Directional approach to gradual cover: the continuous case

The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed "directional gradual cover". Contrary to all gradual cover models, the joint cover depends on the facilities' directions. In order to calculate the joint cover, existing models apply the partial cover by each facility disregarding their direction. We develop a genetic algorithm to solve the facilities location problem and also solve the problem for facilities that can be located anywhere in the plane. The proposed modifications were extensively tested on a case study of covering Orange County, California

A modified Kolmogorov-Smirnov test for normality

In this paper we propose an improvement of the Kolmogorov-Smirnov test for normality. In the current implementation of the Kolmogorov-Smirnov test, a sample is compared with a normal distribution where the sample mean and the sample variance are used as parameters of the distribution. We propose to select the mean and variance of the normal distribution that provide the closest fit to the data. This is like shifting and stretching the reference normal distribution so that it fits the data in the best possible way. If this shifting and stretching does not lead to an acceptable fit, the data is probably not normal. We also introduce a fast easily implementable algorithm for the proposed test. A study of the power of the proposed test indicates that the test is able to discriminate between the normal distribution and distributions such as uniform, bi-modal, beta, exponential and log-normal that are different in shape, but has a relatively lower power against the student t-distribution that is similar in shape to the normal distribution. In model settings, the former distinction is typically more important to make than the latter distinction. We demonstrate the practical significance of the proposed test with several simulated examples.Closest fit; Kolmogorov-Smirnov; Normal distribution

The obnoxious facilities planar p-median problem

In this paper we propose the planar obnoxious p-median problem. In the p-median problem the objective is to find p locations for facilities that minimize the weighted sum of distances between demand points and their closest facility. In the obnoxious version we add constraints that each facility must be located at least a certain distance from a partial set of demand points because they generate nuisance affecting these demand points. The resulting problem is extremely non-convex and traditional non-linear solvers such as SNOPT are not efficient. An efficient solution method based on Voronoi diagrams is proposed and tested. We also constructed the efficient frontiers of the test problems to assist the planers in making location decisions

On minimax optimization problems

We give a short proof that in a convex minimax optimization problem in k dimensions there exist a subset of k + 1 functions such that a solution to the minimax problem with those k + 1 functions is a solution to the minimax problem with all functions. We show that convexity is necessary, and prove a similar theorem for stationary points when the functions are not necessarily convex but the gradient exists for each function.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47909/1/10107_2005_Article_BF01581038.pd

On the quadratic assignment problem

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25006/1/0000433.pd