Postoptimality analysis in integer programming by implicit enumeration: The mixed integer case

This paper develops a method for doing postoptimality analysis on the mixed integer programming problem. The proposed procedures form a natural adjunct to enumerative I.P. algorithms that are linear programming based, and they are designed, in effect, to capitalize on insights generated as the problem is initially solved to do subsequent analysis upon it. In particular, limited ranging analysis is possible on selected parameters, as is the efficient resolving of the problem following parameter changes.     

Optimal and suboptimal procedures in group sequential sampling

This paper investigates the problem of choosing between two simple hypothesis, H₀ and H₁, in terms of independent, identically distributed random variables, when observations can be taken in groups. At any stage in the decision process it must be decided whether to stop and take action now or to continue, in which case the size of the next group of observations must be decided upon. The problem is to find an optimal procedure incorporating a stopping, group size (batch) and terminal action rule. It is proven, in general, that the optimal stopping and terminal action rule is of the sequential probability ratio type (SPRT). Fixed stopping rules of the SPRT type are studied and an iterative procedure of the policy improvement type, both with and without a value determination step, is developed. It is shown, for the general situation, that both the average risk and scheduling rule converge to the optima. Also, six suboptimal scheduling rules are considered with respect to the average risks they achieve. Numerical results are presented to illustrate the effectiveness of the procedures.     

A general treatment of upper unbounded and bounded hitchcock problems

This paper is designed to treat (a) the problem of the determination of the absolute minimum cost, with the associated assignments, when there is no limit, N, on the number of parcels available for shipment in a modified Hitchcock problem. This is accomplished with the use of a transformed cost matrix. C*, to which the so-called transportation paradox does not apply. The general Hitchcock solution using C* gives the cost T*, which is the absolute minimum cost of the original problem, as well as sets of assignments which are readily transformed to give the general assignments of the original problem. The sum of these latter assignments gives the value of N_u, the unbounded N for minimum cost. In addition, this paper is designed to show (b) how the method of reduced matrices may be used, (c) how a particular Hitchcock solution can be used to determine a general solution so that one solution using C* can provide the general answer, (d) how the results may be modified to apply to problems with fixed N, and hence (e) to determine the function of the decreasing T as N approaches N_u, and finally (f) to provide a treatment when the supplies at origin i and/or the demands at destination j, are bounded.     

On a sequential test procedure with delayed observations

This paper considers sequential test procedures to decision problems where there exists time delays in obtaining observations.     

Impact of an all volunteer force upon the navy in the 1972-1973 timeframe

This paper develops estimates of true volunteer levels for 1972 and 1973, based on experience gained through 1970 draft lottery data. The paper also formulates estimates of the qualitative characteristics of a 1972-1973 Navy volunteer force, and establishes a relationship between rate of volunteerism and military pay. Utilizing estimates generated in the paper, Navy military personnel budget requirements for FY '72 and '73 are presented.     

Control variable methods in the simulation of a model of a multiprogrammed computer system

One approach to the evaluation of the performance of multiprogranmed computer systems includes the development of Monte Carlo simulations of transitions of programs within such systems, and their strengthening by control variable and concomitant variable methods. An application of such a combination of analytical, numerical, and Monte Carlo approaches to a model of system overhead in a paging machine is presented.     

On estimation in weibull distributions with random scale parameters

Work by the present authors on life distributions derived from stochastic hazard functions [4] is related to certain articles that have appeared in this journal. This relationship is illustrated. The emphasis of this article is upon problems of parameter estimation.     

War reserve spares kits supplemented by normal operating assets

In peacetime, base stock levels of spares are determined on the assumption of normal resupply from the depot. In the event of war, however, a unit must be prepared to operate from stock on hand for a period of time without being resupplied from the depot. This paper describes a mathematical model for determining such war reserve spares (WRS) requirements. Specifically, the model solves the following kind of optimization problem: find the least-cost WRS kits that will keep the probability of a stockout after K cannibalizations less than or equal to some target objective α. The user of the model specifies the number of allowable cannibalizations, and the level of protection that the kit is supposed to provide. One interesting feature of this model is that in the probability computation it takes into account the possiblility of utilizing normal base operating assets. Results of a sensitivity analysis indicate that if peacetime levels were explicitly taken into account when designing a WRS kit, a cost saving of nearly 40 percent could be effected without degrading base supply performance in wartime.     

A branch and bound algorithm for allocation problems in which constraint coefficients depend upon decision variables

A branch and bound algorithm is developed for a class of allocation problems in which some constraint coefficients depend on the values of certain of the decision variables. Were it not for these dependencies, the problems could be solved by linear programming. The algorithm is developed in terms of a strategic deployment problem in which it is desired to find a least-cost transportation fleet, subject to constraints on men/materiel requirements in the event of certain hypothesized contingencies. Among the transportation vehicles available for selection are aircraft which exhibit the characteristic that the amount of goods deliverable by an aircraft on a particular route in a given time period (called aircraft productivity and measured in kilotons/aircraft/month) depends on the ratio of type 1 to type 2 aircraft used on that particular route. A model is formulated in which these relationships are first approximated by piecewise linear functions. A branch and bound algorithm for solving the resultant nonlinear problem is then presented; the algorithm solves a sequence of linear programming problems. The algorithm is illustrated by a sample problem and comments concerning its practicality are made.