A technique which combines modified pattern search methods with composite designs and polynomial constraints to solve constrained optimization problems

This paper presents a method of selecting design parameters which optimizes a specific measure (aircraft design example: minimum weight, maximum mission effectiveness) and guarantees designated levels of response in specified areas (such as combal ceiling, acceleration time). The method employs direct search optimization applied to a nonlinear functional constrained by nonlinear surfaces. The composite design technique is combined with regression methods to determine adequate surface representations with a minimum of required data points. A sensitivity analysis is conducted at the optimum set of design parameters to test for uniqueness.     

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.     

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.     

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.     

Monotone failure rates for multivariate distributions

It is shown that the monotone multivariate failure rates of Brindley and Thompson have no natural analog involving the multivariate failure rate function of Basu for absolutely continuous distributions. Quantities related to the multivariate failure rate function are used to define monotone failure rates. It is shown that these are equivalent to the monotone failure rates of Brindley and Thompson. Based on these quantities, the loss of memory property of Marshall and Olkin is characterized.     

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.