# Optimal retail shelf space allocation with dynamic programming using bounds

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.

Abstract: Efficient 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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### "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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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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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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