Congestion tolls: Equilibrium and optimality

An example of a network with flow costs depending on congestion is presented for which no system of tolls and subsidies exists which can ensure that all equilibria in the game of route selection are Pareto optimal.     

An approach to the allocation of common costs of multi-mission systems

Many Naval systems, as well as other military and civilian systems, generate multiple missions. An outstanding problem in cost analysis is how to allocate the costs of such missions so that their true costs can be determined and resource allocation optimized. This paper presents a simple approach to handling this problem for single systems. The approach is based on the theory of peak-load pricing as developed by Marcel Boiteux. The basic principle is that the long-run marginal cost of a mission must be equal to its “price.” The implication of this is that if missions can cover their own marginal costs, they should also be allocated some of the marginal common costs. The proportion of costs to be allocated is shown to a function of not only the mission-specific marginal costs and the common marginal costs, but also of the “mission price.” Thus, it is shown that measures of effectiveness must be developed for rational cost allocation. The measurement of effectiveness has long been an intractable problem, however. Therefore, several possible means of getting around this problem are presented in the development of the concept of relative mission prices.     

The mother of all post-mortems

The most striking finding of the Chilcot Report is that the record reveals little that was previously unknown. A key point for its authors is that diplomatic alternatives had not been exhausted when the US and UK went to war. But, short of an armed attack by the other side, it is hard to say when they would have been. Here what was crucial was the belief shared by Bush and Blair that Saddam Hussain would not and could not change. For the British the issue of whether alternatives to war remained is particularly important because of its implications for international law, something that did not trouble the Americans. It remains unclear if Blair would have gained or lost leverage over Bush had he made British participation contingent on better American policy, for example on developing a workable plan for the reconstruction of Iraq.     

Allocation of quality improvement targets based on investments in learning

Purchased materials often account for more than 50% of a manufacturer's product nonconformance cost. A common strategy for reducing such costs is to allocate periodic quality improvement targets to suppliers of such materials. Improvement target allocations are often accomplished via ad hoc methods such as prescribing a fixed, across‐the‐board percentage improvement for all suppliers, which, however, may not be the most effective or efficient approach for allocating improvement targets. We propose a formal modeling and optimization approach for assessing quality improvement targets for suppliers, based on process variance reduction. In our models, a manufacturer has multiple product performance measures that are linear functions of a common set of design variables (factors), each of which is an output from an independent supplier's process. We assume that a manufacturer's quality improvement is a result of reductions in supplier process variances, obtained through learning and experience, which require appropriate investments by both the manufacturer and suppliers. Three learning investment (cost) models for achieving a given learning rate are used to determine the allocations that minimize expected costs for both the supplier and manufacturer and to assess the sensitivity of investment in learning on the allocation of quality improvement targets. Solutions for determining optimal learning rates, and concomitant quality improvement targets are derived for each learning investment function. We also account for the risk that a supplier may not achieve a targeted learning rate for quality improvements. An extensive computational study is conducted to investigate the differences between optimal variance allocations and a fixed percentage allocation. These differences are examined with respect to (i) variance improvement targets and (ii) total expected cost. For certain types of learning investment models, the results suggest that orders of magnitude differences in variance allocations and expected total costs occur between optimal allocations and those arrived at via the commonly used rule of fixed percentage allocations. However, for learning investments characterized by a quadratic function, there is surprisingly close agreement with an “across‐the‐board” allocation of 20% quality improvement targets. © John Wiley & Sons, Inc. Naval Research Logistics 48: 684–709, 2001     

Value added analysis for army equipment modernization

This paper describes the Value Added Analysis methodology which is used as part of the U.S. Army's Planning, Programming, Budgeting, and Execution System to assist the Army leadership in evaluating and prioritizing competing weapon system alternatives during the process of building the Army budget. The Value Added Analysis concept uses a family of models to estimate an alternative system's contribution to the Army's effectiveness using a multiattribute value hierarchy. A mathematical optimization model is then used to simultaneously determine an alternative's cost‐benefit and to identify an optimal mix of weapon systems for inclusion in the Army budget. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 233–253, 1999     

Using multiple searchers in constrained-path,moving-target search problems

The search theory open literature has paid little, if any, attention to the multiple-searcher, moving-target search problem. We develop an optimal branch-and-bound procedure and six heuristics for solving constrained-path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one-, two-, and three-searcher test problem considered. For one- and two-searcher problems, the same heuristic's solution time is less than that of other heuristics. For three-searcher problems, a genetic algorithm implementation obtains the best-known solution in as little as 20% of other heuristic solution times. © 1996 John Wiley & Sons, Inc.     

Scheduling peacetime rotation of Pakistan army units

Because Pakistan has varying climates and terrains, the Pakistan Army rotates its units between peacetime locations so that no unit endures inequitable hardship or enjoys unfair advantage. Army policy specifies strict constraints on unit rotations, such as the length of a unit's stay in any location, the number of units moving at any time, and the allowable replacements for any moving unit. Scheduling rotations manually in accordance with these rules, as is currently practiced, is extremely difficult and time consuming. This article presents an integer programming model that finds feasible, minimum-cost schedules for the Pakistan Army's desired planning horizons. The model also ensures that the units are positioned at the end of the planning horizon so that feasible schedules exist for future planners. The model is implemented with commercially available optimization software. Schedules are obtained for realistic test problems in less than an hour on a personal computer. © 1995 John Wiley & Sons, Inc.     

Equipment replacement under technological change

For infinite-horizon replacement economy problems it is common practice to truncate the problem at some finite horizon. We develop bounds on the error due to such a truncation. These bounds differ from previous results in that they include both revenues and costs. Bounds are illustrated through a numerical example from a real case in vehicle replacement. © 1994 John Wiley & Sons, Inc.