This note makes two contributions to M. Klein's formulation of the multiperiod reject allowance problem. First, a decomposition algorithm involving both linear and dynamic programming is proposed, and its computational savings over the straight simplex method are demonstrated. Second, in Klein's formulation where termination of production is allowed before reaching the set of terminal states, a lacuna is corrected by means of an enlargement of the state space.
The optimum coupon schedule for serial bonds issued by municipalities has been solved as a knapsack problem, and is widely implemented in bank and nonbank underwriting firms. A large subset of issues carries the additional requirement that limits the number of distinct coupons which the underwriters may assign to the issue. The paper formulates this problem as a dynamic programming model and discusses the computational aspects relating to this formulation by comparing it with a direct 0/1 integer programming model. Some computational experience is also provided.
This paper reports a study which developed and empirically tested a simulation model of the process by which zoning ordinances are altered to adapt to the changing needs and conditions of a city. The perceived decision rules of the participants are reported in the form of flow charts which utilize language similar to that used by the participants. The body of the paper indicates methods which were used to translate these judgmental rules into a form suitable for a computer. The model was tested by allowing the computer to decide the one hundred twenty-five proposed changes in the zoning map of the City of Pittsburgh during the period 1963 to 1965 inclusive. The results were good in the sense that the computer model decided most of the cases in the same way as did the human participants. Additional tests and managerial implications are also discussed.
In this study, intuitive aggregate production scheduling performance under various environmental conditions is related to Bowman’s theory of managerial coefficients. Controlled decision environments were established in four hypothetical companies to isolate the effects of differences in information relevance and planning activities. Results illustrate the effects of environmental differences on the formation of intuitive scheduling rules.
This paper describes an operations research approach taken to implement a desegregation plan for the Oklahoma City Public Schools. While the main objective of the plan was desegregation, it also provides for an equal educational opportunity for all students and more efficient utilization of facilities. The essential element of the plan is that students attend their same home schools, but each school is responsible for a certain specialty area, such as science, mathematics, or foreign language. Students taking specialty courses travel to those schools. Thus, inherent in the plan is the technically complex problem of scheduling students among several schools in varying time patterns to minimize total weekly student travel time. A form of modular scheduling was developed which allowed different courses to be taught for different lengths of time. From an educational point of view, class times could be tailored to the needs of a particular course. Since students take courses in overlapping time blocks at more than one school, the problem of building the Master Schedule was quite complex. In general, a Master Schedule could result in a large number of student conflicts. A master scheduling program was, therefore, developed which (1) operates in a time-sharing mode so that it is interactive with the principal, (2) attempts to minimize student conflicts and (3) works for any time block configuration.
This is the sequel to Urban Issues I, the special issue which was edited by this Department and published in Management Science, Vol. 16, No. 12 (August 1970). Like its predecessor the present collection has been pointed toward delineating new possibilities for management science approaches to urban problems. Also like its predecessor, the present compilation is drawn from a variety of sources which include papers presented at scientific-professional society meetings, papers selected from the normal flow of mss. into this department and papers obtained by special invitation.
The emphasis in this issue has been on game theory with six papers on game theory, one on gaming, and one relating game theory to gaming. Collectively, the first three papers present an overview of the subject area. The remaining five papers report on new research.
The successful management of urban systems is becoming increasingly a matter of successful information about the urban area and its environment. Using information as a basis for developing a structure for, and outlining the flows in, an urban area, this paper develops a dual hierarchy of information requirements and management activities. Each level of the hierarchy is discussed in terms of the emergent problems and requirements that are likely to confront management scientists and urban administrators in the future. As the information requirements of urban areas become more complex and as the components of the urban system become more highly interrelated, developments in information technology can be expected to have a direct impact on the activities of urban area administrators. This development is illustrated here through the presentation of a selected number of possible impacts of information technology developments upon the information and management hierarchies of urban systems.
Growth period models, previously treated in the literature, have assumed that the pattern of value increase of the growth asset is deterministic. In this paper, this assumption is relaxed by considering models in which the increase in value of an asset in a period is a random variable whose distribution is a function of either the value or the age of the asset at the start of the period. The expected increase in value is a decreasing function of the value or age of the asset so that the value of additional maturation time decreases as the asset ages. Dynamic programming is used to compute optimal policies as to when stochastic growth assets should be harvested. The steady state value function is shown to be directly analogous to that obtained when deterministic growth is assumed. Procedures for quickly computing both steady state policies and value functions are developed.