Stochastic Multiproduct Capacity and Inventory Problems: Exact Algorithms and Heuristics

随机容量和库存管理是运营管理研究和实践的基本领域之一。该领域的主要研究问题是在广泛的情况下确定最佳库存和容量决策。这些问题的答案对经济学和研究者的理论兴趣都有重要意义。面临这些问题的组织跨越多个领域，从制造业、零售业和医疗保健到银行和其他投资公司等金融服务组织。有一些基本的基本条件和主题是共同的这些问题，使他们既困难和有趣的研究。 它们包括某种类型的不确定性（因此称为随机）（需求，供应，货币波动，手术时间，患者或客户到达系统等），有限的能力（对资本的预算约束、由于高度非线性成本而导致的有限的制造能力、零售环境中的货架空间或卫生保健环境中的有限的手术室容量）、由于在任何时间管理多个产品或服务的事实而经常产生的多个决策以及经常随时间段的动态决策，其中一次做出的决策通常影响随后时段的系统。典型的总体目标包括做出决策，要么最大化某些投资回报（利润、某些服务类别的吞吐量等），或者最小化成本和/或不愉快的事件。** 尽管它们普遍存在，但我们发现，企业和决策者一再诉诸简单的经验法则，而这些经验法则在实践中往往表现平平。这立即意味着有巨大的改进潜力，可以为社会带来重大利益。在实践中，次优行为的原因是多方面的。首先，这些都是非常困难的数学优化问题，最佳或接近最佳的解决方案是很难想象的理论。因此，在实践中表现良好且易于实现的可用解决方案并不容易找到。这导致导出在实践中表现良好的解决方案的潜力，以及具有有吸引力的理论性质，这些理论性质显示近似解的鲁棒性。在过去的几年里，我们已经取得了一些进展，一些这样的困难的问题，使用创新的方法结合动态规划。这一分析推动了我们对这些问题的理解，从理论意义上说，也产生了解决方案的程序，有点容易实现，并优于现有的算法。其中许多已由从业人员实施。 但还有很多工作要做。在当前的研究议程中，我建议研究一系列广泛的问题，并在理论和应用方面取得重大进展。预期成果将是在我所在领域的顶级研究期刊上发表研究论文，以及行业合作伙伴将使用的解决方案程序，这将为整个经济带来积极的收益。

Stochastic Capacity and Inventory Management is one of the fundamental areas of*research and practice in operations management. The main research questions in this field deal with determining optimal inventory and capacity decisions in a wide set of instances. Answers to these are of great significance to the economy as well of theoretical interest to researchers. Organizations that face these problems span multiple areas from manufacturing, retail and health care to financial service organizations such as banks and other investment firms. There are some basic underlying conditions and themes that are common to these problems that make them both difficult and interesting to study. They include uncertainty (hence the name stochastic) of some kind (demand, supply, currency fluctuations, surgical times, patient or customer arrival to systems etc.), limited capacity (budget constraints on capital, limited manufacturing capacity due to highly non linear costs, shelf space in retail settings or limited operating room capacity in health care settings), multiple decisions often arising due to the fact multiple products or services are being managed at any time and dynamic decisions often over time periods where decisions made at one time usually affect the system in subsequent periods. The typical overall objective involves making decisions that either maximize certain returns on investment (profits, throughput for certain service classes etc.) or minimize costs and/or unpleasant incidences. **Despite their prevalence, we find that repeatedly firms and decision makers resort to simple rules of thumb whose performance in practice is often mediocre. This immediately means that there is a huge potential for improvement that can have a significant benefit for society. The reasons for sub-optimal behavior in practice are manifold. First of all, these are extremely hard mathematical optimization problems for which optimal or near optimal solutions are hard to hard to envision theoretically. Therefore, usable solutions that perform well and are simple to implement in practice are not easily found. This leads to the potential of deriving solutions that perform well in practice as well as have attractive theoretical properties that show robustness of the approximate solutions. In the last several years, we have made some progress on some such difficult problems using innovative methods combined with dynamic programming. This analysis has moved our understanding of these problems forward from a theoretical sense and has also yielded solution procedures that are somewhat easy to implement and outperform existing heuristics. Many of these have been implemented by practitioners. But there is a lot left to be done. In the current research agenda, I propose to work on a broad set of these problems and make significant progress on both the theoretical and applied front. Expected outcomes will be research publications in top tier research journals in my field as well as solution procedures that will be used by industry partners which will yield positive gains to the economy at large.