Storage problems when demand is “all or nothing”

An inventory of physical goods or storage space (in a communications system buffer, for instance) often experiences “all or nothing” demand: if a demand of random size D can be immediately and entirely filled from stock it is satisfied, but otherwise it vanishes. Probabilistic properties of the resulting inventory level are discussed analytically, both for the single buffer and for multiple buffer problems. Numerical results are presented.     

Spike swapping in basis reinversion

During basis reinversion of either a product form or elimination form linear programming system, it may become necessary to swap spike columns to effect the reinversion and maintain the desired sparsity characteristics. This note shows that the only spikes which need be examined when an interchange is required are those not yet processed in the current external bump.     

Techniques for establishing ergodic and recurrence properties of continuous-valued markov chains

We present techniques for classifying Markov chains with a continuous state space as either ergodic or recurrent. These methods are analogous to those of Foster for countable space chains. The theory is presented in the first half of the paper, while the second half consists of examples illustrating these techniques. The technique for proving ergodicity involves, in practice, three steps: showing that the chain is irreducible in a suitable sense; verifying that the mean hitting times on certain (usually bounded) sets are bounded, by using a “mean drift” criterion analogous to that of Foster; and finally, checking that the chain is such that bounded mean hitting times for these sets does actually imply ergodicity. The examples comprise a number of known and new results: using our techniques we investigate random walks, queues with waiting-time-dependent service times, dams with general and random-release rules, the s-S inventory model, and feedback models.     

Evaluation of commonly used rules for detecting “steady state” in computer simulation

A definition of the problem of the initial transient with respect to the steady-state mean value has been formulated. A set of criteria has been set forth by which the efficaacy of any proposed rule may be assessed. Within this framework, five heuristic rules for predicting the approximate end of transiency, four of which have been quoted extensively in the simulation literature, have been evaluated in the M/M/1 situation. All performed poorly and are not suitable for their intended use.     

The distribution of recoverable inventory items from a repair center when the number of consumption centers is large

This paper considers real-time decision rules for an inventory system where items are repaired than “used up.” The problem is to decide which user in the system has the greatest need for the newly available inventory items coming out of repair. The main result shows that two published approahes, the Transportation Time Look Ahead policy and METRIC, are optimal when the number of users gets large. A useful byproduct of the proof is a lower bound on the average backorder rate for a repair-inventory system of any size.     

Two queueing systems sharing the same finite waiting room

In this paper, we consider the analysis of two M/G/1 queueing systems sharing the same finite waiting room. An exact analysis is given for several special cases, and then an algorithm is developed which approximates the system behavior for the general problem. Comparisons are made between the special cases and the algorithm.     

A probability model for initial crack size and fatigue life of gun barrels

With constant firing, metal fatigue produces cracks in a gun barrel. The useful life of the barrel comes to an end when a crack develops to a critical size. The theory of Fracture Mechanics suggests a formula for crack size growth rate. This formula can be used to determine the life of a barrel, depending on the initial and critical crack sizes and other factors. The initial crack size turns out to be a dominant factor. Unfortunately, accurate measurements are not generally available on the initial crack size. In this paper, we propose a simple probability model for the initial crack size and this, in turn, leads to a probability distribution of the life of the barrel. This last distribution is the well-known exponential distribution with a location shift. The simplicity of this final result is one of the factors that make the model appealing.     

Counterexamples to optimal permutation schedules for certain flow shop problems

It is well known that a minimal makespan permutation sequence exists for the n × 3 flow shop problem and for the n × m flow shop problem with no inprocess waiting when processing times for both types of problems are positive. It is shown in this paper that when the assumption of positive processing times is relaxed to include nonnegative processing times, optimality of permutation schedules cannot be guaranteed.     

Stochastic duels with displacements (suppression)

The stochastic duel is extended to include the possibility of a near-miss on each round fired, which causes the opponent to displace. During displacement, the displacing contestant cannot return the fire but is still a target for his opponent. An alternative interpretation of this model is to consider the displacement time as the time a contestant's fire is suppressed by his opponent's fire and that he does not move, but merely ceases fire temporarily. All times are exponentially distributed.     

Surrogate duality in a branch-and-bound procedure

Recent research has led to several surrogate multiplier search procedures for use in a primal branch-and-bound procedure. As single constrained integer programming problems, the surrogate subproblems are also solved via branch-and-bound. This paper develops the inner play between the surrogate subproblem and the primal branch-and-bound trees which can be exploited to produce a number of computational efficiencies. Most important is a restarting procedure which precludes the need to solve numerous surrogate subproblems at each node of a primal branch-and-bound tree. Empirical evidence suggests that this procedure greatly reduces total computation time.