Forecasting and Stochastic Optimization: Applications to Capacity, Inventory and Revenue Management Problems.

库存、产能和收益管理是运营管理研究和实践的一些基本领域。***对这一领域的主要研究问题是确定最优库存和产能相关决策以及政策，以增加利润最大化实体的收入，这对加拿大经济具有重要意义。例子包括医疗保健、制造业、零售和金融服务组织，如银行和其他投资公司。以上问题的设置都有一定的共同主题。其中包括某种不确定性、有限的容量、随时间变化的信息，以及随着时间的推移做出动态决策的需求，这些决策的总体目标是最大化/最小化某些投资回报（利润、成本、某些服务类别的吞吐量等）。******处理这些问题自然涉及至少两个数学任务，即预测不确定性和优化合适的目标。这两项任务是截然不同的，但又相互关联。尽管这些问题普遍存在，但我们发现，企业和决策者反复采用简单的次优经验法则来执行上述两项任务，这往往导致平庸的产出。这对经济和社会都是代价高昂的。也就是说，通常有足够的空间来改进从业者使用的解决方案。造成这种情况的原因是多方面的。首先，通常，这些都是非常困难的数学优化问题，在实践中容易实现的最优或接近最优解不容易找到。预测问题（即解决不确定性）通常不是一项容易的任务。尽管有大量的数据，复杂的系统本质上是高度非线性的，往往产生的预测有很大的误差。通常对于预测多少以及在优化中使用什么启发式方法，几乎没有理论或实践指导。我们发现这是一个普遍现象，我们与多个行业的合作伙伴公司合作，如各种医院、农业、零售和其他服务。这就有可能推导出在实践中表现良好的解决方案和技术，并具有吸引人的理论性质。在过去几年里，我们在这方面取得了一些进展。我们对这些问题的理解已经从理论意义上向前发展，并且也产生了一些易于实施和优于现有启发式的解决程序。结合、扩展和发展新的技术和理论，将启发式随机优化与预测结合起来，仍然有很大的潜力。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，并在实践中实施解决方案程序

Inventory, capacity and revenue management are some of the fundamental areas of research and practice in operations management. The main research questions of***interest in this field are about determining optimal inventory and capacity related decisions as well as polices to increase the revenue of a profit maximizing entity in a wide set of instances which are of great significance to the Canadian economy. Examples include Health care, manufacturing, retail and financial service organizations such as banks and other investment firms. The settings of the above problems have certain common themes. These include uncertainty of some kind , limited capacity, information evolving over time and the need for dynamic decisions made over time with the overall objective of maximizing/minimizing certain returns on investment (profits, costs, throughput for certain service classes etc.).******Dealing with these problems naturally involve at least two mathematical tasks, i.e., forecasting of the uncertainty and optimizing a suitable objective. These two tasks are distinct, but are related to each other. Despite the prevalence of these problems, we find that repeatedly firms and decision makers resort to simple sub-optimal rules of thumb to perform the above two tasks which often result in mediocre outputs. This is costly to the economy and our society. That is, often there is ample room to improve the solutions used by practitioners. The reasons for this are manifold. First of all, often, these are extremely hard mathematical optimization problems for which optimal or near optimal solutions that are easy to implement in practice are not easily found. The forecasting problem (i.e., resolving the uncertainty) is often not an easy task. Despite the availability of large amounts of data, complex systems which are intrinsically highly non linear often yield forecasts with large errors. Often there is little theoretical or practical guidance on how much to forecast and what heuristics to use in the optimization. We find this as a common phenomenon with our work with several partner firms spanning industries such as various hospitals, agriculture, retail, and other services. This leads to the potential of deriving solutions and techniques that perform well in practice as well as have attractive theoretical properties. In the last several years, we have made some progress in this front. Our understanding of these problems has moved forward from a theoretical sense and has also yielded solution procedures that are somewhat easy to implement and outperform existing heuristics. There is still significant potential to combine, extend and develop new techniques and theory to combine heuristics to stochastic optimization with forecasting. Expected outcomes will be research publications in top tier research journals in my field as well as solution procedures that will be implemented in practice.**