972;Chen and Lin, 2007;Chandon et al., 2009). Cross-space elasticity is a measurement of the dependency between neighbouring products; it is assumed to be positive for complementary or similar products and negative for substitutable products (Corstjens and Doyle, 1981;Chen and Lin, 2007). Schaal and Hübner (2017) concluded that cross-space effects have a minor impact on the allocation of products on shelves, therefore they can be disregarded in SSAP empirical and modelling research. ...
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.
... However, these models often oversimplified shelf-space allocation by primarily relying on a single one-dimensional value for shelf space and failed to adopt a comprehensive approach by omitting restocking costs. Over time, some studies extended these models to encompass elasticities among products within a category (Corstjens and Doyle, 1981;Zufryden, 1986) and assortment decisions (Borin et al., 1994;Urban, 1998). Subsequently, some studies explored the incorporation of multiple shelves with varying widths, as proposed by Yang (2001) and Hwang et al. (2005). ...
This research examines the economic viability of night shelf stocking in the retail industry. By analyzing real data on the costs and benefits of both night and day stocking, we propose a novel integer linear optimization model to determine the optimal structure of shelf stocker shifts for individual stores. The model is tested on a standard Chilean supermarket, with a sensitivity analysis performed on key parameters including product demands, shelf capacity, and cost factors. The results reveal that a daytime shelf stocking system is impractical and costly for high-demand outlets. We recommend combining day and night stockings, as night stocking proves to be more efficient, reducing stockouts and salary costs. Additionally, an analysis incorporating semi-night shifts as an alternative to traditional shift patterns demonstrates that combining day, night, and semi-night shift structures is the most cost-effective solution, minimizing labor and stocking expenses without compromising service quality. This study highlights the economic advantages of night shelf stocking and provides valuable insights for retailers seeking to optimize their operations.
... The topic of brand cross-elasticity is an important topic in retailing that has attracted academic attention over a long period of time, particularly in the area of shelf allocation (Hansen et al 2010, Hwang et al 2005, Corstjens and Doyle 1981. While the type of crosselasticity typically focused on has been shelf space cross-elasticity, attention has been given, particularly in textbooks and on the internet, to demand cross-elasticity -the idea that a price change in one brand can lead to a demand change in another. ...
... However, these models often oversimplified shelf-space allocation by primarily relying on a single one-dimensional value for shelf space and failed to adopt a comprehensive approach by omitting restocking costs. Over time, some studies extended these models to encompass elasticities among products within a category (Corstjens and Doyle, 1981;Zufryden, 1986) and assortment decisions (Borin et al., 1994;Urban, 1998). Subsequently, some studies explored the incorporation of multiple shelves with varying widths, as proposed by Yang (2001) and Hwang et al. (2005). ...
This research examines the economic viability of night shelf stocking in the retail industry. By analyzing real data on the costs and benefits of both night and day stocking, we propose a novel integer linear optimization model to determine the optimal structure of shelf stocker shifts for individual stores. The model is tested on a standard Chilean supermarket, with a sensitivity analysis performed on key parameters including product demands, shelf capacity, and cost factors. The results reveal that a daytime shelf stocking system is impractical and costly for high-demand outlets. We recommend combining day and night stockings, as night stocking proves to be more efficient, reducing stockouts and salary costs. Additionally, an analysis incorporating semi-night shifts as an alternative to traditional shift patterns demonstrates that combining day, night, and semi-night shift structures is the most cost-effective solution, minimizing labor and stocking expenses without compromising service quality. This study highlights the economic advantages of night shelf stocking and provides valuable insights for retailers seeking to optimize their operations.
... (I) Space-elastic demand. Space-elastic demand D SP ic of item i in channel c describes the effect of an increased demand triggered by an increasing number of facings k ic of item i in channel c (e.g., Hansen and Heinsbroek [1979], Corstjens and Doyle [1981]). The base for the space-elastic demand constitutes the minimum demand α ic , which represents the retailer's forecast for an item that is independent of the facing and assortment configurations, i.e. when an item is not listed and has zero facings. ...
Nowadays the majority of retail customers use multiple channels. We investigate the assortment, space and inventory problem for an omni-channel retailer operating with interconnected bricks-and-mortar stores and an online shop. For this problem it becomes essential to consider customers’ demand interactions across channels. Current literature mainly focuses on single-channel assortments and ignores cross-channel substitution. We contribute the first integrated omni-channel model that determines assortments for the online and bricks-and-mortar channel with stochastic, space-elastic and out-of-assortment and out-of-stock demand both for in-channel substitution and cross-channel substitution. A specialized heuristic is developed that is based on an iterative solution of a binary problem and demand updates. Our approach achieves near-optimal results for small instances and higher objective values as an alternative heuristic for larger instances. With the full integration of channels, omni-channel retailers can realize a profit increase that mainly depends on the magnitude of substitution rates. We further show numerically that in-channel substitution has a stronger impact on profits than cross-channel substitution when costs are equal across channels.
... Empirical evidence in the baseline model showed that store event influences retail sales (Model 1; b = 0.020, p < 0.05), in line with our findings and previous literature (Drèze et al., 1994;Corstjens and Doyle, 1981). The effect is larger and significant when manufacturers work with a distributor to implement store events, in the case of a specialist retailer (Model 5; b = 0.026, p < 0.01). ...
Purpose
As manufacturers and retailers aim to increase return on marketing investments, value- vs experience-related trade promotions gain attention. These two trade promotions become complicated in the presence of different retail format strategies (generalist vs specialist) and channel structures (direct to retailer vs distributors). Building on trade promotion literature, this study aims to show the main effect of value-related and experience-related trade promotions on retailers’ sales and the moderating role of different retail strategies and channel structures.
Design/methodology/approach
The authors use unique panel data from 8 personal care brands with 1,920 observations to test the hypotheses. The authors investigate how consumer goods manufacturer sells products using different channels structures and retail strategies. Estimated panel regressions provide the empirical evidence and robustness analyzes provide extra confidence to the findings.
Findings
Results reveal higher retail sales when the manufacturer invests in value-related trade promotions rather than experience-related trade promotions. The results also demonstrate how the manufacturer successfully invests in trade promotion by adequately accounting for channel structure and retail strategy. While temporary price reduction’s positive effect on retail sales is enhanced in generalist retailers (e.g. supermarket stores), shelf display’s positive impact is enhanced in specialist retailers (drug stores).
Research limitations/implications
The authors used unique panel data accounting for 15 months, limiting the findings. The results supported the investment allocation decisions in each period. However, future research may evaluate the effectiveness over a longer period and thoroughly address each investment’s seasonal effects.
Practical implications
The authors unveil how retailers achieve higher sales with value-related trade promotions when compared to experience-related trade promotions. The authors also shed light on the way manufacturers design their relationships with generalist and specialist retailers by working in direct and indirect channels. Trade promotions yield better results when the direct channel structure couples with a retailer’s generalist strategy.
Originality/value
The empirical findings help manufacturers achieve success in trade promotions by developing an equitable evaluation to contrast value- and experience-related promotions accounting for generalist and specialist retail strategies and direct and indirect channels.
... The difference exists in the profit margin extracted from both the brands with the given space on the racks (Mowrey et al. 2019). Within a brand category, selling more of a national brand leads to loss for private brand but the vice versa is not certain, since the brands have different "procurement, carrying and out-of-stock costs" (Corstjens and Doyle 1981a). In practice even today most retailers allocate spaces based on subjective experience of previously sold merchandise as well as brand influence, which naturally turns out to be in the range of sub-optimal to non-optimal (Curhan 1973). ...
This work examines the role of a non-price variable, shelf-space in inter-brand competition. The retailer introduces a private brand to control the prices of the national brand, which acts as a monopoly in the absence of any competition from other brands. The private brands compete with national brands for demand, which is a function of the allocated shelf space and the brand price. We propose a game-theoretic model involving a national brand and a private brand who compete horizontally in the supermarkets for shelf space. A comparative study is undertaken through two different cases. In the first case, the retailer promotes the private brand manufactured by itself followed by the second case wherein retailer sells the private brand produced by another manufacturer. The retailer allocates shelf space to both the national as well as private brand simultaneously to capture the competition. The manufacturer of the national brand acts as the stackelberg given its power of setting wholesale prices. The equilibrium of the profit maximization game is expressed in terms of prices, shelf-spaces and profit margin of the players. This work is an attempt to gain insights on the conditions of allocation which are profitable for the manufacturer taking into account the consumer preferences between competing brands. The study also indicates that manufacturer’s profits reduces when they compete for space and make the retailer dominant, when the latter is only involved in shelf space allocation without any in-house production. We contribute as building blocks to understand how shelf-space limitation intensifies the manufacturer-retailer competition and also obtain managerial insight on disproportionate distribution of profits.
... As the product goal is to generate incremental revenue the natural metric to optimize is this incremental revenue. This metric or similar is selected and optimized in the works in the field of shelf placement optimization, for example (A Beginner's guide to Shelf Space Optimization using Linear Programming 2016; Corstjens and Doyle 1981;Lim et al. 2004). In our case though, as we were still defining a product proposal, without market adoption yet (so without any feedback signal on revenue) we had to assume some proxy measure for the future incremental revenues. ...
Airlines are increasingly trying to differentiate their offers, so one airline’s bare bones low fare may, for some travelers, be equivalent to another airline’s high fare, if the low fare bundles some ancillaries a traveler wants. Because of differentiation of airline offers the air traveler must simultaneously compare air fares and the ancillaries included. Price comparison is also difficult as the same cabin offers vary by the ancillaries included across the competing airlines. We are proposing a shelf product assortment method for categorizing airline offers into utility levels, thus facilitating the choice task of air travelers. We describe possible known approaches, describe Sabre’s proposal, provide information on the optimization methods used, and propose future work in the field.
... Year EA BB DP H GA SA TS VNS SW ABC PSO GRA Anderson and Amato [15] 1974 • Hansen and Heinsbroek [16] 1979 • Corstjens and Doyle [17] 1981 • Zufryden [18] 1986 • Bultez and Naert [19] 1989 • Borin, Farris, and Freeland [20] 1994 • Borin and Farris [21] 1995 • • Urban [22] 1998 • • • Li and Tsai [23] 2001 • Moholkar and Sanjeev [24] 2001 • Rajaram and Tang [25] 2001 • Yang [5] 2001 • Rodrigues, Lim, and Qian [26] 2002 • • Lim, Rodrigues, and Zhang [1] 2004 • • • Bai and Kendall [27] 2005 • • Hwang, Choi, and Lee [28] 2005 • • ...
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.
... For the production system with nonperishable goods or infinitely patient customers, we can let θ p 0 or θ d 0, which is a special case of our model here. We allow the demand rate to depend on the inventory level; such dependence may be attributed to the "selective effect" and "advertising effect" known in the marketing literature; see Khmelnitsky and Gerchak (2002) and Corstjens and Doyle (1981). ...
Motivated by production systems with nonstationary stochastic demand, we study a double-ended queueing model having back orders and customer abandonment. One side of our model stores back orders, and the other side represents inventory. We assume first-come-first-served instantaneous fulfillment discipline. Our goal is to determine the optimal (nonstationary) production rate over a finite time horizon to minimize the costs incurred by the system. In addition to the inventory-related (holding and perishment) and demand-related (waiting and abandonment) costs, we consider a cost that penalizes rapid fluctuations of production rates. We develop a deterministic fluid-control problem (FCP) that serves as a performance lower bound for the original queueing-control problem (QCP). We further consider a high-volume system for which an upper bound of the gap between the optimal values of the QCP and FCP is characterized and construct an asymptotically optimal production rate for the QCP, under which the FCP lower bound is achieved asymptotically. Demonstrated by numerical examples, the proposed asymptotically optimal production rate successfully captures the time variability of the nonstationary demand.
... A model was presented for Shelf Space Allocation in 1981 using geometric programming and heuristics constraints for optimization (Corstjens and Doyle, 1981). Their idea was based on the demands of the product along with their allowable capacities. ...
Shelf space allocation has always remained a crucial issue for any retail store, as space is a limited resource. This work proposes a model that uses a hyper-heuristic approach to allocate products on shelves to maximize the retailer's profit. This work has concentrated on providing a solution specifically for a consumer packaged goods store. There exist multiple conflicting objectives and constraints which influence the profit. The consequence is a non-linear programming model having a complex objective function, which is solved by using multiple neighborhood approaches using simulated annealing as simulated annealing is a useful tool for solving complex combinatorial optimization problems. Detailed analysis of the proposed technique of using annealing and reheating has revealed the effectiveness in profit maximization in the shelf space allocation problem. Various simulated annealing parameters have been studied in this paper, which provides optimum values for maximizing profit.
Purpose
The purpose is to have appropriate planning for reducing costs during the procurement process and increasing profits during the sales period in a supply cycle at a retail store. To make the proposed model practical, efforts have been made to implement the existing constraints in a business environment and legal factors.
Design/methodology/approach
To achieve the objectives of this research, a mixed-methods approach was employed. Initially, sales data was collected, and industry experts were consulted to identify key products. A mathematical model and a particle swarm optimization algorithm were utilized for simulation and optimization. Furthermore, time series forecasting techniques were employed to estimate demand accurately.
Findings
The findings of this research emphasize the importance of considering all factors affecting costs simultaneously when utilizing tools to reduce costs during the planning period. It was observed that certain tools, which individually have a favorable effect on costs, may collectively result in an increase in costs over the examined period. This highlights the need for a comprehensive and integrated approach to planning.
Research limitations/implications
The business environment and legal factors in each country are among the factors that affect the performance of retailers, which has received less attention in previous research. This research aimed to address this gap by considering various factors. However, it is important to note that the proposed model has been investigated in research in hypermarkets and is applicable, but it cannot be generalized to other retailers.
Originality/value
Applicability and consideration of new limitations in simulation along with consideration of the complete process from buying to selling goods.
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.
This article presents a pricing, warranty, and shelf-space-size decision problem associated with a two-echelon supply chain composed of one retailer and two competing manufacturers. The products (belonging to two distinct manufacturers) come through a non-symmetric market. Demand for them is price sensitive and depends on the warranty period. As the sole leader, the retailer specifies the size of the available shelf space and the retail price for each product. At the same time, the manufacturers determine wholesale prices and warranty periods for their respective products. Mathematical models are developed to derive optimal solutions. Moreover, a sensitivity analysis for the models is performed to analyze how differences in market potential, production cost, warranty service cost, warranty-competition factors, and cross-price sensitivity parameters of products influence optimal solutions. Experimental results show that manufacturers can offset increased warranty service costs by decreasing the warranty competition factor. They can also adopt mixed strategies to reach a pre-specified target profit by considering their capability to either drop the warranty service cost or increase the warranty-competition factor. In addition, the retailer can modify the impact of reduced market potential or increased production cost (the warranty service cost) by using shelf-space cost management strategies.
Research on grocery waste in food retailing has recently attracted particular interest. Investigations in this area are relevant to address the problems of wasted resources and ethical concerns, as well as economic aspects from the retailer’s perspective. Reasons for food waste in retail are already well-studied empirically, and based on this, proposals for reduction are discussed. However, comprehensive approaches for preventing food waste in store operations using analytics and modeling methods are scarce. No work has yet systematized related research in this domain. As a result, there is neither any up-to-date literature review nor any agenda for future research. We contribute with the first structured literature review of analytics and modeling methods dealing with food waste prevention in retail store operations. This work identifies cross-cutting store-related planning areas to mitigate food waste, namely (1) assortment and shelf space planning, (2) replenishment policies, and (3) dynamic pricing policies. We introduce a common classification scheme of literature with regard to the depth of food waste integration and the characteristics of these planning problems. This builds our foundation to review analytics and modeling approaches. Current literature considers food waste mainly as a side effect in costing and often ignores product age dependent demand by customers. Furthermore, approaches are not integrated across planning areas. Future lines of research point to the most promising open questions in this field.
Shelf space analytics have received great attention among researchers for years. The allocation of different products with a certain number of facings (a facing corresponds to one visible unit of the product on the shelf) to limited shelf space is a prime example of applying quantitative methods for a practical use case. Some approaches are of a more generic nature in order to create a basic understanding of the possibilities of decision support models while others aim to investigate specific impacts of different factors (e.g., cross-space elasticity, cost functions). A specific set of approaches provides applicable decision support tools that can be used to determine (almost) final planograms for retail stores. Retailers are subjected to continuous development alongside the many improvements provided by the latest research. The requirements for shelf space planning in practice are increasing with new technologies (whether computational power or data availability) and impacts from different fields of research (marketing, food chemistry, logistics, etc.). When shelf space models are created these specifications should be considered carefully in order to provide beneficial solutions. The intention of researchers and retailers conducting shelf space planning might differ from case to case. We have been able to gain much experience during a collaborative research project with one of Europe’s largest food retailers over the course of three years, drawing intensive comparisons between scientific work and practical requirements. This chapter will share the key findings from related processes based on our experience during this collaboration where several optimization models were developed and actually applied to stores. The goal is to provide insights from practice and point to new issues so that both retailers and researchers gain valuable information.
This chapter addresses the design of retail facilities. In contrast to traditional manufacturing warehouse and facility design, which typically attempts to minimize material handling costs, retail facilities are characterized by revenue-based performance measures that depend heavily on highly variable customer shopping profiles and demand behavior. In this chapter, we propose a modular design structure for a common layout type in retail facilities, namely, grid layout. Using this design, we analyze the effect of customer purchasing and travel behavior on impulse purchase revenue and customer travel distance. We study four different customer route selection strategies. Our results demonstrate that for grid-based retail facilities, impulse purchase revenue is highly dependent on route selection strategy. We conclude that grid-based retail facilities that are designed to minimize the number of alternate routes through the store can outperform those that allow customers to traverse multiple paths.
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.
How Product Locations Drive Traffic Throughout a Retail Store
In “Store-Wide Shelf-Space Allocation with Ripple Effects Driving Traffic,” Flamand, Ghoniem, and Maddah develop a framework for deciding where to place products in a store, in addition to apportioning the shelf space among products, in a way that maximizes impulse profit, a phenomenon that may account for 50% of transactions. By analyzing a large data set of customer receipts from a grocery store in Beirut, the authors develop a regression model that estimates traffic at a shelf based on its location and the “attraction” from products allocated nearby. The traffic model is embedded within a mixed-integer nonlinear program, which they solve via specialized linear approximations. For the store in Beirut, a 65% improvement in impulse profit is anticipated, and the location of products is found to be significantly more important in driving store-wide traffic than the relative shelf-space allocation.
Purpose
The purpose of this paper is to determine the inventory replenishment policies when demand rate is a function of the inventory space allocated to the products on retail shelves. Existing results on inventory policies with inventory-level-dependent demand (ILDD) assume deterministic functional forms of the demand rate. In this paper, the authors model the inventory decisions when demand is a function of shelf-space allocation and random uncertainty. The authors provide managerial insights of this paper's results.
Design/methodology/approach
The demand rate is assumed to be a function of shelf-space allocation based on two settings in the literature. First, the authors model the demand rate as a function of initial shelf-space allocation. In the next setting, the authors assume that the demand rate is a function of instantaneous inventory level on shelves. In both the settings, the authors also model random demand uncertainty in addition to the shelf-space dependency of demand rate. The objective is to maximize the expected profit and determine the inventory parameters.
Findings
In addition to the demand uncertainty, the authors consider linear, power and exponential functional forms of demand rate. Inventory policy that maximizes expected profit is determined when demand rate is a function of initial allocation and displayed inventory level. The results are implementable for practitioners for optimizing the shelf-space allocation and related inventory policy.
Originality/value
Most of the extant results on inventory policy with shelf-space-dependent demand do not model the demand uncertainty. The authors model a variety of functional forms of demand rate with ILDD in addition to the demand uncertainty. The results are a building block for more applications in inventory management for real-life applications.
Category management is known as a strategic approach that can enhance the collaboration between retailers and manufacturers in a supply chain. In this study, we examine two category management scenarios, Retailer Category Management (RCM) and Category Captainship (CC), for a two-stage supply chain in which two manufacturers sell their substitutable products through a common retailer. Based on non-symmetric demand functions, we develop two mathematical models in which the retailer adopts RCM and CC. By comparing these two models’ equilibrium outcomes, the following insights are found. First, the optimal policy for shelf space allocation and pricing decisions are obtained. Second, we indicate three situations under which competitive exclusion does not exist. This supports decisions on whether to switch from RCM to CC. Third, our analysis shows the evidence to support the retailer on choosing the category captain regarding either the retailer's join profit gain or the competitive exclusion. Last, we highlight the various conditions under which the retailer has either low or high flexibility in choosing products for the category, when the competitive exclusion is concerned. Our model is the first to illustrate the interaction impact of non-symmetric market potential, non-symmetric own-price elasticity and cross-price sensitivity on category management.
Traffic is the lifeblood of every e‐commerce platform. The question of how to channel traffic to merchants operating on a platform lies at the heart of platform management. We consider a platform on which two independent merchants sell their products. Merchants compete on inventory in the sense that some of the unmet demand at one merchant will spill over to the other. The platform channels traffic based on products' conversion rates to maximize the total sale on the platform. We show that traffic channeling plays three roles. First, it allows more efficient allocation of traffic; that is, the merchant with a high conversion rate is given a higher priority in receiving traffic. Second, it allows the platform to control demand spillover between the merchants to maximize total sales. The platform either facilitates or prevents demand spillover, depending on product substitutability. Third, traffic channeling intensifies competition between the merchants and hence increases the total inventory. More efficient allocation of traffic and the increase in inventory increase sales inequality between the merchants. In contrast, demand spillover decreases sales inequality. While the platform always benefits from traffic channeling, the merchants do not benefit when their products are moderately substitutable. Interestingly, when the two products are owned and sold by the same merchant, the opposite happens–traffic channeling always benefits the merchant but may hurt the platform. Our study provides a basis for informed discussions on how platforms should channel traffic in response to conversion rates, and how traffic channeling affects the welfare of merchants and platforms.
The advent of omni-channel (OC) retailing makes assortments seamlessly available across channels and affects customer behavior. Whereas the demand effects within channels are well known, the effects across channels are less clear. A vast variety of assortment-related demand effects in bricks-and-mortar stores, webshops, and across channels has a potential impact on retailers’ profitability. The multitude makes it costly to measure each effect empirically, which is further aggravated by interdependencies between products, channels and effects, and the resulting numerical complexity. Despite most retailers adopting OC assortments, the relevance and interplay of these demand effects is neither fully clear from an empirical nor an optimization perspective. It becomes necessary to better understand how assortment-related decisions impact customer behavior and optimal assortments.
We approach this research gap by identifying and integrating demand effects in a novel model for OC assortment optimization. Our results show that in-channel effects matter more than cross-channel transitions. This also holds true when demand effects exceed the empirically measured values in a single-channel context. Generalizing, the impact depends on demand rates, channel package sizes, and channel size. These findings are relevant for the OR community, empirical researchers, and retailers and help streamlining further research in two ways. First, further advances of OC assortment models with cross-channel effects should be based on our findings. Second, given that the empirical tests for these effects are very voluminous and costly, our findings serve as “guardrails” to define the scope of such empirical investigations.
Objective: Increasing sales profits and inventory control leads to productivity in the retailing industry. To minimize inventory costs and reach an optimal order quantity, it is essential to develop a mathematical model for inventory control that is suited to industries. It is a common practice in the retailing industry to consider the shelf space for storing perishable products without taking the warehouse space into account. This study intends to address the issue and touch upon selling high-profit products and signing total minimum commitment contracts with suppliers in order to optimize total costs in the order time.
Methods: Reviewing the literature comprehensively, the authors could identify the effective parameters of the model through desk research. On the basis of the defects found, a model was proposed for inventory control considering the new limitations. The particle swarm optimization algorithm was used in MATLAB in order to reach an optimal response in the problem-solving process and a time series analysis was performed by Minitab for demand forecasting.
Results: The proposed model can have applied implications for the industry. The results from the numerical analyses of the model revealed that an effective change in product face and a total minimum commitment contract with suppliers reduce the costs during the planning period. However, using both of them doesn’t always deliver favorable results. When a total minimum commitment contract is signed with the supplier and a change is made in the product face, it is necessary to reconsider the extent of commitment.
Conclusion: This study addressed the utility obtained from the effects of product face changes on the number of demands and number of orders together with total minimum commitment. The quantity of orders was considered according to the shelf space limitations in order to lower the costs. Results showed that the methods adopted to boost sales and lower costs can be profitable for retailers.
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.
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 in the 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.
We introduce an original concept of the backroom effect for perishable products when the deterioration rate in a backroom is lower than that on retail shelves. With IoT-generated real-time information about the perishable products, this phenomenon has a significant impact on joint shelf-space and inventory decisions. We define the deterioration rate gap, formulate the perceived on-shelf product freshness, and describe the freshness-dependent demand distribution, with continuous backroom-shelf replenishment. Assuming that demand depends on both perceived freshness and shelf level, we develop a decision-making model that simultaneously determines the inventory replenishment policy and the shelf space allocation for multiple items. To facilitate the solution process, we propose a hybrid solution approach by combining genetic algorithm (GA) and variable neighbourhood search (VNS). The results provide a prioritised inventory policy for item selection that incorporates the deterioration improvement. The results of the performance analysis show that a policy considering the backroom effect achieves increased profit when the backroom/shelf deterioration gap increases. The optimal solutions for the problems with large backroom/shelf gap also show that the practitioner should increase the ordering quantity, which is contradictory to the outcome of traditional models.
Store space is limited and one of the most costly resources of retailers. Retailers have to apportion available store space among the individual product categories of a store and therefore assign a certain share of shelf space to each category. Assigning more shelf space to one category requires reducing the number of shelves for another category as total space is limited. Reducing available shelf space in turn decreases assortment size and lessens the presentation quantity of products and vice versa. Both affect the demand of products and ultimately the profitability of the entire category such that the profit contribution of a category depends on its shelf size. This interrelation between category sizes and store profits needs to be taken into account for the shelf space assignment to categories and the space allocation for individual products.
We introduce a store-wide shelf space model that optimizes shelf space assignment for categories based on the profit contribution of the corresponding product allocations. We decompose the problem into two hierarchically interlinked subproblems and show that the solution approach suggested works efficiently and provides solutions that are applicable to large problems in retail practice. In a case study with a major European retailer, we show that profits at stores can be improved by 3.2% using our approach. Further, we use simulated data to generalize the findings and derive managerial insights.
A model of the interaction between products for normative strategy recommendations is described, an a priori product line model for finding the best marketing mix for each product in a line. The model includes aggregate product group marketing mix, product interdependency, and competitive brand effects.
This article describes an application of factorial design and analysis to a pricing experiment. The general approach appears promising for marketing experimentation involving multiple factors, particularly those in which factor interactions are anticipated.
The influence of shelf space upon sales of branded products is tested in a randomized block field experiment. Sales of two brands of salt and powdered coffee cream are measured. Managerial implications using opportunity cost indicate that retailers might limit shelf allocations for a number of brands to some minimal level.
Conceptual models and empirical studies of the relationship of shelf space allocation to unit sales are reviewed in this article. This knowledge is organized to support specific recommendations for the practical management of shelf space for profit maximization.
Sales-to-shelf facing relationships for three drug store products were proven significant in eight chain drug stores over a period of nine to sixteen weeks. Courses of action for the manufacturer and the retailer are defined by the significance of the relationship.
A general or signomial geometric program is a nonlinear mathematical program involving general polynomials in several variables both in the objective function and the constraints. A branch-and-bound method is proposed for this extensive class of nonconvex optimization programs guaranteeing convergence to the global optimum. The subproblems to be solved are convex but the method can easily be combined with a cutting plane technique to generate subproblems which are linear. A simple example is given to illustrate the technique.
This paper addresses a fundamental short-run resource-allocation problem confronting retail distribution: simultaneously finding the specific brands, from many, that should be displayed, and the amount of retail product-display area that should be assigned to these brands, in order to maximize the retail institution's profit. The paper decomposes total market demand according to the various levels of brand preference that could conceivably exist in final markets, and then, employs an algorithm, similar to the one used to solve the fixed-charge problem, to find the optimal brand mix and display-area allocation.
Channel optimization in multiple-channel systems is a basic problem in marketing and one which has not received much attention in the literature. A model is presented which simultaneously solves three distribution decisions--the manufacturer's choice of channels (channel strategy), the number of outlets to operate within each channel (channel intensity), and the pricing structure between channels (channel management). The general form of this model is not solvable by conventional programming techniques because it is intrinsically nonconvex. The paper shows how signomial geometric programming can provide a theoretically attractive and practical solution procedure. The model is estimated and solved on a real-life case study and the important managerial and theoretical implications are discussed.
Comment on "Solving the `Marketing Mix' Problem using Geometric Programming" (Management Sci., Vol. 21, No. 2, October 1974, pp. 160-171.).
A model and an algorithm are proposed for the simultaneous optimal selection among a given set of products of the assortment of products to be sold in a supermarket and the allocation of shelf space to these products. The model takes into account the space elasticity of the sales as well as the constraints that any chosen product must receive a minimum shelf space and that the shelf space allocated to each product must be equal to an integer number of facings.Computational results are presented, including a comparison with the results given by several rules for space allocation currently used. Some marketing implications are discussed.
The introduction of new products to US supermarket chains represents a strategic area of business conduct with significant economic implications for agribusiness companies, food manufacturers and retailers, and consumers. Development of new products by manufacturers and their subsequent evaluation by retailers absorbs enormous resources in the grocery distribution system. This research examined new product buying practices in the top 200 US supermarket chains. Typical findings show the reasons that nearly 70% of all newly introduced products are rejected by buyers and never make it to store shelves and approximately one-half of newly accepted products are removed from stores within 1 year. This study demonstrates that a food or agribusiness firm must first understand the standard procedures, wants and needs, of the key “gatekeeper” buyer before focusing on the final consumer. �1994 by John Wiley & Sons, Inc.
Optimal allocation of the marketing budget within the marketing-mix decision variables so that sales (or profit) is maximized in a planning horizon. Since the influence of marketing mix variables upon sales are, in reality, nonlinear and interactive, a geometric programming algorithm is used. A procedure to estimate a functional of sales on the marketing mix and environmental variables utilizing the judgments of the firm’s executives and the raw data is provided. The derived functional is later optimized by the Geometric Programming algorithm under a constraint set consisting of budget and strategy restrictions imposed by a firm’s marketing environment, and conditions under which the optimal solution is either local or global are identified.
The paper proposes a branch-and-bound method to find the global solution of general polynomial programs. The problem is first transformed into a reversed posynomial program. The procedure, which is a combination of a previously developed branch-and-bound method and of a well-known cutting plane algorithm, only requires the solution of linear subproblems.
De Maximalisatie van de Schapruinit-etoewi/zing in de Supermarkt, Doctoral Dissertation
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La Productivite de la Surface de Vente Passe Maintenant par L'Ordinateur
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Het Belang van Weloverwogern Assortimnentsbeheer
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Shelf Allocation Breakthrough
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Increase in Sales Due to In-Store Display
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The Economics of Food Distributors, General Foods
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Cifrino's Space Yield Formula: A Breakthrough for Measuring Product Profit
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