Plant Location Under Economies-of-ScaleDecentralization and ComputationManne, Alan S.
doi: 10.1287/mnsc.11.2.213pmid: N/A
An exploration of the margin of error entailed in using a one-point move algorithm for solving a class of fixed-charge problems. The algorithm is of interest both from the viewpoint of numerical analysis and also from the analogy with market mechanisms. Despite the presence of economies-of-scale, there is the possibility of operating a decentralized system. This is a two-price system; it implies discriminatory and also marginal cost pricing.
The Past, Present, and Future of General Simulation LanguagesKrasnow, Howard S.; Merikallio, Reino A.
doi: 10.1287/mnsc.11.2.236pmid: N/A
The widespread use of simulation in the design and analysis of complex systems has received a great impetus in the past few years with the advent of various general simulation languages. Simulation models of a wide variety of physical situations can now be developed with these languages. This paper summarizes and compares various characteristics of five major general simulation languages. The historical background from which these languages developed is discussed first. Predictions are also made on the future development of general simulation languages.
Bounds for the Optimal Scheduling of n Jobs on m ProcessorsEastman, W. L.; Even, S.; Isaacs, I. M.
doi: 10.1287/mnsc.11.2.268pmid: N/A
The problem of scheduling n jobs on m identical processors has been introduced by R. McNaughton, but as yet no efficient algorithm has been found for determining an optimal sequencing of jobs. In this paper lower and upper bounds are given for the cost of an optimal schedule. Since the two bounds are not far apart, they may be helpful in practical scheduling problems. A procedure is described for obtaining a schedule which costs less than the given upper bound.
On Scheduling Problems with Deferral CostsLawler, Eugene L.
doi: 10.1287/mnsc.11.2.280pmid: N/A
A class of scheduling problems involving deferral costs has been formulated by McNaughton, who has described a simple method of solution for the linear, single-processor case. In this report dynamic programming and linear programming techniques are applied to nonlinear and multiple-processor problems. A dynamic programming solution of the nonlinear, single processor problem is possible, provided the number of jobs is small. Transportation methods of linear programming can be used to solve large nonlinear, multiple-processor problems, provided the processing times for the jobs are equal. Approximate and/or partial solutions are possible for other cases.
On the Mathematical Theory of SchedulesMayhugh, J. O.
doi: 10.1287/mnsc.11.2.289pmid: N/A
The elapsed time to complete a scheduled task is expressed as a function of the completion times of the component tasks and the path matrix of the scheddule graph. The schedule function is interpreted geometrically as a polyhedron. If the scheduled activities have random completion times, the probability distribution of the time to complete the entire task is found by integrating over the contours of the polyhedron. Composite schedule functions are represented by algebraic formulae which are applicable in both the probabilistic and non-probabilistic cases. A method for joint control of cost and schedule is presented.
Some Stochastic Inventory Models for Rental SituationsTainiter, M.
doi: 10.1287/mnsc.11.2.316pmid: N/A
Some stochastic models are analyzed which describe the time fluctuations of the inventory levels of companies which are in the rental business. The stochastic process which describes the fluctuations is shown to be applicable to a wide variety of physical situations. Examples are given, and analyses are made of several types of profit functions which are applicable to rental situations.
Measuring Risk on Consumer Instalment CreditSmith, Paul F.
doi: 10.1287/mnsc.11.2.327pmid: N/A
The advantages of statistical measures for grading credit risks in lending to consumers have been widely recognized but relatively little use has been made of such systems. The paper develops a relatively simple statistical method for measuring risk on individual accounts that can also be used for measuring and controlling portfolio quality and for estimating loss rates. The procedure entails four steps:Comparison of good and bad accounts in the search for characteristics that are associated with bad accounts;Calculation of bad account probabilities for discriminating characteristics;Development of a risk index from bad account probabilities to be used in grading accounts;Evaluation of the risk index.A test of the Method the accounts of a commercial bank is described and the judgements implied by the risk index are compared to the criteria used by interviewers in rejecting applicants. A great many similarities are found between the results of the two methods but a number of striking dissimilarities are observed.The last section of the paper illustrates the ways in which the risk index can be used to adjust credit quality to the desired volume and loss experience. It also demonstrates its use in measuring portfolio quality and in estimating loss rates.
A Problem in Making Resources LastMacQueen, J.
doi: 10.1287/mnsc.11.2.341pmid: N/A
An individual uses up a certain resource at a constant rate, but from time to time has a chance to gamble some of the resource in order to gain more. The expectation of each gamble is zero, i.e., the gambles are fair. This means that eventually the resource will run out. However, the form of the risk can be varied arbitrarily. The question is what form of risk to choose, when the object is maximize the expectation of the utility, u(T), of having the resources run out at time T. This problem is solved for a more or less arbitrary function u(T).Various possible interpretations of such a function u(T) are discussed briefly.The model is mainly intended to provide a basis for empirical studies of individual decision making, where its complete mathematical tractibility is convenient.