Optimal Decisions Under Uncertainty

Understanding the stochastic enviornment is as much important to the manager as to the economist. From production and marketing to financial management, a manager has to assess various costs imposed by uncertainty. The economist analyzes the role of incomplete and too often imperfect information structures on the optimal decisions made by a firm. The need for understanding the role of uncertainty in quantitative decision models, both in economics and management science provide the basic motivation of this monograph. The stochastic environment is analyzed here in terms of the following specific models of optimization: linear and quadratic models, linear programming, control theory and dynamic programming. Uncertainty is introduced here through the para­ meters, the constraints, and the objective function and its impact evaluated. Specifically recent developments in applied research are emphasized, so that they can help the decision-maker arrive at a solution which has some desirable charac­ teristics like robustness, stability and cautiousness. Mathematical treatment is kept at a fairly elementary level and applied as­ pects are emphasized much more than theory. Moreover, an attempt is made to in­ corporate the economic theory of uncertainty into the stochastic theory of opera­ tions research. Methods of optimal decision rules illustrated he re are applicable in three broad areas: (a) applied economic models in resource allocation and economic planning, (b) operations research models involving portfolio analysis and stochastic linear programming and (c) systems science models in stochastic control and adaptive behavior.

Contenu

1. Decision Analysis for Management.- Risk Aversion in Decision Models.- Evaluating Decisions Under Uncertainty.- 2. Decision Analysis in Management: Methods and Models.- Optimization Models: Theory and Practice.- Theory of LP.- Applications of LP Models.- Stochastic Systems as Queuing Models.- Markovian Queue.- Case of Multiple Channels.- Infinite Channel Queue.- Optimizing Decisions Under Queuing Models.- Dynamically Optimum Systems.- Continuous Time Systems.- Discrete Time Systems.- 3. Optimal Decision Rules Under Uncertainty in Linear and Quadratic Models.- Linear Quadratic Models: Selected Examples.- Stochastic Programming Models: Selected Examples and New Applications.- Stochastic Control: Selected Examples.- Concluding Remarks.- 4. Information and its Efficient Use in Decision Models.- Information and Efficiency in Economic Models.- Optimality of Information in Statistical Models.- Applications in Management Science and Communication Theory.- Concluding Remarks.- 5. Portfolio Models in Financial Management.- Investment Portfolios and Firm's Production Behavior.- Optimal Diversification of Portfolios.- Portfolio Models Under MSE Criterion.- Econometric Analysis of Portfolio Models.- General Implications.- 6. Applied Stochastic Models in Operations Research.- Efficiency of Water Allocation Under Stochastic Demand.- Risk Sensitivity of Supply Response.- Optimal Fleet Selection and Bus Scheduling.- Optimal Monopolist Strategy Under Uncertainty.- Applied Models in Stochastic Programming.- Stochastic Program in a Fuzzy Environment.- Robust Decisions in Stochastic Models.- Efficiency in Stochastic Input-Output Systems.- 7. Optimal Decisions and Management Models.- Economic Planning Under Uncertainty.- Research Trends and Problems.