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Retail Analytics and Optimization for Store-Wide Shelf-Space Management

A major constituent of modern-time economies, retailing is a vibrant business sector that is marked by high competition, tight profit margins, novel business strategies in online and in-store environments, and demanding consumers. Driven by massive volumes of point-of-sale data, retail analytics has become instrumental for unveiling better managerial practices. Our research falls under the umbrella of retail shelf space management. In self-service outlets, shelf space constitutes a scarce resource and its management is central to ensuring an attractive shopping experience and a profitable business. We investigate how, under a given store layout, the allocation of product categories can be optimized in a fashion that guides in-store traffic and stimulates unplanned purchases -- an aspect that is understudied in the management science literature. Our study is predicated on the notion that effective store-wide shelf space allocation of products, be it fast- or slow-movers, can significantly improve product visibility and induce a lucrative stream of so-called impulse purchases. The latter correspond to unplanned, "on-the-spot" purchases (Piron, 1991) that are triggered by in-store stimuli (Piron, 1991; Clover 1950) and may account for over 50% of purchases in supermarkets (Kollat and Willet, 1967). Although impulse buying has been well-documented in the marketing literature, the notion of planning shelf space at the store-level in order to stimulate impulse buying remains unexplored in the operations management literature. This dissertation contributes to filling this gap in the literature and has the following two overarching objectives: (i) To examine how retail shelf space allocation can be tactically planned using analytics, optimization methodology, and effective algorithmic procedures, in order to improve the visibility of products to consumers and to maximize the expected profit from impulse buying and (ii) to tackle the computational challenges posed by the associated class of optimization problems by crafting effective exact and heuristic solution approaches. In Essay 1, we investigate how store-wide retail shelf space allocation can impact the visibility of product categories and drive customer impulse buying. We consider a setting where the retailer, due to historical practice, affinities between product categories, or cross-selling opportunities, has pre-grouped products that ought to be allocated to the same shelf and to the same aisle (e.g., pasta and pasta sauce). We introduce a 0-1 integer programming model that optimizes the following decisions with the objective of maximizing impulse buying: (i) The location of each product group; (ii) the specific location of each product category within its group on its allocated shelf; and (iii) the shelf space allocated to each product category in a group between its minimum/maximum space requirements. The proposed model employs a preprocessing scheme that explores feasible assignments of subsets of product groups to available aisles and enables exact solutions to large-scale instances in manageable times. 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. We provide qualitative insights for the retailers by comparing the current allocation and the optimized allocation in the case study. In Essay 2, we focus on a class of generalized assignment problems with location/allocation considerations (GAPLA) that is prompted by our research in the store-wide shelf space allocation problem. In this regard, shelves may be viewed as variable-sized knapsacks, each is discretized into consecutive segments having different levels of attractiveness. This segment discretization constitutes a novel feature that distinguishes GAPLA from traditional generalized assignment problems and makes it more computationally challenging. Further, product categories can be viewed as items that must be assigned to knapsacks and allocated a space between their minimum/maximum space requirements. To maximize a total reward function, the decision-maker optimizes item-knapsack assignments, the specific location of items in their assigned knapsack, and the total space allocated to each item within its minimum/maximum space requirements. Optimization models are proposed for the single- and the multiple-knapsack variants of the problem along with model enhancements and valid inequalities. Moreover, the problem is reformulated as a set partitioning model that is tackled by a branch-and-price algorithm. Our computational experience shows that our methodology significantly outperforms the use of commercial software packages such as CPLEX. Essay 3 introduces an effective heuristic solution methodology, namely, a very large-scale neighborhood search algorithm (VLNS), in order to solve large-scale instances of GAPLA. The heuristic employs a restricted variant of the mixed-integer program developed in Essay 2 and iteratively optimizes selected subsets of knapsacks. We conduct a computational study on large-scale instances including up to 210 items and 42 knapsacks and on a realistic case study motivated by a shelf space allocation problem. Our computational results reveal that the proposed heuristic significantly outperforms the best solution provided by CPLEX in one hour time limit and consistently provides high-quality solutions in manageable CPU times. In Essay 4, we conduct data analysis over nearly 40,000 customer receipts from a grocery store in Beirut (Lebanon) in order to correlate in-store customer traffic with product shelf allocations and the store layout. Our statistical analysis is encapsulated in a predictive model that allows the retailer to anticipate customer traffic levels as a result of changes in product shelf space allocation. Further, the predictive model is embedded within a mixed-integer nonlinear optimization model that can prescribe improved store-wide shelf space allocations. The computational intractability of the model is overcome by using a surrogate linear objective function (in lieu of the original nonlinear objective) that guides a variable neighborhood search in the spirit of Essay 3. We demonstrate that our prescriptive analytics has the potential of improving the current store configuration via enhanced shelf space allocations, better in-store traffic, and greater impulse buying.
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