A NOTE ON OPTIMAL PORTFOLIO SELECTION UNDER STABLE PARETIAN DISTRIBUTIONS*

Elton, Gruber, and Padberg's [2] [3] ranking procedure and Kwan's [6] nonranking procedure for optimal portfolio selection lead to the same solution. This is because of a particular functional property of the cutoff rate for security performance. In this note, the robustness of that functional property is demonstrated the normality of security returns assumed in the above studies is relaxed to encompass the general family of stable Paretian distributions. The proof here is an important step toward portfolio analysis using some multiindex models when securities cannot be ranked.     

PORTFOLIO MODELING IN MULTIPLE-CRITERIA SITUATIONS UNDER UNCERTAINTY: COMMENT

In a recent issue of Decision Sciences, Muhlemann, Lockett, and Gear [8] developed a multiple-objective, stochastic linear programming formulation of the multiperiod portfolio selection problem under uncertainty. The purpose of this note is to offer some extensions to their multicriteria approach which is otherwise viewed as an excellent attempt at modeling realistic aspects of the portfolio selection problem. Further, integer goal programming combined with simulation is suggested as an alternate approach for solving the dynamic multiple-objective problem.     

Notes and Communications ON SENSITIVITY ANALYSIS IN DECISION THEORY*

This note points out a crucial flaw in Evans's recent article [1] on decision sensitivity analysis which was published in this journal. This flaw leads to errors in the majority of his formulae and examples. Correct distance formulae in “probability space,” easily computed from the problem data, are provided. After a critical discussion of some of the concepts Evans employed, we bring to the reader's attention a body of prior work in this area that apparently was overlooked.     

INDUSTRY RESOURCE ALLOCATION TO BASIC RESEARCH UNDER NORMALLY DISTRIBUTED BENEFITS*

The failure of a free market system to attain socially optimal allocation of resources to research and development (R&D) is a generally recognized problem. However, we are just beginning to understand the types of R&D activities that receive relatively serious underinvestment from specific types of industries and the types of governmental intervention strategies that are likely to be effective and efficient in the correction of that underinvestment. Recently, Joglekar and Hamburg [16] [17] sought answers to these types of questions using models of the resource allocation behavior of firms considering investment in basic research related to their industry. It was assumed that the firms' benefits were exponentially distributed. In the present article, such benefits are assumed to be normally distributed, and an attempt is made to verify the earlier conclusions and policy implications of [16] and [17]. The results are similar for these two substantially different types of distribution, but the earlier conclusions and policy implications are clarified, qualified, and extended.     

A NOTE ON HOLDING COSTS AND LOT-SIZE ERRORS

This note examines the sensitivity of the basic economic-order-quantity inventory model to lot-size errors when holding costs are assumed to be a strictly increasing (though not necessarily linear) function of average inventory. In particular, we show that the penalty associated with ordering either too much or too little is a function not only of the size of the error but of the shape of the holding-cost curve as well. We demonstrate that, under certain conditions, even relatively small lot-size errors can be extremely costly.     

IMPLICIT OPTIMAL AND HEURISTIC LABOR STAFFING IN A MULTIOBJECTIVE,MULTILOCATION ENVIRONMENT*

This paper presents a tractable set of integer programming models for the days-off scheduling of a mix of full- and part-time employees working α to β days/week (cycle) in a multiple-objective, multiple-location environment. Previous models were formulated to specifically schedule part-time employees working either two or three days per week. These models were intractable because they required complete employee schedule information. The new models are deemed implicit optimal since they are required to supply only essential information. While the number of variables in previous models is an exponential increasing function of β-α, the size of three of the new models is independent of α and β. The first three models developed here (as in [18]) deal with the trade-offs between idle time, the number of employees required to work at multiple “locations,” and the size of the total labor pool. The inherent flexibility of the implicit modeling approach is illustrated by the presentation of various modifications of the basic models. These modifications permit the use of preference weights on the number of employee work days/week (cycle) or the minimization of payroll costs where differential pay rates exist. These latter models may also be formulated such that idle time is ignored, constrained or minimized. The execution time for the implicit models (on a CDC CYBER 730 computer with commercially available software) averaged well under five seconds on 1200 trial problems for the type of application considered in [18]. A solution was obtained in less than 46 seconds of CPU time for a trial problem which would have required over 1.4 million integer variables with previous models. The availability of optimal solutions was invaluable in the development of two heuristics designed to deal with the trade-offs of [16]. In an experimental analysis a previous heuristic produced results which averaged from 74 to 508 percent above optimum across six experimental conditions. The comparable new heuristic produced results which averaged from 3 to 8 percent above optimum for the same experimental conditions. The paper concludes by developing a framework to integrate the results of this research with the tour scheduling problem and by identifying several other areas for related research.     

A NOTE ON THE RELATIONSHIPS AMONG FINENESS,GARBLING, AND SUFFICIENCY FOR THE COMPARISON OF INFORMATION SYSTEMS*

Choice among competing information systems is an important problem for both the providers and users of information. When the attributes of the decision makers and decision problems for which information is produced are unknown or heterogeneous, it is difficult to choose among alternative information sources. Three criteria for such comparisons of information systems are available in the theory of information economics. These criteria may be distinguished by the differing restrictions that they impose on the generality of the studies in which they are used. This note explicates the relationships among these criteria and discusses the various limitations that they impose on generality.