The connection location and sizing problem: Models, methods, and applications to supply chain design

This dissertation considers a typical two-stage network where the movement of people, goods, or information between an origin location and a destination location must go through at least one facility called a connection . The goal of the connection location and sizing problem is to find the optimal location and sizing for connections as well as flow routing through them, simultaneously. The motivation of the dissertation is based on the view that the design of such a system can be improved by simultaneous consideration of connection location, sizing and routing.; For the discrete deterministic connection and sizing location problem, mathematical programming formulations are presented under a variety of circumstances: whether sizing decisions are discrete or continuous as well as whether the costs for these decisions are proportional or increasing concave.; For the discrete stochastic connection location and sizing problem, the connections are modeled as M/G/1 or M/G/c queueing systems and their sizes are controlled either by their system throughput rate or by the number of servers. In the M/G/1 case, mathematical programming formulations are presented for both the fixed and variable service rate cases. For the fixed service rate case, the first two moments of the service time are given. For the variable service rate case, the size is controlled by both the mean and the variability of service time at each connection. In the M/G/c case, the decisions include: (i) the location and flow routing; and (ii) the size of each connection to satisfy a pre-determined service level, where the service level is measured by the probability that an arriving flow finds no server available (i.e., the system is busy) at a connection.; For the planar problem, we first propose both uncapacitated and capacitated p-connection location problems. We establish discretization results for general polyhedral gauges as well as other relevant properties. Then, we study the planar connection location and sizing problem. This problem minimizes the total transportation cost and connection sizing costs.; The final part of the dissertation considers potential applications of this work to supply chain design.