Stochastic Multiproduct Capacity and Inventory Problems: Exact Algorithms and Heuristics

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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.