Simplicial fixed point algorithms: Volume 129 in: Mathematical Centre Tracts,Mathematisch Centrum,Amsterdam, 1980, iv + 172 pages,Dfl.21.00

This work provides a reliability analysis for power units which are deliberately shutdown when undemanded. A gas turbine is a common example of such a unit. Two appropriate interrelated reliability criteria are mathematically formulated and the relation to their ordinary counterparts is investigated. Using semi-Markov and renewal theory methods these criteria are computed under different assumptions with regard to the stochastic behavior of the demand on the unit and the time to failure and repair time distributions.     

Local networks for computer communications: A. WEST and P. JANSON (Eds.) Proceedings of the IFIP Working Group 6.4, International Workshop on Local Networks,Zürich,Switzerland, August 27–29, 1980, North-Holland,Amsterdam, 1981, xiii + 470 pages,Dfl.125.00

In this paper we present two lower bounds for the p-median problem, the problem of locating p facilities (medians) on a network. These bounds are based on two separate lagrangean relaxations of a zero-one formulation of the problem with subgradient optimisation being used to maximise these bounds. Penalty tests based on these lower bounds and a heuristically determined upper bound to the problem are developed and shown to result in a large reduction in problem size. The incorporation of the lower bounds and the penalty tests into a tree search procedure is described and computational results are given for problems with an arbitrary number of medians and having up to 200 vertices. A comparison is also made between these algorithms and the dual-based algorithm of Erlenkotter.