An operator theory of parametric programming for the generalized transportation problem—IV—global operators

This paper investigates the effect of the optimal solution of a (capacitated) generalized transportation problem when the data of the problem (the rim conditions—i.e., the available time of machine types and demands of product types, the per unit production costs, the per unit production time and the upper bounds) are continuously varied as a linear function of a single parameter. Operators that effect the transformation of optimal solution associated with such data changes, are shown to be a product of basis preserving operators (described in our earlier papers) that operate on a sequence of adjacent basis structures. Algorithms are furnished for the three types of operators—rim, cost, and weight. The paper concludes with a discussion of the production and managerial interpretations of the operators and a comment on the “production paradox”.     

Optimal schedules for special structure flowshops

This paper considers the problem of scheduling a given number of jobs on a specified number of machines in a flowshop where the objective function is to minimize the total throughput time in which all jobs complete processing on all machines. Based on the combinatorial analysis of the problem, several simple algorithms are developed for solving special structure flowshop scheduling problems where the process times are not completely random, but bear a well-defined relationship to one another. The proposed algorithms are both simple and computationally efficient and can optimally solve large-sized problems even with manual computational devices.     

A note on allocating jobs to two machines

A recent article in this journal by Mehta, Chandrasekaran, and Emmons [1] described a dynamic programming algorithm for assigning jobs to two identical parallel processors in a way that minimizes the average delay of these jobs. Their problem has a constraint on the sequence of the jobs such that any group of jobs assigned to a processor must be processed in the order of the sequence. This note has two purposes. First, we wish to point out a relationship between this work and some prior work [2]. Second, we wish to point out that Mehta, Chandrasekaran, and Emmons formulation, slightly generalized, can be used to find the optimum assignment of jobs to two machines in a more general class of problems than they considered including a subclass in which the jobs are not constrained to be processed in a given sequence.     

Isoquants of continuous production correspondences

Bol has discussed consequences of the continuity of production correspondences in connection with relations between efficient input and output vectors. Isoquants of continuous production correspondences are used here to extend this work. Simplifications to existing theory are discussed.     

Efficient computational devices for the capacitated transportation problem

This paper presents the details for applying and specializing the work of Ellis Johnson [10] and [11] to develop a primal code for the well-known capacitated transportation problem. The code was developed directly from the work of Johnson, but is similar to codes developed by Glover, Karney, Klingman, and Napier [6] and Srinivasan and Thompson [14]. The emphasis in the presentation is the use of the graphical representation of the basis to carry out the revised simplex operations. This is a means of exploiting the special structure and sparseness of the constraint matrix to minimize computational effort and storage requirements. We also present the results of solving several large problems with the code developed.     

Comparison of stochastic processes used in sonar detection models

In any model for a sonar detection process, some assumption must be made about the nature of the acoustic fluctuation process. Two processes that are widely used in this role are the jump process and the Gauss-Markov process. These processes are similar in that they are both stationer) Markov processes and have autocovariance functions of the form s?²exp(—γt). For these reasons, it might be believed that one could use either of these processes and get comparable results if all one is interested in is computing cumulative detection probabilities or mean time to gain or lose contact. However, such is not the case in that vastly different results can be obtained in some applications. An application of this sort is presented. We also present necessary and sufficient conditions for a threshold to have the property that it is almost surely crossed by the jump process, or by the Gauss-Markov process. This affords another method of comparison.     

Upper and lower bounds for a pattern bombing problem

This paper includes two simple analytic formulas for kill probability that are applicable in circumstances where shots should be fired in a pattern. The two formulas bracket the maximum kill probability achievable with an optimal pattern. The upper bound corresponds to an optimal nonfeasible pattern, and the lower bound to a nonoptimal feasible pattern.     

On the evaluation of investment proposals having multiple attributes

A framework is developed for analyzing the likelihood of acceptance of an investment project proposal when objectives are uncertain. The foundation is a utility model of top management's choice process, modified if need be through a Bayesian approach which takes into account any apparent inconsistency in the history of past proposal acceptances and rejections.     

Stochastic control of queueing systems

Suppose that the state of a queueing system is described by a Markov process { Y_t, t ≥ 0}, and the profit from operating it up to a time t is given by the function f(Y_t). We operate the system up to a time T, where the random variable T is a stopping time for the process Yt. Optimal stochastic control is achieved by choosing the stopping time T that maximizes Ef(Y_T) over a given class of stopping times. In this paper a theory of stochastic control is developed for a single server queue with Poisson arrivals and general service times.     

Bayes adaptive control of two-echelon inventory systems,II: The multistation case

The present paper extends the results of [7] to cases of multistation lower echelon. For this purpose an algorithm for the optimal allocation of the upper echelon stock among the lower echelon stations is developed. The policy of ordering for the upper echelon is an extension of the Bayes prediction policy developed in [7]. Explicit formulae are presented for the execution of this policy. Several simulation runs are presented and analyzed for the purpose of obtaining information on the behavior of the system, under the above control policy, over short and long periods.