Optimal maintenance models for systems subject to failure–A Review

This paper is a state-of-the-art review of the literature related to optimal maintenance models of systems subject to failure. The emphasis is on work appearing since the 1976 survey, “A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems,” by W.P. Pierskalla and J.A. Voelker, published in this journal.     

Solving a (0, 1) hyperbolic program by branch and bound

A problem in (0, 1) hyperbolic programming is formulated and solved by the use of branch and bound methods. Computational results are presented including a comparison among several branching rules. Heuristic methods for quickly finding relatively good feasible solutions are presented and tested. The problem finds application in the scheduling of common carriers. In the solution of the main problem, a subproblem is identified and solved. A geometric analogue is presented, which allows an interesting interpretation of the subproblem. The subproblem itself finds application in the design of gambles.     

Simulating stable stochastic systems,V: Comparison of ratio estimators

The regenerative method for estimating parameters in a simulation requires the simulator to estimate the ratio of two means. Five point estimates and four confidence intervals for this ratio have been computed for three stochastic simulations. The jackknife method appears to be the most promising for both point and interval estimation.     

Algorithms for minimizing total cost,bottleneck time and bottleneck shipment in transportation problems

We consider the transportation problem of determining nonnegative shipments from a set of m warehouses with given availabilities to a set of n markets with given requirements. Three objectives are defined for each solution: (i) total cost, TC, (ii) bottleneck time, BT (i.e., maximum transportation time for a positive shipment), and (iii) bottleneck shipment, SB (i.e., total shipment over routes with bottleneck time). An algorithm is given for determining all efficient (pareto-optimal or nondominated) (TC, BT) solution pairs. The special case of this algorithm when all the unit cost coefficients are zero is shown to be the same as the algorithms for minimizing BT. provided by Szwarc and Hammer. This algorithm for minimizing BT is shown to be computationally superior. Transportation or assignment problems with m=n=100 average about a second on the UNIVAC 1108 computer (FORTRAN V)) to the threshold algorithm for minimizing BT. The algorithm is then extended to provide not only all the efficient (TC, BT) solution pairs but also, for each such BT, all the efficient (TC, SB) solution pairs. The algorithms are based on the cost operator theory of parametric programming for the transportation problem developed by the authors.     

An M/M/1 queue with delayed feedback

We present some results for M/M/1 queues with finite capacities with delayed feedback. The delay in the feedback to an M/M/1 queue is modelled as another M-server queue with a finite capacity. The steady state probabilities for the two dimensional Markov process {N(t), M(t)} are solved when N(t) = queue length at server 1 at t and M(t) = queue length at server 2 at t. It is shown that a matrix operation can be performed to obtain the steady state probabilities. The eigenvalues of the operator and its eigenvectors are found. The problem is solved by fitting boundary conditions to the general solution and by normalizing. A sample problem is run to show that the solution methods can be programmed and meaningful results obtained numerically.     

The divisionalized firm revisited—A comment on Enzer's “the static theory of transfer pricing”

Three different solutions to a very simple transfer pricing problem are outlined and contrasted. These are labeled by their authors: Hirshleifer, Enzer, and Ronen and McKinney. Weaknesses associated with each solution are pointed out.     

Estimating normal tail probabilities

The estimation problem of normal tail probabilities is considered. The form of generalized Bayes estimators is derived and the asymptotic behavior of the mean square errors is studied. This study shows that the best unbiased estimator, a formula for which is given, is superior to the maximum likelihoood estimator or to a class of generalized Bayes procedures for large parametric values, but can be significantly improved for moderate values of the parameter.