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.     

Test selection for a mass screeening program

Periodic mass screening is the scheduled application of a test to all members of a population to provide early detection of a randomly occurring defect or disease. This paper considers periodic mass screening with particular reference to the imperfect capacity of the test to detect an existing defect and the associated problem of selecting the kind of test to use. Alternative kinds of tests differ with respect to their reliability characteristics and their cost per application. Two kinds of imperfect test reliability are considered. In the first case, the probability that the test will detect an existing defect is constant over all values of elapsed time since the incidence of the defect. In the second case, the test will detect the defect if, and only if, the lapsed time since incidence exceeds a critical threshold T which characterizes the test. The cost of delayed detection is an arbitrary increasing function (the “disutility function”) of the duration of the delay. Expressions for the long-run expected disutility per unit time are derived for the above two cases along with results concerning the best choice of type of test (where the decision rules make reference to characteristics of the disutility function).     

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.     

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.     

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.     

The estimation of P(x < Y) for distributions useful in life testing

In this paper the reliability function K = P(X < Y) has been estimated when X and Y follow gamma, exponential or bivariate exponential distributions. The paper is partly expository.     

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.     

A new storage reduction technique for the solution of the group problem

This paper shows that by making use of an unusual property of the decision table associated with the dynamic programming solution to the goup problem, it is possible to dispense with table storage as such, and instead overlay values for both the objective and history functions. Furthermore, this storage reduction is accomplished with no loss in computational efficiency. An algorithm is presented which makes use of this technique and incorporates various additional efficiencies. The reduction in storage achieved for problems from the literature is shown.