This paper presents a computational alternative to simulation for a large class of stochastic management models involving functions of random variables. An example of a model in this class is the well-known “risk analysis” problem studied by Hertz and Hillier. Our computational approach includes (i) a versatile framework to describe the univariate and dependence characteristics of a model's random variables, and (ii) formulas for computing the central moments of the model's objective variable. The usefulness of these central moments in decision making is then illustrated and discussed.

Abstract ABSTRACT: By analyzing the performance of various alternative approaches under a set of reasonable criteria, this paper demonstrates that, contrary to popular implications, direct simulation is the superior approach for stochastic CVP analysis. Also presented are simple formulas for controlling and determining the accuracy of simulation results. Besides being relevant to practitioners seeking an efficient approach for stochastic CVP analysis and other similar problems, this study should also affect the future direction of stochastic CVP research.

Abstract The often substantial amount of uncertainty associated with unit volume, unit variable cost, fixed cost, or even unit price in cost-volume-profit (CVP) analysis has made apparent the need for an easy-to-use and accurate means of making probabilistic statements about profit. Over the last dozen years, three main approaches to stochastic CVP analysis have evolved. They are Chebyshev-type inequalities approach, direct simulation approach and theoretical distribution approach. The study of Ferrara-Hayya-Nachman (FHN) considers an important aspect of the third approach. However, the purpose of this paper is to show that the study of FHN is based on inappropriate statistical methodology and their recommendation is, therefore, invalid. Thus, at the current stage of development, it appears that a practitioner should seriously consider using the direct simulation approach. This approach, is easily implemented on even a small computer and provides reasonable levels of accuracy. On the other hand, the facility of application of the theoretical distribution approach to CVP analysis continues to be attractive.

Abstract This article presents a general framework for handling a large class of stochastic management models that includes the stochastic CVP problem and stochastic present value analysis. After demonstrating the need of more flexibility and realism in risk analysis modeling, the authors consider the "four-moments" approach in describing diverse probability forms. Next, a set of easy-to-use formulas are presented for computing the exact values of the first four moments of the model's objective variable. Finally, methods. are discussed for achieving the two most important purposes of stochastic management modeling: estimating the probability of realizing various objective variable levels and determining the expected utility of a risky project. The entire framework blends several original formulas with some well-established techniques previously little known in the accounting/management literature. Compared to other recently published approaches, this framework permits more realistic modeling, requires less computations and provides more accurate and meaningful managerial information.