The Expected Value of Perfect Information in the Optimal Evolution of Stochastic Systems

This paper uses abstract optimization theory to characterize and analyze the stochastic process describing the current marginal expected value of perfect information in a class of discrete time dynamic stochastic optimization problems which include the familiar optimal control problem with an infinite planning horizon. Using abstract Lagrange multiplier techniques on the usual nonanticipativity constraints treated explicitly in terms of adaptation of the decision sequence, it is shown that the marginal expected value of perfect information is a nonanticipative supermartingale. For a given problem, the statistics of this process are of fundamental practical importance in deciding the necessity for continuing to take account of the stochastic variation in the evolution of the sequence of optimal decisions

Modelling the U.S. Federal Spending Process: Overview and Implications

The purpose of this paper is to show how inflation is endemic to the budgetary process of the United States Federal Government. We relate models of government expenditure to models of the economy, thus joining in theory what has in practice always been together. The description given -- although presented in summary rather than detail -- is based on hard statistical and econometric evidence amassed over more than a decade. We attempt to show that, while they are complex, the relevant processes can be modeled reasonably simply. We conclude that the forces influencing U.S. Federal expenditures -- bureaucratic, political and economic -- are too entrenched and powerful to be easily deflected from their current course. Although expenditures decline during restrictive periods, they do not decline by nearly as much as they previously increased; thus each cycle of spending begins from a higher base. After brief descriptions of the process by which fiscal and budgetary policy are formed in the name of the President and of the evolution of the broad pattern of Federal expenditure post World War II, we present simple, empirically supported models of the formation and coordination of budget requests, Congressional appropriations and the timing of Federal expenditures. Next we outline, by means of the comparative static analysis of a simple macroeconomic model with an endogenous government sector, the short and medium term economic implications of a government reacting -- through its wage bill, "mandatory" transfer payments and attempted fiscal policy -- to output, the price level and unemployment. When government involves a sizable proportion of economic activity, its budget deficit -- rather than private consumer and investment credit alone -- represents a major intertemporal credit demand, fueling both growth and inflation. In these circumstances a tight fiscal and monetary policy, which reduces this credit in response to inflation, can have precisely the opposite effect to that desired, namely, simultaneous stagnation and accelerating inflation. Finally, we speculate on the long term effects of the resulting growth of the public sector necessitated by short term political and economic forces in light of the slowly adapting nature of bureaucratic processes captured in our models

A Stochastic Approach to Hierarchical Planning and Scheduling

This paper surveys recent results for stochastic discrete programming models of hierarchical planning problems. Practical problems of this nature typically involve a sequence of decision over time at an increasing level of detail and with increasingly accurate information. These may be modeled by multistage stochastic programs whose lower levels (later stages) are stochastic versions of similar NP-hard deterministic combinatorial optimization problems and hence require the use of approximations and heuristics for near-optimal solution. After a brief survey of distributional assumptions on processing times under which SEPT and LEPT policies remain optimal for m-machine scheduling problems, results are presented for various 2-level scheduling problems in which the first stage concerns the acquisition (or assignment) of machines. For example, heuristics which are asymptotically optimal in expectation as the number of jobs in the system increases are analyzed for problems whose second stages are either identical or uniform m-machine scheduling problems. A 3-level location, distribution and routing model in the plane is also discussed

Nested Optimization in DOA Estimation for Nonlinear Dynamical Systems: Spacecraft Large Angle Manoeuvres

This paper discusses the formulation and numerical development of an algorithm for the estimation of the domain of attraction of a general nonlinear autonomous dynamical system. The method is based on stability analysis using Lyapunov's direct method with quadratic Lyapunov functions. It requires the nesting of an unconstrained and a constrained optimization problem -- both highly nonlinear. The Powell '64 conjugate direction algorithm and the BFGS quasi-Newton algorithm may be used as alternatives at the outer loop, while the recent Powell-Han projected Lagrangean algorithm is used for the inner loop nonlinear programme. Difficulties intrinsic to the Powell-Han algorithm, in obtaining global constrained minima and in providing sensitivity analysis of the inner loop problem in order to use BFGS at the outer loop are discussed in the context of stable control of large angle manoeuvres for astronomical satellites

The Expected Value of Perfect Information in the Optimal Evolution of Stochastic Systems

Methodological research into optimization problems and techniques has a long history in the System and Decision Sciences Program at IIASA. Most recently, effort -- of which this paper forms a part -- has concentrated on the analysis of stochastic systems. For a very general model of a stochastic optimization problem with an infinite planning horizon of discrete time, the author analyzes the stochastic process describing the marginal expected value of perfect information (EVPI) about the future of the system. He demonstrates two intuitively obvious properties of this marginal EVPI process: that its values are completely predictable at each actual decision point and that its expected values tend to decline over the future since information is potentially worth more the sooner it is available. The author is currently working on continuous time analogs of these results, which are unfortunately fraught with technical difficulties. This work should be viewed as a theoretical prolegomenon to computational studies aimed at estimating the value of perfect or partial information in the control of stochastic systems. The central observation here is that the extra complexity and computational burden of introducing random parameters into planning or control models may sometimes be unnecessary. The (marginal) EVPI at decision points is the natural measure by which their modeling efficacy can be evaluated

Bibliography of Soviet and Western European Publications on Large-Scale Linear Programming

This bibliography originates from the Workshop on Large-Scale Linear Programming held at IIASA over the period June 2-6 1980. The Proceedings of this Workshop (edited by G.B. Dantzig, M.A.H. Dempster and M. Kallio, IIASA CP-81-S1) contains a bibliography covering North American and Western European publications. This bibliography is a supplement which covers Eastern European work on large-scale linear programming. As some important work may still be missing, further contributions (with English translations of titles published in other languages) are most welcome. Such contributions should be sent to H. Gasking at IIASA, where a computerized bibliography is maintained. Revised versions will be issued from time to time

Large-Scale Linear Programming

During the week of June 2-6, 1980, the System and Decision Sciences Area of the International Institute for Applied Systems Analysis organized a workshop on large-scale linear programming in collaboration with the Systems Optimization Laboratory (SOL) of Stanford University, and co-sponsored by the Mathematical Programming Society (MPS). The participants in the meeting were invited from amongst those who actively contribute to research in large-scale linear programming methodology (including development of algorithms and software). The first volume of the Proceedings contains five chapters. The first is an historical review by George B. Dantzig of his own and related research in time-staged linear programming problems. Chapter 2 contains five papers which address various techniques for exploiting sparsity and degeneracy in the now standard LU decomposition of the basis used with the simplex algorithm for standard (unstructured) problems. The six papers of Chapter 3 concern aspects of variants of the simplex method which take into account through basis factorization the specific block-angular structure of constraint matrices generated by dynamic and/or stochastic linear programs. In Chapter 4, five papers address extensions of the original Dantzig-Wolfe procedure for utilizing the structure of planning problems by decomposing the original LP into LP subproblems coordinated by a relatively simple LP master problem of a certain type. Chapter 5 contains four papers which constitute a mini-symposium on the now famous Shor-Khachian ellipsoidal method applied to both real and integer linear programs. The first chapter of Volume 2 contains three papers on non-simplex methods for linear programming. The remaining chapters of Volume 2 concern topics of present interest in the field. A bibliography a large-scale linear programming research completes Volume 2

A Standard Input Format for Multiperiod Stochastic Linear Programs

Data conventions for the automatic input of multiperiod stochastic linear programs are described. The input format is based on the MPSX standard and is designed to promote the efficient conversion of originally deterministic problems by introducing stochastic variants in separate files. A flexible "header" syntax generates a useful variety of stochastic dependencies. An extension using the NETGEN format is proposed for stochastic network programs

Analytical Evaluation of Hierarchical Planning Systems

Hierarchical planning systems have become popular for multilevel decision problems. After reviewing the concept of hierarchical planning and citing some examples, the authors describe a method for analytic evaluation of a hierarchical planning system. They show that multilevel decision problems can be nicely modeled as multistage stochastic programs. Then any hierarchical planning system can be measured against the yardstick of optimality in this stochastic program. They demonstrate this approach on a hierarchical system that can be shown to be asymptotically optimal for a job shop design/scheduling problem