Quantification of contractor risk

This paper presents a quantitative index of the level of risk assumed by a contractor in various contract type situations. The definition includes expression of real world uncertainty and contractor's utility for money. Examples are given for the major contract types and special applications are discussed.     

Differential game theoretic analysis of a problem of warfare

The present article considers a problem of missile warfare. It is formulated as a problem of economics and treated as a differential game. Some optimal strategies of targeting and firing of missiles are derived. Conditions under which such a war can be prevented are also developed.     

A test for the hypothesis that two extreme-value scale parameters are equal

A statistic is determined for testing the hypothesis of equality for scale parameters from two populations, each of which has the first asymptotic distribution of smallest (extreme) values. The probability distribution is derived for this statistic, and critical values are determined and given in tabular form for a one-sided or two-sided alternative, for censored samples of size n₁ and n₂, n₁ = 2, 3, …. 6, n₂ = 2, 3, …. 6. The power function of the test for certain alternatives is also calculated and listed in each case considered.     

A note on cycling in the simplex method

Although cycling in the simplex method has long been known, a number of theoretical questions concerning cycling have not been fully answered. One of these, stated in [3], is to find the smallest example of cycling, and Beale's example with three equations and seven variables is conjectured to be the smallest one. The exact bounds on dimensions of cycling examples are established in this paper. We show that Beale's example is the smallest one which cycles at a non-optimal solution, that a smaller one can cycle at the optimum, and that, in general (including the completely degenerate case), a cycling example must have at least two equations, at least six variables, and at least three non-basic variables. Examples and geometries are given for the extreme cases, showing that the bounds are sharp.     

Solutions for a class of n-person games in partition function form

A unique polyhedral solution is given for most n-person games in partition function form when only partitions into coalitions with 1, n-1, and n players have large payoffs.     

Heuristic modeling of supply availabilities in large networks

The objective of this article is to describe heuristic solutions to the problem of modeling inventories at each node of a large network in the context of a computer simulation model of that network. The heuristic solutions are compared with the mathematical solution which is too unwieldy for use in a simulation model. The Weibull cumulative distribution is used as an approximation for the heuristic models. We question whether the good performance of the Weibull is coincidence or perhaps mathematically justifiable.     

Cyclic preference scheduling for nurses using branch and price

This paper presents a new methodology to solve the cyclic preference scheduling problem for hourly workers. The focus is on nurse rostering but is applicable to any organization in which the midterm scheduling decision must take into account a complex of legal, institutional, and preferential constraints. The objective is to strike a balance between satisfying individual preferences and minimizing personnel costs. The common practice is to consider each planning period independently and to generate new rosters at the beginning of each. To reduce some of the instability in the process, there is a growing trend toward cyclic schedules, which are easier to manage and are generally perceived to be more equitable. To address this problem, a new integer programming model is presented that combines the elements of both cyclic and preference scheduling. To find solutions, a branch‐and‐price algorithm is developed that makes use of several branching rules and an extremely effective rounding heuristic. A unique feature of the formulation is that the master problem contains integer rather than binary variables. Computational results are reported for problem instances with up to 200 nurses. Most were solved within 10 minutes and many within 3 minutes when a double aggregation approach was applicable. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

Simulation of nonhomogeneous poisson processes by thinning

A simple and relatively efficient method for simulating one-dimensional and two-dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.