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

库存、产能和收入管理是运营管理研究和实践的一些基本领域。该领域的主要研究问题是确定最佳库存和产能相关决策以及在对加拿大经济具有重要意义的广泛情况下增加利润最大化实体收入的政策。例子包括医疗保健、制造、零售和金融服务组织，例如银行和其他投资公司。上述问题的设定都有一定的共同主题。这些包括某种不确定性、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要，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。这两项任务截然不同，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一再诉诸简单的次优经验法则来执行上述两项任务，这往往会导致产出平平。这对经济和社会来说代价高昂。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，通常这些都是极其困难的数学优化问题，在实践中不容易找到易于实现的最优或接近最优的解决方案。预测问题（即解决不确定性）通常不是一件容易的事。尽管可以获得大量数据，但本质上高度非线性的复杂系统通常会产生具有较大误差的预测。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，在与多家医院、农业、零售和其他服务业等行业的合作伙伴公司合作时，这是一种常见现象。这带来了产生在实践中表现良好并且具有有吸引力的理论特性的解决方案和技术的潜力。过去几年，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，并且还产生了一些易于实施且优于现有启发式的解决方案。结合、扩展和开发新技术和理论，将启发式随机优化与预测相结合，仍然具有巨大的潜力。 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，以及将在实践中实施的解决方案程序。**

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.**