UC Berkeley

Disasters strike suddenly and cause destruction which disrupts the availability of basic survival supplies for people living in affected areas. The efficiency of humanitarian organizations in providing relief has a direct and crucial impact on the survival, health, and recovery of affected people and their communities. To better prepare to respond to disasters, many relief organizations use supply pre-positioning. However, the real and potential needs of different locations change over time and when an organization uses traditional warehouse pre-positioning, relief operations are limited by set inventory locations that are difficult to alter. For this reason, a well known organization recently considered including a large supply holding ship in its operations. By holding inventory on a ship, the organization would be able to dynamically relocate its inventory over time in response to changing relief supply demand forecasts.

To our knowledge, the research contained herein is the first to examine dynamic inventory relocation for responding to disasters over time. Specifically, we examine how to optimally relocate and manage inventory for a single mobile inventory to serve stochastic demand at a number of potential disaster sites over time. While we keep in mind the motivating example of a supply holding ship in the disaster relief setting throughout this dissertation, the model and most of the results are applicable to any type of mobile inventory, facility, or server in any setting.

We first examine the dynamic relocation problem. We model the problem using dynamic programming and develop analytical and numerical results regarding optimal relocation policies, the optimal path and speed of relocation decisions, and the value of inventory mobility over traditional warehouse pre-positioning. To help overcome the computational complexity of the problem, we develop a heuristic which solves relatively large problem instances in our numerical experiments within 0.5% of optimality in less than 0.1% of the time required by an exact algorithm.

As it is suboptimal to consider relocation decisions and inventory management decisions separately, we also examine the joint dynamic relocation and inventory management problem. To our knowledge, we are the first to examine the dynamic relocation and inventory management problem with stochastic demand. Similarly to the dynamic relocation problem, we model this problem using dynamic programming. We develop a number of analytical results characterizing the optimal relocation and inventory management policies.

As the first to examine these problems, we hope this research serves as a catalyst for other research in this area; accordingly, we conclude this dissertation by discussing a number of areas for future research.