Periodic replacement with minimal repair at failure and adjustment costs

We investigate periodic replacement policies with minimal repair at failure, thereby, minimizing the average expected cost per unit time over an infinite time span. The standard cost structure is modified by the introduction of a term which takes adjustment costs into account.     

A heuristic routine for solving large loading problems

The loading problem involves the optimal allocation of n objects, each having a specified weight and value, to m boxes, each of specified capacity. While special cases of these problems can be solved with relative ease, the general problem having variable item weights and box sizes can become very difficult to solve. This paper presents a heuristic procedure for solving large loading problems of the more general type. The procedure uses a surrogate procedure for reducing the original problem to a simpler knapsack problem, the solution of which is then employed in searching for feasible solutions to the original problem. The procedure is easy to apply, and is capable of identifying optimal solutions if they are found.     

The search for an intelligent evader concealed in one of an arbitrary number of regions

This paper considers the search for an evader concealed in one of an arbitrary number of regions, each of which is characterized by its detection probability. We shall be concerned here with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move; his aim is to maximize the expected time to detection, while the searcher attempts to minimize it. The situation where two regions are involved has been studied previously and reported on recently. This paper represents a continuation of this analysis. It is normally true that as the number of regions increases, optimal strategies for both searcher and evader are progressively more difficult to determine precisely. However it will be shown that, generally, satisfactory approximations to each are almost as easily derived as in the two region problem, and that the accuracy of such approximations is essentially independent of the number of regions. This means that so far as the evader is concerned, characteristics of the two-region problem may be used to assess the accuracy of such approximate strategies for problems of more than two regions.     

A cost analysis of sampling inspection under Military Standard 105D

Military Standard 105D has been almost universally adopted by government and private consumers for the lot-by-lot sampling inspection of product which may be inspected on a dichotomoun basis The plan specifies, for each lot size, a random sample size and set of acceptance numbers (maximum allowable number of defectives in each sample). The acceptance numbers are based upon the binomial distribution and depend upon the quality required by the purchaser. Where several consecutive lots are submitted, a shift to less severe (“reduced”) inspection or more severe (“tightened”) inspection is specified when the ongoing quality is very high or low. Further experience permits a return to normal sampling from either of these states This paper examines the long range costs of such a sampling scheme. The three inspection types are considered as three distinct Markov chains, with periodic transitions from chain to chain. The expected sample size and the expected proportion of rejected product are determined as a function of the two parameters under control of the manufacturer, lot size and product quality. Some numerical examples are given which illustrate how to compute the overall cost of sampling inspection. Suggestions are made concerning the choice of parameters to minimize this cost.     

The initial provisioning decision for insurance type items

Initial provisioning decisions (inventory stocking requirements) for low demand items often have to be made without much knowledge of what future demand rates will be. When the nature of an item is such that little demand for it is expected, the problem of whether to stock initially or risk not stocking the item is most critical. This report discusses this problem and presents decision procedures which can be used to handle this aspect of initial provisioning. The procedures relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion. The criterion function measures the total system degredation as a function of the events of having items out of stock when demand occurs. Several different policy functions are discussed and the provisioning decision rules which apply to each are presented. Demand rate information is handled through a Bayesian type approach. The decision rules presented in this report can be utilized to either determine stocking requirements within a budgetary constraint, or determine the relative stocking desirability on an item-by-item basis.     

A chance-constrained distribution problem

The transportation model with supplies (S_i) and demands (D_i) treated as bounded variables developed by Charnes and Klingman is extended to the case where the S_i and D_i are independently and uniformly distributed random variables. Chance constraints which require that demand at the jth destination will be satisfied with probability at least β_i and that stockout at the ith origin will occur with probability less than α_i are imposed. Conversion of the chance constraints to their linear equivalents results in a transportation problem with one more row and column than the original with some of the new arcs capacitated. The chance-constrained formulation is extended to the transshipment problem.     

The effect of correlated exponential service times on single server tandem queues

An investigation via simulation of system performance of two stage queues in series (single server, first-come, first-served) under the assumption of correlated exponential service times indicates that the system's behavior is quite sensitive to departures from the traditional assumption of mutually independent service times, especially at higher utilizations. That service times at the various stages of a tandem queueing system for a given customer should be correlated is intuitively appealing and apparently not at all atypical. Since tandem queues occur frequently, e.g. production lines and the logistics therewith associated, it is incumbent on both the practitioner and the theoretician that they be aware of the marked effects that may be induced by correlated service times. For the case of infinite interstage storage, system performance is improved by positive correlation and impaired by negative correlation. This change in system performance is reversed however for zero interstage storage and depends on the value of the utilization rate for the case where interstage storage equals unity. The effect due to correlation is shown to be statistically significant using spectral analytic techniques. For correlation equal unity and infinite interstage storage, results are provided for two through twenty-five stages in series to suggest how adding stages affects system performance for ρ>0. In this extreme case of correlation, adding stages has an effect on system performance which depends markedly on the utilization rate. Recursive formulae for the waiting time per customer for the cases of zero, one, and infinite interstage storage are derived.     

The development and evaluation of a cost-based composite scheduling rule

A cost-based composite scheduling rule is developed and evaluated in comparison with three other well-researched scheduling rules—SPT, S/OPN, and SST. This cost rule permits the optimization of more than one performance measure at a time. The priority number that is used for scheduling operations through each machine group is based on four separate performance measures—(1) In-process Inventory, (2) Facilities Utilization, (3) Lateness, and (4) Mean Setup Time. The factorial experimental design involved three factor levels of loads, three factor levels of cost, and three factor levels of mean time. Analysis of variance was performed on each of the five output measures to study the effects of each of the three factors on each individual rule. Rank-order comparisons between rules were also made; and, finally, general conclusions with regard to the effectiveness and flexibility of the Cost Rule were drawn.     

A note on some series representations of the integral of a bivariate normal distribution over an offset circle

Consider the problem of computing an offset circle probability under a normal distribution. One approach is to utilize an infinite series representation in which case it is important to have rapid convergence and a good upper bound on the error introduced by consideration of only a finite number of terms of the series. We relate three seemingly different series representations. In particular we show how two series representations for the bivariate case can be obtained by specializing more general results of Harold Ruben.