Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project 10704-0188], Washington, DC 20503. AGENCY USE ONLY (Leave blank)2. REPORT DATE 17.Jul.00 REPORT TYPE AND DATES COVERED DISSERTATION TITLE AND SUBTITLE COMPOSITE VARIABLE FORMULATIONS FOR EXPRESS SHIPMENT SERVICE NETWORK DESIGN AUTHOR(S)CAPT ARMACOST ANDREW P FUNDING NUMBERS PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) MASSACHUSETTS INSTITUTE OF TECHNOLOGY PERFORMING ORGANIZATION REPORT NUMBER SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)THE AbstractIn this thesis, we consider large-scale network design problems, specifically the problem of designing the air network of an express shipment (i.e., overnight) delivery operation. We focus on simultaneously determining the route structure, the assignment of fleet types to routes, and the flow of packages on aircraft. Traditional formulations for network design involve modeling both flow decisions and design decisions explicitly. The bounds provided by their linear programming relaxations are often weak. Common solution strategies strengthen the bounds by adding cuts, but the shear size of the express shipment problem results in models that are intractable.To overcome this shortcoming, we introduce a new modeling approach that 1) removes the flow variables as explicit decisions and embeds them within the design variables and 2) combines the design variables into composite variables, which represent the selection of multiple aircraft routes that cover the demands for some subset of commodities. The resulting composite variable formulation provides tighter bounds and enables very good solutions to be found quickly. We apply this type of formulation to the express shipment operations of the United Parcel Service (UPS). Compared with existing plans, the model produces a solution that reduces the number of required aircraft by almost 11 percent and total annual cost by almost 25 percent. This translates to potential annual savings in the hundreds of millions of dollars.We establish the composite variable formulation to be at least as strong as the traditional network design formulation, even when the latter is strengthened by Chvätal-Gomory rounding, and we demonstrate cases when strength is strictly improved. We also place the composite variable formulation in a more general setting by presenting it as a Dantzig-Wolfe decomposition of the traditional (intractable) network design formulation and by comparing com...

The focus of this research is to model and solve a large-scale service network design problem involving express package delivery. The objective is to find the cost minimizing movement of packages from their origins to their destinations, given very tight service windows, limited package sort capacity, and a finite number of ground vehicles and aircraft. We have developed a model for large scale transportation service network design problems with time windows. With the use of route-based decision variables, we capture complex cost structures and operating regulations and policies. The poor linear programming bounds limit our ability to solve the problem, so we strengthen our linear programming relaxation by adding valid inequalities. By exploiting problem structure using a specialized network representation and applying a series of novel problem reduction methods, we achieve dramatic decreases in problem size without compromising optimality of the model. Our solution optimization approach synthesizes column and row generation optimization techniques and heuristics to generate solutions to an express package delivery application containing hundreds of thousands of constraints and billions of variables, using only a small fraction of the constraint matrix. The results are potential savings in annual operating costs of tens of millions of dollars, reductions in the fleet size required, dramatic decreases in the time required to develop operating plans, and scenario analysis capabilities for planners and analysts. Through this and additional computational experiments, we conclude that, although state-of-the-art integer programming methods can work well for relatively small, uncongested service network design problems, they must be used in concert with heuristics to be effective for large-scale, congested problems encountered in practice.

Operations research specialists at UPS and the Massachusetts Institute of Technology (MIT) created a system to optimize the design of service networks for delivering express packages. The system simultaneously determines aircraft routes, fleet assignments, and package routings to ensure overnight delivery at minimal cost. It has become central to the UPS planning process, fundamentally transforming the process and the underlying planning assumptions. Planners now use the system's solutions and insights to improve plans. UPS management credits the system with identifying operational changes that have saved over $87 million between 2000 and 2002. Anticipated future savings are expected to be in the hundreds of millions of dollars.

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