Systems defense games: Colonel blotto,command and control

The classical “Colonel Blotto” games of force allocation are generalized to include situations in which there are complementarities among the targets being defended. The complementarities are represented by means of a system “characteristic function,” and a valuation technique from the theory of cooperative games is seen to indicate the optimal allocations of defense and attack forces. Cost trade-offs between systems defense and alternative measures, such as the hardening of targets, are discussed, and a simple example is analyzed in order to indicate the potential of this approach.     

On convexity proofs in location theory

It is often assumed in the facility location literature that functions of the type ø_i(x_i, y) = β_i[(x_i-x)²+(y_i-y)²]^K/2 are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are given.     

Insurance type item provisioning guidelines

Policy decisions for insurance type items, where zero or one unit is maintained at the depot, are more difficult and more critical than decisions for common supply items. This report presents results of developing initial provisioning guidelines for insurance type items. The guidelines are based on examination of lifetime costs and benefits. Costs of stocking an item as compared with not stocking are developed through a sinking fund annual payment formulation. Benefits of stocking are developed as stationary reduction in time weighted backorders experienced. A resource allocation formulation yields an optimal policy for allocating a fixed budget. The guideline is presented with refinements based on a sample of items. A figure of merit is calculated for each item, and if it is large the item is stocked while if small it is not stocked. Empirical definitions for large and small are developed based on sample data. Estimation techniques are discussed for deriving all of an item's parameters needed to compute its figure of merit. A Bayes procedure is suggested based on family group Experienced Demand Replacement Factors. This and other techniques are discussed.     

A note on a computational model for a data/voice communication queueing system

Certain types of communication nodes can be viewed as multichannel queueing systems with two types of arrival streams. Data arrivals are characterized by high arrival and service rates and have the ability to queue if all service channels are busy. Voice arrivals have small arrival and service rates and do not have the ability to wait when the channels are full. Computational procedures are presented for obtaining the invariant probabilities associated with the queueing model.     

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.