Visibility probabilities on line segments in three-dimensional spaces subject to random poisson fields of obscuring spheres

The methodology of determining simultaneous visibility probabilities and points on line segments is extended to problems of three-dimensional spaces, with Poisson random fields of obscuring spheres. Required functions are derived analytically and a numerical example is given for a special case of a standard Poisson field, with uniform distribution of sphere diameters.     

An assumption-free convergence analysis for a perturbation of the scaling algorithm for linear programs,with application to the L1 estimation problem

This article is concerned with the scaling variant of Karmarkar's algorithm for linear programming problems. Several researchers have presented convergence analyses for this algorithm under various nondegeneracy types of assumptions, or under assumptions regarding the nature of the sequence of iterates generated by the algorithm. By employing a slight perturbation of the algorithm, which is computationally imperceptible, we are able to prove without using any special assumptions that the algorithm converges finitely to an ε-optimal solution for any chosen ε > 0, from which it can be (polynomically) rounded to an optimum, for ε > 0 small enough. The logarithmic barrier function is used as a construct for this analysis. A rounding scheme which produces an optimal extreme point solution is also suggested. Besides the non-negatively constrained case, we also present a convergence analysis for the case of bounded variables. An application in statistics to the L₁ estimation problem and related computational results are presented.     

A general age replacement model with minimal repair

A general age replacement is introduced which incorporates minimal repair, planned and unplanned replacements, and costs which depend on time. Finite and infinite horizon results are obtained. Various special cases are considered. Furthermore, a shock model with general cost structure is considered.     

A poissonian binomial model with constrained parameters

The article examines ways of computing cumulative probabilities for a constrained Poissonian binomial distribution arising from a model of a weapon defense system.     

Algorithmic and approximation analyses of the shorter queue model

A system of two parallel queues where the arrivals from a single stream of customers join the shorter queue is considered. Arrivals form a homogeneous Poisson stream and the service times in each of the two queues are independent exponential variates. By treating one of the queues as bounded, the steady-state probability vector for the system can be expressed in a modified matrix-geometric form and can be computed efficiently. Computational procedures for the sojourn time distribution and characteristics of the departure stream are developed. Some numerical results are presented, and based on these results an efficient approximation scheme for the model is developed which can be readily extended to systems with more than two parallel queues.     

The orienteering problem

Orienteering is a sport in which start and end points are specified along with other locations. These other locations have associated scores. Competitors seek to visit, in a fixed amount of time, a subset of these locations on the way from the start point to the end point in order to maximize the total score. An effective center-of-gravity heuristic is presented that outperforms heuristics from the literature.     

A flow-shop problem with sequence-dependent additive setup times

The flow-shop scheduling problem with sequence-dependent additive setup times is considered as a special case of the general problem, and a polynomially bounded approximate method is developed to find a minimum makespan permutation schedule. The approximate algorithm is shown to yield optimal results for the two-machine case. A version of Sule's model is defined that produces the first approximation of the optimal solution for this problem. Computational experience along with numerical examples are provided to test the effectiveness of the method.     

Extension of Bolzano search to rectangles which preserves rectangles as iterates

Multivariable elimination algorithms, which may be regarded as generalizations of various one-dimensional search procedures, have not found wide application. A probable reason may be the generally very irregularly shaped regions of uncertainty that evolve iteratively in the procedures. Hence hope for practical salvage of this class of algorithms seems to lie in controlling the shape of the successively smaller regions of uncertainty. In this article an extension of Bolzano search to rectangles which preserves rectangular iterates is given. Since the result is essentially geometrical in nature, a geometric proof of this procedure is given. Hopefully the proof procedure will be of independent interest. A numerical illustration of the procedure is given for a game problem, such problems lending themselves to this method.     

A dual criteria sequencing problem with earliness and tardiness penalties

We consider the problem of sequencing n jobs on a single machine, with each job having a processing time and a common due date. The common due date is assumed to be so large that all jobs can complete by the due date. It is known that there is an O(n log n)‐time algorithm for finding a schedule with minimum total earliness and tardiness. In this article, we consider finding a schedule with dual criteria. The primary goal is to minimize the total earliness and tardiness. The secondary goals are to minimize: (1) the maximum earliness and tardiness; (2) the sum of the maximum of the squares of earliness and tardiness; (3) the sum of the squares of earliness and tardiness. For the first two criteria, we show that the problems are NP‐hard and we give a fully polynomial time approximation scheme for both of them. For the last two criteria, we show that the ratio of the worst schedule versus the best schedule is no more than . © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 422–431, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10020