A backward recursive technique for optimal sequential sampling plans

This paper presents a procedure akin to dynamic programming for designing optimal acceptance sampling plans for item-by-item inspection. Using a Bayesian procedure, a prior distribution is specified, and a suitable cost model is employed depicting the cost of sampling, accepting or rejecting the lot. An algorithm is supplied which is digital computer oriented.     

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 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.     

A priori error bounds for procurement commodity aggregation in logistics planning models

A complete logistical planning model of a firm or public system should include activities having to do with the procurement of supplies. Not infrequently, however, procurement aspects are difficult to model because of their relatively complex and evanescent nature. This raises the issue of how to build an overall logistics model in spite of such difficulties. This paper offers some suggestions toward this end which enable the procurement side of a model to be simplified via commodity aggregation in a “controlled” way, that is, in such a manner that the modeler can know and control in advance of solving his model how much loss of accuracy will be incurred for the solutions to the (aggregated) overall model.     

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.     

Some simple scheduling algorithms

This paper considers situations in which jobs require only one operation on a single machine, or on one of a set of identical machines. Penalty-free interruption is allowed. Some simple algorithms are given for finding optimum schedules to minimize maximum lateness and total delay, for the single-machine case, and maximum lateness for a restricted multi-machine case. A simple flow problem formulation permits minimizing maximum lateness for the more general multimachine case.     

A problem of restricted partitions

This paper presents a simple algorithm for finding the number of restricted k-partitions of a natural number n. The unrestricted k-partitions of n are expressed as the sum of these restricted k-partitions, called inadmissible, and the admissible k-partitions. The simplicity of the algorithm is striking, though all the implications are unclear.     

An efficient algorithm for the location-allocation problem with rectangular regions

The location-allocation problem for existing facilities uniformly distributed over rectangular regions is treated for the case where the rectilinear norm is used. The new facilities are to be located such that the expected total weighted distance is minimized. Properties of the problem are discussed. A branch and bound algorithm is developed for the exact solution of the problem. Computational results are given for different sized problems.