Abstract Retail shelves are adjustable by varying the number of shelf boards as well as the height and depth of each shelf board. Shelf planners adjust the boards accordingly at regular intervals when they create the shelf plans and allocate products. Current shelf planning models assume given shelf configurations and allocate only products. However, the dimensioning of a shelf segment and product allocation are interdependent. For instance, the height of one segment may be reduced if only small products are allocated or products cannot be stacked. This paper proposes the first integrated approach for shelf segment dimensioning and product allocation. It jointly determines the number of facings for each product, the shelf quantity and the size and number of shelf segments. We also identify and consider several restrictions for the shelf structure (e.g., technical options), allocation rules (e.g., maximum inventory reach) and allocation- and shelf-layout-dependent demand. We formulate the decision problem at hand which is an Integer Non-linear Program and apply a solution algorithm based on the application of bounds that are obtained by transferring constraints to a preprocessing stage. Doing so, we can reformulate the problem as Binary Integer Program, provide an exact approach and generate practical applicable and optimal solutions in a time-efficient manner. We show that integrating shelf dimensioning into product allocation results in up to 5% higher profits than benchmarks available in literature. By means of a case study we show how planning can be improved, and that the retailer’s profit margin can be improved by up to 7%.

中文翻译：

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零售店的货架空间尺寸和产品分配

摘要 零售货架可通过改变货架板的数量以及每个货架板的高度和深度来调节。货架规划师在创建货架计划和分配产品时会定期相应地调整板。当前的货架规划模型假设给定的货架配置并仅分配产品。然而，货架段的尺寸和产品分配是相互依赖的。例如，如果只分配小产品或不能堆叠产品，可能会降低一个段的高度。本文提出了第一个货架分段尺寸和产品分配的集成方法。它共同决定了每种产品的饰面数量、货架数量以及货架段的大小和数量。我们还确定并考虑了货架结构（例如，技术选项）、分配规则（例如，最大库存范围）以及与分配和货架布局相关的需求的几个限制。我们制定了手头的决策问题，它是一个整数非线性程序，并基于通过将约束转移到预处理阶段获得的边界的应用来应用求解算法。这样做，我们可以将问题重新表述为二进制整数程序，提供精确的方法并以省时的方式生成实际适用的最佳解决方案。我们表明，将货架尺寸整合到产品分配中会导致比文献中可用的基准高出 5% 的利润。通过案例研究，我们展示了如何改进规划，