Numerical performance of matrix inversion with block pivoting

An experiment with matrix inversion using block pivots is presented. Large scale matrix computations can often be performed more efficiently by use of partitioning. Such matrix manipulation lends itself to paged or cache memory systems since computation is staged to be completely performed in local blocks of controllable size. On other systems retrieval overhead can be balanced with computation for 'in-memory/out-of-memory' applications. Parallelism in such schema leads to efficient utilization of some multiple processor environments. Timing results indicate, however, that choice of block size should not necessarily be dictated by hardware page size for most efficient operation and that classical methods of estimating computation times are not always adequatesponsored by a grant from the Research Foundation, Naval Postgraduate Schoolhttp://archive.org/details/numericalperform00browN0001475WR5000

Dynamic Factorization in Large-Scale Optimization

Mathematical Programming, 64, pp. 17-51.Factorization of linear programming (LP) models enables a large portion of the LP tableau to be represented implicitly and generated from the remaining explicit part. Dynamic factorization admits algebraic elements which change in dimension during the course of solution. A unifying mathematical framework for dynamic row factorization is presented with three algorithms which derive from different LP model row structures: generalized upper bound rows, pure network rows,and generalized network TOWS. Each of these structures is a generalization of its predecessors, and each corresponding algorithm exhibits just enough additional richness to accommodate the structure at hand within the unified framework. Implementation and computational results are presented for a variety of real-world models. These results suggest that each of these algorithms is superior to the traditional, non-factorized approach, with the degree of improvement depending upon the size and quality of the row factorization identified

Consolidation of Customer Orders Into Truckloads at a Large Manufacturer

Journal of the Operational Research Society, 48, pp. 779-785.We describe the development and operation of an interactive system based on a mathematical optimization model which is used by a major US manufacturer to consolidate customer orders into truckloads. Dozens of users employ the system daily for planning delivery of orders from manufacturing plants to customers by truckload carriers, saving numerous hours of the users' time and reducing transportation costs

Automatic identification of embedded network rows in large-scale optimization models

The solution of a contemporary large-scale linear, integer, or mixed-integer programming problem is often facilitated by the exploitation of intrinsic special structure in the model. This paper deals with the problem of identifying embedded pure network rows within the coefficient matrix of such models and presents two heuristic algorithms for identifying such structure. The problem of identifying the maximum-size embedded pure network is shown to be among the class of NP-hard problems; therefore, the polynomially bounded, efficient algorithms presented here do not guarantee network sets of maximum size. However, upper bounds on the size of the maximum network set are developed and used to evaluate the algorithms. Computational tests with large-scale, real-world models are presented.Office of Naval Research, Code 434, Arlington, VAApproved for public release; distribution is unlimited

Consolidating and Dispatching Truck Shipments of Mobil Heavy Petroleum Products

Interfaces, 25, pp. 1-17.Mobil Oil Coporation consolidates and dispatches truck shipments of heavy petroleum products-lubricants in packages and in bulk from 10 lubricant plants nationwide. It dispatches hundreds of orders daily either individually or as consolidated truckloads, using a very nonhomogeneous fleet of Mobil controlled and contract vehicles and common carriers..

Scheduling Ocean Transportation of Crude Oil

Management Science, 33, p. 335-346. (Nominated for 1987 International Management Science Achievement Award.)The article of record as published may be found at http://links.jstor.org/sici?sici=0025-1909%28198703%2933%3A3%3C335%3ASOTOCO%3E2.0.CO%3B2-FNominated for 1987 International Management Science Achievement Award.A crude oil tankerscheduling problem faced by a major oil company is presented and solved using an elastic set partitioning model. The model takes into account all fleet cost components, including the opportunity cost of ship time, port and canal charges, and demurrage and bunker fuel. The model determines optimalspeeds for the ships and the best routing of ballast (empty) legs, as well as which cargos to load on controlled ships and which to spot charter. All feasible schedules are generated, the cost of each is accurately determined and the best set of schedules is selected. For the problems encountered, optimal integer solutions to set partitioning problems with thousands of binary variables have been achieved in less than a minute

Estimating Total Program Cost of a Long-Term, High-Technology, High-Risk Project with Task Durations and Costs That May Increase Over Time

Military Operations Research, 11, 2006, pp. 41-62.We plan a long-term project schedule for which the total budget depends upon the year the project finishes. Each task in the project can begin only when all its predecessor tasks have been completed, and each task has a range of feasible durations with a month-by-month cost profile for each duration. A task start can be delayed, but once started for some chosen duration, a task cannot be interrupted. Each task suffers some risk of delay and changed cost. Ignoring budget constraints, we use Monte Carlo simulation of the duration of each task in the project to infer the probability distribution of the project completion time. We then optimize a deterministic project schedule following budget guidance. Finally, we successively reschedule as the project progresses, simulating annual review of the active tasks, and possibly delaying each active task's duration and changing its monthly costs for its forecast duration. We do not require an independence assumption, so we can accommodate learning effects from completed tasks. U.S. Army Future Combat Systems (FCS) is our motivating application. FCS is a complex of information technologies, sensors, and command systems expected to require more than a decade and $16 billion to develop. The U.S. General Accounting Office finds FCS at significant risk of cost and schedule growth, and suggests two alternatives to a baseline Army plan. We analyze these three alternate project plans for FCS to discover which one can most likely be completed soonest and cheapest

Scheduling Coast Guard District Cutters

Interfaces, 26, March - April 1996, pp. 59-72Center for Infrastructure Defense (CID) Paper.United States Coast Guard (USCG) districts schedule cutters 180 feet or less in length to weekly statuses (statuses is USCGjargon for assignments) from which they primarily respond to calls for search and rescue, law enforcement, and pollution control. The First Coast Guard District, based in Boston, has one of the largest scheduling problems: Each of 16 cutters is as- signed weekly to one of six statuses to ensure patrol coverage, enforce equitable distribution of patrols, and honor restrictions on consecutive cutter statuses. When we state this quarterly scheduling problem as an elastic mixed-integer linear program, we obtain face-valid schedules—superior to manually prepared schedules for all measures of effectiveness considered—within a few minutes on a personal computer. Initial acceptance of the model was hampered by disruptive schedule revisions that re- sulted from minor changes in input. Modifications to preserve run-to-run persistence of solutions have brought success

How the U.S. Air Force Space Command Optimizes Long-Term Investment in Space Systems

Interfaces, 33, p.p. 1-14.United States Air Force Space Command spends billions of dollars each year acquiring and developing launch vehicles and space systems. The space systems in orbit must continually meet defensive and offensive requirements and remain interoperable over time. Space command can launch additional space systems only if it has a launch vehicle of sufficient capacity. Space planners using space and missile optimization analysis (SAMOA) consider a 24-year time horizon when determining which space assets and launch vehicles to fund and procure. A key tool which in SAMOA is an integer linear program called the space command optimizer of utility toolkit (SCOUT) that Space Command uses for long-range planning. SCOUT gives planner insight into the annual funding profiles needed to meet Space Command's acquisition goals. The 1999 portfolio of 74 systems will cost about #310 billion and includes systems that can lift satellites into orbit; yield information on space, surface, and subsurface events, activities, and threats; and destroy terrestrial, airborne, and space targets