Showing papers by "Robert S. Kaplan published in 1971"

Admissible Decision Rules for the E-Model of Chance-Constrained Programming

Abstract: This paper is concerned with characterizing decision rules for the sequential E-model of chance-constrained programming. A key feature of our characterization will be a detailed discussion of various interpretations of the probability operator in the chance constraints. Specifically we define two new classes of decision rules by exhibiting those sets of constraints which locally support the corresponding probability requirements. The question of how the probabilistic constraints for future periods are affected by previous decisions and realizations of the random variables is considered in detail. Since we are primarily concerned with the feasibility of decision rules, we deal mainly with the constraints of the model. The procedure for selecting the optimum rule from among a particular class of feasible rules depends on the objective function and is briefly discussed in the final section along with some implications concerning the form of the optimum rule. The application of our proposed rules to a two-period example previously appearing in the literature concludes the paper.

A Model for Integrating Sampling Objectives in Auditing

Abstract: : The four sampling objectives in auditing - representative, corrective, protective, and preventive - are described. A model of the population to be sampled is developed which stratifies the population along two independent dimensions; estimated error rate and reported dollar value. This model enables one to identify the value of sampling in a given stratum for each of the auditor's objectives. A simple overall sampling procedure is suggested when little prior information is available to the auditor while non-linear and goal programming models are developed when the auditor can provide good estimated of population parameters. (Author)

On the Objective Function for the Sequential P-Model of Chance-Constrained Programming

Abstract: The P-model objective of chance-constrained programming reflects the desire of management to maximize the probability of achieving or exceeding a given level of performance. This paper explores the implications of being able to make a sequence of decisions with the P-model objective function, and introduces some new possibilities for the P-model objective function that arise from the sequential nature of the problem. However, it is shown that, except for a special form of the objective function, the maximization in the sequential problem is not of a quasiconcave function, so that local optimality conditions are not sufficient to guarantee that a proposed solution is a global optimum. An example is worked out in detail to illustrate the computations involved for the objectives considered.