The economic effects of inspector error on attribute sampling plans

In this paper the effects of inspector error on a cost-based quality control system are investigated. The system examined is of a single sampling plan design involving several cost components. Both type I and type II inspector errors are considered. The model employs a process distribution, thus assuming that a stochastic process of some kind governs the quality of incoming lots. Optimal plan design is investigated under both error-free and error-prone inspection procedures and some comparisons are made.     

Sequential determination of inspection epochs for reliability systems with general lifetime distributions

The problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel. Lifetime distribution is arbitrary, but known. The optimization is carried with respect to two cost factors: the cost of inspecting a component and the cost of failure. The inspection epochs are determined so that the expected cost of the whole system per time unit per cycle will be minimized. The optimization process depends in the general case on the whole failure history of the system. This dependence is characterized. The cases of Weibull lifetime distributions are elaborated and illustrated numerically. The characteristics of the optimal inspection intervals are studied theoretically.     

A convex property of an ordered flow shop sequencing problem

A flow shop sequencing problem with ordered processing time matrices is considered. A convex property for the makespan sequences of such problems is discussed. On the basis of this property an efficient optimizing algorithm is presented. Although the proof of optimality has not been developed, several hundred problems were solved optimally with this procedure.     

Optimum sequential search with discrete locations and random acceptance errors

Much work has been done in search theory; however, very little effort has occurred where an object's presence at a location can be accepted when no object is present there. The case analyzed is of this type. The number of locations is finite, a single object is stationary at one location, and only one location is observed each step of the search. The object's location has a known prior probability distribution. Also known are the conditional probability of acceptance given the object's absence (small) and the conditional probability of rejection given the object's presence (not too large); these Probabilities remain fixed for all searching and locations. The class of sequential search policies which terminate the search at the first acceptance is assumed. A single two-part optimization criterion is considered. The search sequence is found which (i) minimizes the probability of obtaining n rejections in the first n steps for all n, and (ii) maximizes the probability that the first acceptance occurs within the first n steps and occurs at the object's location for all n. The optimum sequential search policy specifies that the next location observed is one with the largest posterior probability of the object's presence (evaluated after each step from Bayes Rule) and that the object is at the first location where acceptance occurs. Placement at the first acceptance seems appropriate when the conditional probability of acceptance given the object's absence is sufficiently small. Search always terminates (with probability one). Optimum truncated sequential policies are also considered. Methods are given for evaluating some pertinent properties and for investigating the possibility that no object occurs at any location.     

The performance of cannibalization policies in a maintenance system with spares,repair, and resource constraints

This article presents the results of comparing the performance of several cannibalization policies using a simulation model of a maintenance system with spares, repair, and resource constraints. Although the presence of cannibalization has been incorporated into a number of maintenance system models reported in the literature, the questions of whether cannibalization should be done and what factors affect canibalization have received little attention. Policies tested include both no cannibalization and unlimited cannibalization as well as other based on the number of maintenance personnel available, the short-term machine failure rate at the time of cannibalization, and the relationship between the mean cannibalization and repair rates. The best policies found are those that allow cannibalization only when it can be done quickly relative to repair or when it can be done without delaying part repair actions. The policy of complete cannibalization (always cannibalize when it is possible) is found to perform poorly except when either average maintenance personnel utilization is very low or when mean cannibalization times are very short relative to mean repair times. The latter result casts doubts on the appropriateness of the assumption of complete cannibalization in many models in the literature.     

A note on the limitations of goal programming as observed in resource allocation for marine environmental protection

After first formulating the problem of the Marine Environmental Protection program of the Coast Guard as a multiple-objective linear program, we investigate the applicability and limitations of goal programming. We point out how the preemptive goal-programming approach is incompatible with utility preferences. Then we observe the tendency of optimal solutions for standard linear goal programs to occur at extreme points. We also note problems of more general approaches, such as dealing with additively separable approximations to preferences.     

A decomposable transshipment algorithm for a multiperiod transportation problem

A dynamic version of the transportation (Hitchcock) problem occurs when there are demands at each of n sinks for T periods which can be fulfilled by shipments from m sources. A requirement in period t₂ can be satisfied by a shipment in the same period (a linear shipping cost is incurred) or by a shipment in period t₁ < t₂ (in addition to the linear shipping cost a linear inventory cost is incurred for every period in which the commodity is stored). A well known method for solving this problem is to transform it into an equivalent single period transportation problem with mT sources and nT sinks. Our approach treats the model as a transshipment problem consisting of T, m source — n sink transportation problems linked together by inventory variables. Storage requirements are proportional to T² for the single period equivalent transportation algorithm, proportional to T, for our algorithm without decomposition, and independent of T for our algorithm with decomposition. This storage saving feature enables much larger problems to be solved than were previously possible. Futhermore, we can easily incorporate upper bounds on inventories. This is not possible in the single period transportation equivalent.     

A simulated port facility in a theatre of operations

A hypothetical port facility in a theatre of operations is modeled and coded in a special purpose simulation language, for the purpose of conducting simulation experiments on a digital computer. The experiments are conducted to investigate the resource requirements necessary for the reception, discharge, and clearance of supplies at the port. Queue lengths, waiting times, facility utilizations, temporary storage levels, and ship turn-around times are analyzed as functions of transportation and cargo handling resources, using response surface methodology. The resulting response surfaces are revealing in regard to the sensitivity of port operations to transportation resource levels and the characteristics of the port facility's load factor. Two specific conclusions of significant value are derived. First, the simulation experiments clearly show that the standard procedures for determining discharge and clearance capacities take insufficient account of the effects of variability. Second, the response surfaces for ship turn-around times and temporary storage levels indicate that an extremely steep gradient exists as a function of troop levels.     

Minimizing reductions in readiness caused by time-phased decreases in aircraft overhaul and repair activities

The Navy is often required to conduct personnel planning studies, A recent study on the assessment of effects of personnel reductions at the various aircraft Overhaul and Repair Activities (O & Rs) of the Bureau of Naval Weapons was carried out by one of the writers of the present paper. The methodology was systematic but relied on informal, judgmental decision procedures rather than on formal models incorporating optimization. Later study of the problem resulted in the approach described herein. The paper addresses this question: How can a personnel reduction in the Navy's aircraft O & Rs be distributed among activities with minimum reduction in readiness? A two-stage procedure involving linear programming models is developed. Solutions involve either extensions of aircraft overhaul cycles or a combination of such extensions with reductions in aircraft inventories.