| This dissertation studies the problem of managing a system which is subject to global system interruptions; that is, random interruptions which disrupt all service but do not affect demand for the system's services. Such systems are frequently encountered and include banks' ATM networks, airports, and computer systems, among others.; In this work, we assume that these systems consist of a series of tasks or jobs which have a finite cost of preemption; in this way, tasks can be restarted (at an additional cost) when the system experiences a random interruption. We study this system under a variety of conditions by developing several analytical models and analyzing these models for managerial implications.; In the deterministic case, we introduce the problem of scheduling preemptive jobs with known arrival and processing times on a single machine where there is a finite cost of preempting a job. Although the problem is NP-hard, we develop an algorithm for finding the optimal solution for small problems using a branch-and-bound method that utilizes a lower bound based on a Lagrangian relaxation formulation of the original problem. Given the problem difficulty, we also propose several heuristic algorithms including a look-ahead heuristic with knapsack backfill. We found that this heuristic was particularly effective, especially as the variance in arrival and processing times increased.; In the case of stochastic scheduling, we develop an analytical model to analyze the problem of scheduling preemptive jobs with random (exponential) arrivals, an Erlang type-k phase type service distribution, and a finite number of servers when there are global system interruptions. We solve the problem using numerical methods under the assumptions that there is a maximum number of customers in the system and customers are served in first-come, first-served order. The theoretical results from this model are tested against actual data from a marine-lightering operation, which was found to closely represent the operation. It was this operation that provided the original motivation for this dissertation. |
