A network isolation algorithm

A set of edges D called an isolation set, is said to isolate a set of nodes R from an undirected network if every chain between the nodes in R contains at least one edge from the set D. Associated with each edge of the network is a positive cost. The isolation problem is concerned with finding an isolation set such that the sum of its edge costs is a minimum. This paper formulates the problem of determining the minimal cost isolation as a 0–1 integer linear programming problem. An algorithm is presented which applies a branch and bound enumerative scheme to a decomposed linear program whose dual subproblems are minimal cost network flow problems. Computational results are given. The problem is also formulated as a special quadratic assignment problem and an algorithm is presented that finds a local optimal solution. This local solution is used for an initial bound.     

Optimal replacement of parts having observable correlated stages of deterioration

A single component system is assumed to progress through a finite number of increasingly bad levels of deterioration. The system with level i (0 ≤ i ≤ n) starts in state 0 when new, and is definitely replaced upon reaching the worthless state n. It is assumed that the transition times are directly monitored and the admissible class of strategies allows substitution of a new component only at such transition times. The durations in various deterioration levels are dependent random variables with exponential marginal distributions and a particularly convenient joint distribution. Strategies are chosen to maximize the average rewards per unit time. For some reward functions (with the reward rate depending on the state and the duration in this state) the knowledge of previous state duration provides useful information about the rate of deterioration.     

Optimality conditions for convex semi-infinite programming problems

This paper gives characterization of optimal Solutions for convex semiinfinite programming problems. These characterizations are free of a constraint qualification assumption. Thus they overcome the deficiencies of the semiinfinite versions of the Fritz John and the Kuhn-Tucker theories, which give only necessary or sufficient conditions for optimality, but not both.     

A branch-bound algorithm for the capacitated facilities location problem

This paper discusses a mixed integer programming method for solving the Facilities Location Problem with capacities on the facilities. The algorithm uses a Decomposition technique to solve the dual of the associated continuous problem in each branch-bound iteration. The method was designed to produce the global optimum solution for problems with up to 100 facilities and 1,000 customers. Computational experience and a complete example are also presented in the appendix.     

Problems in life cycle support cost estimation

Although industry is expected to design hardware to fit into a general support system and to be capable of arguing life-cycle system costs, adequate information has not been available on the support system in terms of policies and operating decision rules. Policies and operating decisions by users dominate engineering design decisions in determining life-cycle support costs. The relative effect of each of these decision areas on support costs has yet to be resolved empirically. Without an understanding of the sensitivity of support costs to alternative designs, capability is limited in design improvement and support of end items. Life-cycle costing of analysis under cost-effectiveness and the maintainability of integrated logistics support is open to question.     

Bayes sequential strategies for crossing a field containing absorption points

A sequential decision problem is considered in which N particles have to cross a given field. Two alternative crossing paths are available. An unknown number of absorption points J₁ and J₂ are planted at each of the crossing paths. The bivariate prior distribution of (J₁,J₂) is given. If a particle passes close to an absorption point it may survive with probability s, 0 < s < 1. If a particle is absorbed, both the particle and the absorption point are ruined. There is no replacement of ruined absorption points. All absorption points act independently. The particles crciss the field in a consecutive order, and a crossing path can be chosen for each particle. The objective is to maximize the expected number of survivors. The Bayes sequential procedure is characterized. The csmditions under which the Bayes strategy is determined by the maximal posterior survival probabilities are specified.     

Estimating critical path and arc probabilities in stochastic activity networks

This article describes a new procedure for estimating parameters of a stochastic activity network of N arcs. The parameters include the probability that path m is the longest path, the probability that path m is the shortest path, the probability that arc i is on the longest path, and the probability that arc i is on the shortest path. The proposed procedure uses quasirandom points together with information on a cutset ? of the network to produce an upper bound of O[(log K)^N?|?|+1/K] on the absolute error of approximation, where K denotes the number of replications. This is a deterministic bound and is more favorable than the convergence rate of 1/K^1/2 that one obtains from the standard error for K independent replications using random sampling. It is also shown how series reduction can improve the convergence rate by reducing the exponent on log K. The technique is illustrated using a Monte Carlo sampling experiment for a network of 16 relevant arcs with a cutset of ? = 7 arcs. The illustration shows the superior performance of using quasirandom points with a cutset (plan A) and the even better performance of using quasirandom points with the cutset together with series reduction (plan B) with regard to mean square error. However, it also shows that computation time considerations favor plan A when K is small and plan B when K is large.