Stochastic Multiproduct Capacity and Inventory Problems: Exact Algorithms and Heuristics

随机产能与库存管理是运营管理研究与实践的基础领域之一。该领域的主要研究问题是在广泛的实例集中确定最优库存和产能决策。这些问题的答案对经济学具有重要意义，同时也引起了研究者的理论兴趣。面临这些问题的组织横跨多个领域，从制造业、零售业和医疗保健到金融服务组织（如银行和其他投资公司）。这些问题都有一些共同的基本条件和主题，这使得研究这些问题既困难又有趣。它们包括某种不确定性（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（资本预算限制、由于高度非线性成本导致的制造能力有限、零售场所的货架空间或卫生保健场所的手术室容量有限）、由于在任何时间管理多个产品或服务，经常会产生多个决策，而动态决策通常会在一段时间内产生，其中一次做出的决策通常会影响随后的系统。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），要么最小化成本和/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，而这些法则在实践中的表现往往是平庸的。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。实践中导致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，最优或接近最优解很难从理论上想象出来。因此，在实践中执行良好且易于实现的可用解决方案并不容易找到。这就有可能推导出在实践中表现良好的解，并具有显示近似解鲁棒性的有吸引力的理论性质。在过去的几年里，我们利用创新的方法与动态规划相结合，在一些这样的难题上取得了一些进展。这种分析使我们对这些问题的理解从理论意义上向前发展，也产生了一些易于实施和优于现有启发式的解决程序。其中许多已经由从业者实现。但还有很多工作要做。在目前的研究议程中，我建议对这些问题进行广泛的研究，并在理论和应用方面取得重大进展。预期的结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 ofresearch 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.