Product category management (PCM) plays a pivotal role in today’s large stores. PCM manages to answer questions such as assortment planning (AP) and shelf space allocation (SSA). AP problem seeks to determine a list of products and suppliers, while SSA problem tries to design the layout of the selected products in the available shelf space. These problems aim to maximize the retailer sales under different constraints, such as limited purchasing budget, limited space of classes for displaying the products, and having at least a certain number of suppliers. This paper makes an attempt to develop an integrated mathematical model to optimize integrated AP, SSA, and inventory control problem for the perishable products. The objective of the model is to maximize the sales and retail profit, considering the costs of supplier contracting/selecting and ordering, assortment planning, holding, and procurement cost. GAMS BARON solver is hired to solve the proposed model in small and medium scales. However, because the problem is NP-hard, an evolutionary genetic algorithm (GA), and an efficient local search vibration damping optimization (VDO) algorithm are proposed. A real case study is considered to evaluate the effectiveness and capabilities of the model. Besides, some test problems of different sizes are generated and solved by the proposed metaheuristic solvers to confirm the efficient performance of proposed algorithms in solving large-scale instances.
There is a huge and growing gap between the speed of accesses to data stored in main memory vs cache. Thus, cache misses account for a significant portion of runtime overhead in virtually every program and minimizing them has been an active research topic for decades. The primary and most classical formal model for this problem is that of Cacheconscious Data Placement (CDP): given a commutative cache with constant capacity 𝑘 and a sequence Σ of accesses to data elements, the goal is to map each data element to a cache line such that the total number of cache misses over Σ is minimized. Note that we are considering an offline singlethreaded setting in which Σ is known a priori. CDP has been widely studied since the 1990s. In POPL 2002, Petrank and Rawitz proved a notoriously strong hardness result: They showed that for every 𝑘 ≥ 3, CDP is not only NP-hard but also hard-to-approximate within any non-trivial factor unless P = NP. As such, all subsequent works gave up on theoretical improvements and instead focused on heuristic algorithms with no theoretical guarantees.In this work, we present the first-ever positive theoretical result for CDP. The fundamental idea behind our approach is that real-world instances of the problem have specific structural properties that can be exploited to obtain efficient
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