We study the warehouse problem, arising in the area of inventory management and production planning. Here, a merchant wants to decide an optimal trading policy that computes quantities of a single commodity to purchase, store and sell during each time period of a finite discrete time horizon. Motivated by recent applications in energy markets, we extend the models by Wolsey and Yaman (2018) and Bansal and G\"unl\"uk (2023) and consider markets with multiple vendors and a more general form of the complementarity constraints. We show that these extensions can capture various practical conditions such as surge pricing and discounted sales, ramp-up and ramp-down constraints and batch pricing. We analyze the extreme points of the underlying non-linear integer program and provide an algorithm that exactly solves the problem. Our algorithm runs in polynomial time under reasonable practical conditions. We also show that the absence of such conditions renders the problem NP-Hard.

翻译：本文研究库存管理与生产规划领域的仓库问题。在该问题中，商人需在有限离散时间序列的每个时段内，就单一商品的采购、存储及销售数量制定最优交易策略。受能源市场最新应用启发，我们扩展了Wolsey与Yaman（2018）及Bansal与Günlük（2023）的模型，考虑了多供应商市场及更广义形式的互补约束。研究表明，这些扩展模型可涵盖多种实际场景，如激增定价与折扣销售、爬坡/降坡约束及批次定价。我们分析了底层非线性整数规划的极值点，并给出精确求解该问题的算法。在合理实际条件下，该算法可在多项式时间内运行。同时证明，缺乏此类条件将使问题变为NP难问题。