Approximation algortihms for stochastic inventory models

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Stochastic inventory management is one of the fundamental areas of research and practice in operations management and management science. The main research questions of interest in this field are about determining optimal inventory and capacity related decisions in a wide set of instances which are of great significance to the economy. These decisions enable firms to hold the right inventory at the right location at the right time. The importance of such decisions cannot be underestimated as almost 11% of the Canadian GNP is spent on logistical activities that involve moving and storing physical inventory. In today's economic climate with rising fuel prices, making optimal decisions and reducing waste is particularly crucial. Thus, good research in this field often directly helps practitioners cut costs and improve profitability and improve social surplus. Despite its maturity as a research area, as of today, there are large classes of problem settings which pose significant theoretical and practical challenges. In this research, I propose to study a set of inventory problems, for which little is known in terms of the structure or algorithms that compute the near-optimal policies. For these problems, my research will construct approximation algorithms which will result in policies that are relatively easy to implement, that will yield close to optimal performance under a wide set of realistic instances and often offer an understanding of the worst case performance. In this process, important properties of the optimal policy will also be understood. The settings I am particularly interested include multiple sourcing, perishable products, large scale multi stage capacitated systems, multiple products which are partial substitutes of each other and with capacity constraints and settings with random yield.