Management Science

Hakansson, Nils H.; Miller, Bruce L.

doi: 10.1287/mnsc.22.4.391pmid: N/A

The implications of concentrating on the lowest moment(s) of average compound return over N periods in making investment decisions have recently been examined. In particular, maximization of expected average compound return has been shown to imply the existence of a utility of wealth function in each period with the right properties for all finite N 2 as well as in the limit. More importantly, for large N a close (or exact) approximation to the set of mean-variance efficient portfolios (with respect to average compound return) is obtainable via a subset of the isoelastic class of utility of wealth functions. The properties of this class render it both empirically plausible and highly attractive analytically: among them are monotonicity, strict concavity, and decreasing risk aversion; moreover, the optimal mix of risky assets is independent of initial wealth (providing a basis for the formation of mutual funds) and the optimal investment policy is myopic. The purpose of this paper is to extend the class of return distributions for which the preceding results hold and to demonstrate that portfolios which are efficient with respect to average compound return, at least for large N, do not risk ruin either in a short-run or a long-run sense.

Brosh, I.; Shlifer, E.; Zeira, Y.

doi: 10.1287/mnsc.22.4.401pmid: N/A

The optimal maintenance and replacement policy for a fleet of vehicles is discussed in this paper that reflects a research effort of three years. The tasks that faced the research team were to list feasible policies, formulate their stochastic behaviour and recommend solution techniques on the strength of the available data.

Frerichs, Ralph R.; Prawda, Juan

doi: 10.1287/mnsc.22.4.411pmid: N/A

A simulation model is developed describing the transmission of canine rabies within and between 116 spatially distributed barrios (neighborhoods) in Cali, Colombia. The discrete time, dynamic model considers both discrete random variables (incubation and infective periods, appearance and movement of rabid dogs through the city, etc.) and deterministic variables (demographic components of barrio canine populations). Values for the input variables were acquired through field observations, other Colombian sources, and a review of the literature. Various canine vaccination strategies were tested in the model over a ten-year planning horizon for their cost-effectiveness with regard to the prevention of canine rabies. The model is recommended to the Pan American Health Organization to be used as an interactive gaming model to aid health system managers in Cali, Colombia and in other Latin American cities in scheduling the time and locations of vaccination teams in a more cost-effective manner.

Schneller, Meir I.

doi: 10.1287/mnsc.22.4.422pmid: N/A

Betathe systematic riskis generally accepted as a measure for the risk involved in holding a portfolio of risky securities. It will be shown in this paper that, because beta is measured by regressing one multiplicative variable (the rate of return of a security or a portfolio) on another multiplicative variable (the market), in the long run, the systematic risk will approach either zero or infinity. It will also be shown that in the long run the unsystematic risk will dominate the systematic risk, and that, regardless of the value of this latter risk. This implies that for investors with long planning horizon the information conveyed in the systematic risk of an investment is rather limited.

Rao, Arza K.

doi: 10.1287/mnsc.22.4.427pmid: N/A

Consider the linear complementarity problem given in the system:\documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\begin{array}{r@{\enskip}l} (1) & W = MZ + q\\ (2) & W \geq 0, Z \geq 0\\ (3) & Z^TW=0 \end{array} \eqno{(I)}$$\end{document}where, W, Z and q are vectors of dimension n. M is a matrix of order n n and ZT is the transpose of Z. Any (Z, W) satisfying (1), (2), and (3) is a complementary feasible solution to system (I).In the literature, a class of matrices is defined such that if M belongs to this class, then existence of a feasible solution to system (I) implies the existence of a complementary feasible solution to system (I) with W 0. In this paper, a new class of matrices is developed. It is shown that membership of a matrix M in is equivalent to the property; for any q existence of a feasible solution to system (I) implies the existence of complementary feasible solution to system (I) for that q with W 0. This new class of matrices is not contained in any one of the known classes, namely, copositive plus, positive definite or semidefinite, P-matrices, P-matrices, Z-class, etc.

Keeney, Ralph L.; Kirkwood, Craig W.

doi: 10.1287/mnsc.22.4.430pmid: N/A

This paper addresses the problem of constructing a group cardinal social welfare function whose arguments are the individual utility functions of group members. Representation theorems are given which show that the social welfare function is restricted to special forms if certain reasonable conditions hold. The appropriateness of these conditions for different types of group decision problems is discussed.

Charnes, A.; Cooper, W. W.; Klingman, D.; Niehaus, R. J.

doi: 10.1287/mnsc.22.4.438pmid: N/A

Goal programming has now become an important tool in areas such as public management science. There is therefore a need for examining ways of securing improved computational efficiency, as is done in this paper, instead of resting only on the linear programming equivalences that were set forth when the original goal programming article was published in Vol. 1, No. 2 of Management Science. Based on lemmata which permit reduction of various important classes of convex goal programming models to problems of full row rank-interval programming type, explicit solutions to convex goal programming problems are exhibited. Some of the equivalences herein established are also useful in their own right and for other classes of problemse.g., interval programmingas well as advanced start procedures and other such computational matters.

Ponssard, Jean-Pierre

doi: 10.1287/mnsc.22.4.449pmid: N/A

An experiment is defined as a random variable which may take some posterior probability distributions according to a marginal probability. Elementary properties of this definition with respect to information value theory are derived as well as their practical implications.

Glover, Fred

doi: 10.1287/mnsc.22.4.455pmid: N/A

A variety of combinatorial problems (e.g., in capital budgeting, scheduling, allocation) can be expressed as a linear integer programming problem. However, the standard devices for doing this often produce an inordinate number of variables and constraints, putting the problem beyond the practical reach of available integer programming methods.This paper presents new formulation techniques for capturing the essential nonlinearities of the problem of interest, while producing a significantly smaller problem size than the standard techniques.

Perry, Arnon; Soland, Richard M.

doi: 10.1287/mnsc.22.4.461pmid: N/A

Public lotteries form an important source of revenue for many national and state governments, but little quantitative effort has been applied to their efficient operation. We here formulate a model in which the net revenue per unit time from the operation of a lottery depends upon the prizes offered, the price charged per ticket, and the time interval between successive drawings. The model is solved for the optimal values of these decision variables, and some illustrative numerical results are presented.