We introduce in this note the consistent organizational structure (COS) problem, which can be viewed as a generalization of the college admission and room-mates problems. Both the room-mates problem and the COS problem may have no stable solution. When side payments are allowed, the COS problem, but not the room-mates problem, always has a nonempty core. We further study some nucleoli of the COS problem with side payments.
We examine a multi-server queueing system with Poisson arrivals in which customers require simultaneous service from a random number of servers. Servers assigned to the same customer begin and end service concurrently. Service times are, in general, assumed to be exponentially distributed. A system point approach is presented as a framework for obtaining the waiting time distribution for each customer type. Explicit solutions are derived for the two-server system.
In this paper the problems of using aggregate monthly data to estimate learning curves are investigated. Here, aggregate monthly data on labor hours are assumed to contain some of both fixed and variable labor hours. They are also assumed to be influenced by fluctuating quantities of work in process. A distributed lag model is developed to deal with these two characteristics of aggregate monthly data. The model is generalized to permit production rate to influence labor productivity. This generalized model is then estimated and compared to a cumulative average learning curve in analyzing the impact of a production break. A set of production data which arose from a government contract claim is used for this purpose.
Optimal solutions for the dynamic lot-sizing problem with deterministic demands but stochastic lead times are “lumpy.” If lead time distributions are arbitrary except that they are independent of order size and do not allow orders to cross in time, then each order in an optimal solution will exactly satisfy a consecutive sequence of demands, a natural extension of the classic results by Wagner and Whitin. If, on the other hand, orders can cross in time, then optimal solutions are still “lumpy” in the sense that each order will satisfy a set, not necessarily consecutive, of the demands. An example shows how this characterization can be used to find a solution to a problem where interdependence of lead times is critical. This characterization of optimal solutions facilitates dynamic programming approaches to this problem.
Control charts are given for monitoring an input-output model against changes in form, against changes in its coefficients, and against changes in process variance. When a process is not in control due to changes in some coefficients, monitoring shifts to a diagnostic mode to identify the altered coefficients and thus the needed adjustments to the process. Control limits from special aid tables are used; these are considered along with the choice of design. Operating characteristics of the charts are summarized under standard assumptions.
One reason existing approaches for dealing with benefit interactions in economic R and D project selection models are difficult to apply is that it is difficult to assess the interactions directly. This difficulty can be traced at least in part to the lack of a modeling framework within which different types of interaction can be identified and related to project and portfolio benefit. In this paper, a modeling framework is proposed within which certain kinds of benefit interactions, called present value (PV) interactions, are assessed indirectly by explicitly modeling R and D project impacts on profitability. Within the proposed framework, the role of traditionally recognized types of interaction in the calculation of present value is clarified, and it is shown that PV interaction exists even when traditionally recognized types of interaction are assumed to be absent. The proposed framework offers one method for assessing PV interactions. An example illustrates the framework and shows that ignoring PV interactions can result in both nonoptimal project selections and resource allocations, even when traditionally recognized types of interactions are absent. The framework and resulting model should be useful in enhancing decision making in firms using PV-based approaches to project selection, whether or not they are interested in using a model that accounts for PV interactions. This is expected since the overall framework provides a basis for analyzing the probable consequences of assuming that no PV interaction is present and for communicating these probable consequences to management
It is well known that all betting systems applied to independent, repeated, and identically distributed trials will result in the same expected gain per average unit wagered as that which applies to a single trial. This paper develops the asymptotic and paradoxical manner in which that constant win rate is maintained for optimal proportional betting according to the Kelly criterion. The appropriateness of using this traditional measure of win rate for proportional betting is contrasted with that of various alternatives.
The multi-attribute utility model serves as a basis for many marketing decisions such as new product planning and advertising message selection. The estimation of individuals' attribute weights can be performed using several data types and estimation techniques. There is evidence to suggest that the estimates derived from ordinal preference data through linear programming show greater stability and predictive validity. In this paper we address two fundamental issues which have not been addressed in the context of this latter type estimation: the theoretical foundations for estimating cardinal utility functions from ordinal preference data and the properties of the linear programming estimators. First, we establish the theoretical foundations from economics, mathematical psychology, and decision analysis of obtaining a cardinal (interval scaled) multi-attribute function from ordinal data. This leads us to recommend that in addition to the collection of paired preference comparisons, also comparisons of pairs of pairs be collected. We then describe the type of errors which are likely to arise in the measurement stage, and their relationship to the phenomenon of intransitivities. We formulate a linear program, LINPAC, for the estimation of attribute weights from the above preference data. The previously proposed LINMAP procedure is a special case of this formulation when only the information on the paired preferences is utilized. Next, the statistical properties of the estimators, such as uniqueness, unbiasedness, consistency and efficiency, are examined. Then, through a simulation study we examine the rate of convergence of the estimated weights to the true weights as a function of the number of brands. In the simulation study we also examine the conditions under which the estimators outperform equal weights and compare the estimates derived from LINPAC with those derived from LINMAP. Finally, the estimation procedures are examined with actual data while the simulation results, an equal weights model, and a stated weights model serve as benchmarks.
A reappraisal of previously suggested strategies for betting on football games using results of the period 1975–1981 casts considerable doubt on the profitability of relying on the past history of games for guidance in placing bets.
Risk attitude and time preference are well-known and distinct concepts in the study of individuals' preferences for goods such as money. This paper reviews and explores the application of these concepts to the field of health. A mathematical model is presented, both in a general form and in an exponential form, which relates an individual's risk attitude in health to three effects—a quantity effect, a gambling effect and a time preference effect. It is shown that the overall risk attitude, as measured by its direction and magnitude, is merely the sum of the individual effects, as measured by their directions and magnitudes. Measurement methods are presented which can be used in a given situation to determine which effects are operating, in what directions and with what magnitudes. A new measurement procedure based on the temporary palliation of a chronic condition is described as a method of obtaining an individual's time preference pattern for health.