带边界、固定成本与互补性约束的仓库问题
Warehouse Problem with Bounds, Fixed Costs and Complementarity Constraints
AI总结：
本文针对带固定成本、互补性约束和数量边界的仓库问题，基于极点刻画构建网络，用最小费用流算法解决，还提供扩展线性公式，同时为无固定成本的时间依赖边界场景提出全多项式时间近似方案。
摘要：
本文研究仓库问题中的一个开放问题：经营某商品的商家试图找到最优的库存交易策略，以在固定时间范围内决定采购与销售数量，利用销售价格与成本价格的波动最大化总收益。针对采购和销售存在固定成本、禁止同一时期内同时采购与销售的可选互补性约束、以及采购和销售数量存在边界的情况，我们提供了首个已知的多项式时间算法。我们通过精确刻画可行域的极点，并用其构建合适的网络，通过最小费用流计算得到最优解。我们还能为原始可行域提供多项式扩展线性规划公式。我们的方法基于Wolsey和Yaman（《离散优化》2018年）的研究工作。我们还考虑了无固定成本的问题，并在具有时间依赖边界的场景中提供了全多项式时间近似方案。
英文摘要：
This paper studies an open question in the warehouse problem where a merchant trading a commodity tries to find an optimal inventory-trading policy to decide on purchase and sale quantities during a fixed time horizon in order to maximize their total pay-off, making use of fluctuations in sale and cost prices. We provide the first known polynomial-time algorithms for the case when there are fixed costs for purchases and sales, optional complementarity constraints that prohibit purchasing and selling during the same time period, and bounds on purchase and sales quantities. We do so by providing an exact characterization of the extreme points of the feasible region and using this to construct a suitable network where a min-cost flow computation provides an optimal solution. We are also able to provide polynomial extended linear formulations for the original feasible regions. Our methods build on the work by Wolsey and Yaman (Discrete Optimization 2018). We also consider the problem without fixed costs and provide a fully polynomial time approximation scheme in a setting with time-dependent bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
