COMPACT FORMULATION OF MULTICOMMODITY NETWORK FLOWS WITH APPLICATIONS TO THE BACKHAUL PROFIT MAXIMIZATION PROBLEM AND FIXED CHARGE NETWORK FLOW PROBLEM

The triples formulation is a compact formulation of multicommodity network flow problems that provides a different representation of flow than the traditional and widely used node-arc and arc-path approaches. In the literature, the triples formulation has been applied successfully to the maximum concurrent flow problem and to a network optimization problem with piecewise linear convex costs. This dissertation applies the triples formulation to the backhaul profit maximization problem (BPMP) and the fixed charge network flow problem (FCNF). It is shown that the triples representation of multicommodity flow significantly reduces the number of variables and constraints in the mixed integer programming formulations of the BPMP and FCNF. For the BPMP, this results in significantly faster solution times. For dense problem instances, the triples-based formulation of FCNF is found to produce better solutions than the node-arc formulation early in the branch-and-bound process. This observation leads to an effective hybrid method which combines the respective advantages of the smaller size of the triples formulation and the stronger linear programming relaxation of the node-arc formulation. In addition to empirical studies, the dissertation presents new theoretical results supporting the equivalence of the triples formulation to the node-arc and arc-path formulations. The dissertation also proposes a multi-criteria Composite Index Method (CIM) to compare the performance of alternative integer programming formulations of an optimization problem. Using the CIM, the decision maker assigns weights to problem instance sizes and multiple performance measures based on their relative importance for the given application. The weighting scheme is used to produce a single number that measures the relative improvement of one alternative over the other and provides a method to select the most effective approach when neither one dominates the other when tested on different sizes of problem instances. The dissertation demonstrates a successful application of the CIM to evaluate a series of eleven techniques for improving the node-arc and triples formulations of the BPMP previously proposed in the literature

DYNAMIC DECISION MAKING FOR LESS-THAN-TRUCKLOAD TRUCKING OPERATIONS

On a typical day, more than 53 million tons of goods valued at about $36 million are moved on the US multimodal transportation network. An efficient freight transportation industry is the key in facilitating the required movement of raw materials and finished products. Among different modes of transportation, trucking remains the shipping choice for many businesses and is increasing its market share. Less-than-truckload (LTL) trucking companies provide a transportation service in which several customers are served simultaneously by using the same truck and shipments need to be consolidated at some terminals to build economical loads. Intelligent transportation system (ITS) technologies increase the flow of available data, and offer opportunities to control the transportation operations in real-time. Some research efforts have considered real-time acceptance/rejection of shipping requests, but they are mostly focused on truckload trucking operations. This study tries to use real-time information in decision making for LTL carriers in a dynamically changing environment. The dissertation begins with an introduction of LTL trucking operations and different levels of planning for this type of motor carriers, followed by the review of literature that are related to tactical and operational planning. Following a brief discussion on multi commodity network flow problems and their solution algorithm, a mathematical model is proposed to deal with the combined shipment and routing problem. Furthermore, a decision making procedure as well as a decision support application are developed and are presented in this dissertation. The main step in the decision making procedure is to solve the proposed mathematical problem. Three heuristic solution algorithms are proposed and the quality of the solutions is evaluated using a set of benchmark solutions. Three levels of numerical experiments are conducted considering an auto carrier that operates on a hub-and-spoke network. The accuracy of the mathematical model and the behavior of the system under different demand/supply situations are examined. Also, the performance of the solutions provided by the proposed heuristic algorithms is compared and the best solution method is selected. The study suggests that significant reductions in operational costs are expected as the result of using the proposed decision making procedure