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Proceedings ArticleDOI

Optimal retail shelf space allocation with dynamic programming using bounds

01 Dec 2008-pp 1068-1072

TL;DR: It is found from experimental studies that NDP using bound was much more efficient to solve large problems as compared to original dynamic programming (ODP) without using bound.

AbstractEfficient shelf space allocation increases profitability of a retail store and thus provides competitive advantage to the retailer. Several shelf space allocation models exist in literature. However, these models are generally solved using heuristic approaches due to NP-hard nature and there is a need to develop exact methods. In this paper, we present a non-linear shelf-space allocation model (NLSSAM) and optimally solve it with a new dynamic programming (NDP) using bounds which fathoms unpromising states. It is found from experimental studies that NDP using bound was much more efficient to solve large problems as compared to original dynamic programming (ODP) without using bound. ODP could not solve all problem instances of problem sizes (number of products, n = 30 and 40) within specified CPU time limit of 400 seconds while NDP could solved problem instances of size (n = 200) with average CPU time of 7.89 seconds.

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References
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21 Oct 1957
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Abstract: From the Publisher: An introduction to the mathematical theory of multistage decision processes, this text takes a functional equation approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, strategies behind multistage games, and Markovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls a rich lode of applications and research topics. 1957 edition. 37 figures.

13,951 citations

Journal ArticleDOI
TL;DR: It is found that location had a large impact on sales, whereas changes in the number of facings allocated to a brand had much less impact as long as a minimum threshold (to avoid out-of-stocks) was maintained.
Abstract: Shelf management is a difficult task in which rules of thumb rather than good theory and hard evidence tend to guide practice. Through a series of field experiments, we measured the effectiveness of two shelf management techniques: “space-to-movement,” where we customized shelf sets based on store-specific movement patterns; and “product reorganization” where we manipulated product placement to facilitate cross-category merchandising or ease of shopping. We found modest gains (4%) in sales and profits from increased customization of shelf sets and 5–6% changes due to shelf reorganization. Using the field experiment data, we modeled the impact of shelf positioning and facing allocations on sales of individual items. We found that location had a large impact on sales, whereas changes in the number of facings allocated to a brand had much less impact as long as a minimum threshold (to avoid out-of-stocks) was maintained.

608 citations

Journal ArticleDOI
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.

382 citations


"Optimal retail shelf space allocati..." refers background or methods in this paper

  • ...Yang and Chen [1] developed a comprehensive model from the model of Corstjens and Doyle [ 15 ] considering location effect....

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  • ...The geometric programming model of Corstjens and Doyle [ 15 ] does not consider the integer nature of number of displayed products in a store....

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  • ...Corstjens and Doyle [ 15 ] developed a geometric programming model considering space elasticity and cross elasticity in demand function and solved it using the branch and bound algorithm as proposed by Gochet and Smeers [16]....

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  • ...Zufryden [8] proposed a ‘forward’ dynamic programming model in which demand function considered space elasticity while neglecting cross elasticity between products and fixing non space variables for tractability and efficiency of the solution procedure. The models of Corstjens and Doyle [ 15 ] and...

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Journal ArticleDOI
TL;DR: A simple O(n) partitioning algorithm for deriving the optimal linear solution to the Multiple-Choice Knapsack Problem is presented, and it is shown how it may be incorporated in a dynamic programming algorithm such that a minimal number of classes are enumerated, sorted and reduced.
Abstract: The Multiple-Choice Knapsack Problem is defined as a 0–1 Knapsack Problem with the addition of disjoined multiple-choice constraints. As for other knapsack problems most of the computational effort in the solution of these problems is used for sorting and reduction. But although O(n) algorithms which solve the linear Multiple-Choice Knapsack Problem without sorting have been known for more than a decade, such techniques have not been used in enumerative algorithms. In this paper we present a simple O(n) partitioning algorithm for deriving the optimal linear solution, and show how it may be incorporated in a dynamic programming algorithm such that a minimal number of classes are enumerated, sorted and reduced. Computational experiments indicate that this approach leads to a very efficient algorithm which outperforms any known algorithm for the problem.

264 citations


"Optimal retail shelf space allocati..." refers methods in this paper

  • ...A convex profit function gi(xi) for product i in continuous range of xi is shown in Figure 1. We use the following greedy algorithm given by Pisinger [ 25 ] to obtain the upper bound UBh for a state h....

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Journal ArticleDOI
Abstract: 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.

224 citations


"Optimal retail shelf space allocati..." refers background in this paper

  • ...Few integrated models jointly consider product assortment, shelf space allocation and inventory replenishment decisions to maximize retailer’s profit under the given operating constraints [ 20 ]-[23]....

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