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Showing papers on "Stochastic programming published in 1993"


Journal ArticleDOI
TL;DR: In this article, the authors present a model for renewable-resource harvesting based on the Schaefer model with a focus on the one-dimensional control problem and its application to policy problems.
Abstract: Introduction. 1. Elementary Dynamics of Exploited Populations. 1.1 The Logistic Growth Model. 1.2 Generalized Logistic Models: Depensation. 1.3 Summary and Critique. 2. Economic Models of Renewable-Resource Harvesting. 2.1 The Open-Access Fishery. 2.2 Economic Overfishing. 2.3 Biological Overfishing. 2.4 Optimal Fishery Management. 2.5 The Optimal Harvest Policy. 2.6 Examples Based on the Schaefer Model. 2.7 Linear Variational Problems. 2.8 The Possibility of Extinction. 2.9 Summary and Critique. 3. Capital-Theoretic Aspects of Resource Management. 3.1 Interest and Discount Rates. 3.2 Capital Theory and Renewable Resources. 3.3 Nonautonomous Models. 3.4 Applications to Policy Problems: Labor Mobility in the Fishery. 4. Optimal Control Theory. 4.1 One-Dimensional Control Problems. 4.2 A Nonlinear Fishery Model. 4.3 Economic Interpretation of the Maximum Principle. 4.4 Multidimensional Optimal Control Problem. 4.5 Optimal Investment in Renewable-Resource Harvesting. 5. Supply and Demand: Nonlinear Models. 5.1 The Elementary Theory of Supply and Demand. 5.2 Supply and Demand in Fisheries. 5.3 Nonlinear Cost Effects: Pulse Fishing. 5.4 Game-Theoretic Models. 5.5 Transboundary Fishery Resources: A Further Application of the Theory. 5.6 Summary and Critique. 6. Dynamical Systems. 6.1 Basic Theory. 6.2 Dynamical Systems in the Plane: Linear Theory. 6.3 Isoclines. 6.4 Nonlinear Plane-Autonomous Systems. 6.5 Limit Cycles. 6.6 Gause's Model of Interspecific Competition. 7. Discrete-Time and Metered Models. 7.1 A General Metered Stock-Recruitment Model. 7.2 The Beverton-Holt Stock-Recruitment Model. 7.3 Depensation Models. 7.4 Overcompensation. 7.5 A Simple Cohort Model. 7.6 The Production Function of a Fishery. 7.7 Optimal Harvest Policies. 7.8 The Discrete Maximum Principle. 7.9 Dynamic Programming. 8. The Theory of Resource Regulation. 8.1 A Behavioral Model. 8.2 Optimization Analysis. 8.3 Limited Entry. 8.4 Taxes and Allocated Transferable Quotas. 8.5 Total Catch Quotas. 8.6 Summary and Critique. 9. Growth and Aging. 9.1 Forestry Management: The Faustmann Model. 9.2 The Beverton-Holt Fisheries Model. 9.3 Dynamic Optimization in the Beverton-Holt Model. 9.4 The Case of Bounded F. 9.5 Multiple, Cohorts: Nonselective Gear. 9.6 Pulse Fishing. 9.7 Multiple Cohorts: Selective Gear. 9.8 Regulation. 9.9 Summary and Critique. 10. Multispecies Models. 10.1 Differential Productivity. 10.2 Harvesting Competing Populations. 10.3 Selective Harvesting. 10.4 A Diffusion Model: The Inshore-Offshore Fishery. 10.5 Summary and Critique. 11. Stochastic Resource Models. 11.1 Stochastic Dynamic Programming. 11.2 A Stochastic Forest Rotation Model. 11.3 Uncertainty and Learning. 11.4 Searching for Fish. 11.5 Summary and Critique. Supplementary Reading. References. Index.

2,744 citations


Journal ArticleDOI
TL;DR: In this paper, a branch-and-cut procedure for stochastic integer programs with complete recourse and first stage binary variables is presented, which is shown to provide a finite exact algorithm for a number of integer programs, even in the presence of binary variables or continuous random variables in the second stage.

598 citations


Journal ArticleDOI
TL;DR: A scheme based on a blending of classical Benders decomposition techniques and a special technique, called importance sampling, is used to solve this general class of multi-stochastic linear programs.
Abstract: The paper demonstrates how multi-period portfolio optimization problems can be efficiently solved as multi-stage stochastic linear programs. A scheme based on a blending of classical Benders decomposition techniques and a special technique, called importance sampling, is used to solve this general class of multi-stochastic linear programs. We discuss the case where stochastic parameters are dependent within a period as well as between periods. Initial computational results are presented.

249 citations


Journal ArticleDOI
TL;DR: In this article, a methodology for expansion planning of power systems under uncertainty in factors such as demand growth, fuel cost, delay in project completion, and financial constraints is described, and case studies within the Brazilian system are presented.
Abstract: A methodology is described for expansion planning of power systems under uncertainty in factors such as demand growth, fuel cost, delay in project completion, and financial constraints The approach draws upon three classes of techniques: decomposition and stochastic optimization provide the basic framework, and allow an implicit representation of alternative investment strategies; decision analysis is used to represent the dynamic aspects of decision-making as uncertainties are resolved over time; and hedging objectives from tradeoff analysis help select flexible and resilient expansion strategies. Case studies within the Brazilian system are presented and discussed. >

244 citations


Journal ArticleDOI
TL;DR: New techniques of local sensitivity analysis for nonsmooth generalized equations are applied to the study of sequences of statistical estimates and empirical approximations to solutions of stochastic programs.
Abstract: New techniques of local sensitivity analysis for nonsmooth generalized equations are applied to the study of sequences of statistical estimates and empirical approximations to solutions of stochastic programs. Consistency is shown to follow from a certain local invertibility property, and asymptotic distributions are derived from a generalized implicit function theorem that characterizes asymptotic behavior in situations where estimates are subjected to constraints and estimation functionals are nonsmooth.

205 citations


Journal ArticleDOI
TL;DR: A new decomposition method for multistage stochastic linear programming problems is proposed and it is shown that for large problems the authors can obtain substantial gains in efficiency with moderate numbers of processors.
Abstract: A new decomposition method for multistage stochastic linear programming problems is proposed. A multistage stochastic problem is represented in a tree-like form and with each node of the decision tree a certain linear or quadratic subproblem is associated. The subproblems generate proposals for their successors and some backward information for their predecessors. The subproblems can be solved in parallel and exchange information in an asynchronous way through special buffers. After a finite time the method either finds an optimal solution to the problem or discovers its inconsistency. An analytical illustrative example shows that parallelization can speed up computation over every sequential method. Computational experiments indicate that for large problems we can obtain substantial gains in efficiency with moderate numbers of processors.

169 citations


Journal ArticleDOI
TL;DR: In this article, the problem of evaluating and optimizing the probability of feasible operation for a design that is described by a nonlinear model is formulated as a sequence of optimization problems, which can be extended to design optimization problems for maximizing the stochastic flexibility subject to a cost contraint.

142 citations


Journal ArticleDOI
TL;DR: In this article, the authors used nonlinear simulation-regression applied to a transient groundwater flow model to estimate parameter values and their uncertainties and use steady state flow path analyses to confirm the model's consistency with the location of contaminants.
Abstract: groundwater management model is developed for a shallow, unconfined sandy aquifer at a Superfund site at which a vinyl chloride plume is migrating toward Lake Michigan. We use nonlinear simulation-regression applied to a transient groundwater flow model to estimate parameter values and their uncertainties and use steady state flow path analyses to confirm the model's consistency with the location of contaminants. Parameter uncertainty is translated into flow model prediction uncertainty using a first-order Taylor series approximation. Optimal minimum-pumping strategies for steady state hydraulic containment of the plume are designed, and model prediction uncertainty is accounted for with stochastic programming. It is impossible to achieve a reliability level higher than 60% using only two pumping wells. For the 10-well case, pumping rates must increase about 40% to extend reliability from 50 to 90%. Monte Carlo analyses indicate that for the I 0-well 90% reliability formulation, the first-order method of propagating uncertainty results in a solution with accurate performance reliabilities. We find that the coefficient of variation in hydraulic gradient dictates whether the probabilistic constraints are obeyed. Comparison of the probabilistic constraint and "safety factor" approaches to overcoming model uncertainty reveals that the ability of probabilistic constraints to accommodate local variations in model prediction uncertainty is highly important. Postoptimization solute transport studies show that increased reliability levels for hydraulic containment do not necessarily translate into faster plume cleanup times.

124 citations


Journal ArticleDOI
TL;DR: Applicability of the involved regularity conditions to nondifferentiable cases, and in particular to stochastic programming with recourse, is discussed, and an expansion in terms of a parametrized mathematical programming problem, depending on a single random vector is given.
Abstract: Asymptotic behavior of optimal solutions xI‚n of a sequence of stochastic programming problems is studied. Variational and generalized equations approaches are discussed. An expansion of xI‚n in terms of a parametrized mathematical programming problem, depending on a single random vector, is given. When optimal solutions of the parametrized program are directionally differentiable, this expansion leads to a close form expression for the asymptotic distribution of xI‚n. Applicability of the involved regularity conditions to nondifferentiable cases, and in particular to stochastic programming with recourse, is discussed.

114 citations


Journal ArticleDOI
TL;DR: Reoptimizing the policy when a decision is made within the simulation resulted in better system performance, particularly when severe penalties were incurred for water and power shortages and coarse discretizations were employed in the SDP.
Abstract: This paper compares two approaches for implementing reservoir operating policies derived using stochastic dynamic programming (SDP) models. In particular, operating policies for the Shasta-Trinity system in Northern California are generated using SDP algorithms that employ either multilinear or multidimensional piecewise cubic functions to approximate the cost-to-go function. Release decisions in the simulations are then determined by either (1) interpolating in the policy tables or (2) reoptimizing the policy within the simulation, using the cost-to-go function generated by the SDP. The impact on simulated system performance of several discretization and interpolation schemes in the SDP is also evaluated. Reoptimizing the policy when a decision is made within the simulation resulted in better system performance, particularly when severe penalties were incurred for water and power shortages and coarse discretizations were employed in the SDP.

113 citations


Proceedings Article
29 Nov 1993
TL;DR: This work uses second order local trajectory optimization to generate locally optimal plans and local models of the value function and its derivatives, and maintains global consistency of the local Models of thevalue function, guaranteeing that the locally optimal Plans are actually globally optimal.
Abstract: Dynamic programming provides a methodology to develop planners and controllers for nonlinear systems. However, general dynamic programming is computationally intractable. We have developed procedures that allow more complex planning and control problems to be solved. We use second order local trajectory optimization to generate locally optimal plans and local models of the value function and its derivatives. We maintain global consistency of the local models of the value function, guaranteeing that our locally optimal plans are actually globally optimal, up to the resolution of our search procedures.

Journal ArticleDOI
TL;DR: In this paper, a stochastic programming procedure is proposed for managing asset/liability portfolios with interest rate contingent claims, using scenario generation to combine deterministic dedication techniques with stochastically duration matching methods, and providing the portfolio manager with a risk/return Pareto optimal frontier from which a portfolio may be selected based on individual risk attitudes.
Abstract: Drawing on recent developments in discrete time fixed income options theory, we propose a stochastic programming procedure, which we call stochastic dedication, for managing asset/liability portfolios with interest rate contingent claims. The model uses scenario generation to combine deterministic dedication techniques with stochastic duration matching methods, and provides the portfolio manager with a risk/return Pareto optimal frontier from which a portfolio may be selected based on individual risk attitudes. We employ a fixed income risk metric that can be interpreted as the fair market value of a collection of interest rate options that eliminates bankruptcy risk from the asset/liability portfolio. We incorporate this metric into a risk/return stochastic optimization model, using a binomial lattice sampling procedure to construct interest rate paths and cash flow streams from an arbitrage-free term structure model. The resulting parametric linear program has a particularly simple subproblem structure,...

Journal ArticleDOI
TL;DR: The linear two-level programming problem is restated as a global optimization problem and a new solution method based on this approach is developed that attempts to take full advantage of the structure in the constraints using some recent global optimization techniques.
Abstract: Linear two-level programming deals with optimization problems in which the constraint region is implicity determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the linear two-level programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques. A small example is solved in order to illustrate the approach.

Journal ArticleDOI
TL;DR: This paper poses a general stochastic assignment model that includes as special cases most models which have appeared in the literature, and verifies that the probability distributions of an equivalent Markovian model converge to a stationary distribution.
Abstract: Recent interest in stochastic traffic assignment models has been motivated by a need to determine the stationary probability distribution of a network's traffic volumes and by the possibility of using time-series of traffic counts to fit and test travel demand models. Because of the way traffic volumes are generated as the sum of path flows from different origin-destination pairs, and because of the nonlinear nature of the process relating traffic conditions to traveler route selection, most plausible assignment models tend to be intractable. In this paper, we first pose a general stochastic assignment model that includes as special cases most models which have appeared in the literature, and then verify that the probability distributions of an equivalent Markovian model converge to a stationary distribution. We next verify that as the number of individual travelers becomes large, the general model can be approximated by the sum of a nonlinear deterministic process and a time-varying linear Gaussian proce...

Journal ArticleDOI
TL;DR: In this paper, the authors present optimization models for waste load allocation from multiple point sources which include both parameter (Type II) and model (Type I) uncertainty, and explore the effects of Type I uncertainty on control decisions.
Abstract: This paper presents optimization models for waste load allocation from multiple point sources which include both parameter (Type II) and model (Type I) uncertainty. These optimization models employ more sophisticated water quality simulation models, for example, in the case of dissolved oxygen modeling, QUAL2E and WASP4, than is typically the norm in studies on the optimization of waste load allocation. Variability in selected input parameters to the water quality simulation models gives rise to stochastic dynamic programming approaches. Two types of reliability and feasibility attributes are highlighted, associated with the management options that are generated. Several dissolved oxygen simulation models are incorporated into the optimization procedures to explore the effects of Type I uncertainty on control decisions. Information from simultaneous consideration of multiple simulation models is aggregated in the dynamic programming framework through two regret-based formulations. By accommodating both model and parameter uncertainty in the modeling framework, trade-offs can be generated between the two so as to assess their influence on control decisions. The models are applied to a waste load allocation problem for the Schuylkill River in Pennsylvania.

Journal ArticleDOI
TL;DR: F fuzzy mathematical programming problems are formulated based on the idea analogous with the chance constrained programming problem, where the difference in meaning between the ambiguity of the coefficients and that of the decision maker's preference is emphasized.

Journal ArticleDOI
TL;DR: In this paper, the authors analyze life cycle consumption plans and distinguish between temporal risk aversion and intertemporal substitution, and find a rationale for precautionary saving and a larger sensitivity of changes in consumption to income innovations.
Abstract: This paper analyses life-cycle consumption plans and distinguishes between temporal risk aversion and intertemporal substitution. The results assume that felicity functions are quadratic and that income follows a linear model with normally distributed errors. Stochastic dynamic programming then yields closed-loop linear decision rules. Certainty equivalence no longer holds, but instead households play a min-max strategy against nature. One finds a rationale for precautionary saving and a larger sensitivity of changes in consumption to income innovations.

Journal ArticleDOI
TL;DR: Sufficient conditions for the (Lipschitz) continuity of the expectation of second-stage costs are given for two-stage stochastic programs, where the optimization problem in the second stage is a mixed-integer linear program.
Abstract: Sufficient conditions for the (Lipschitz) continuity of the expectation of second-stage costs are given for two-stage stochastic programs, where the optimization problem in the second stage is a mixed-integer linear program. We also present counterexamples to show that, in general, the results can no longer be maintained when relaxing assumptions as well as multivariate probability distributions for which the theory works.

Journal ArticleDOI
TL;DR: This paper introduces the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in Stochastic continuous programs.
Abstract: Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic continuous programs. Analytical as well as computational properties of the expected recourse function of simple integer recourse problems are studied. This includes sharp bounds on this function and the study of the convex hull. Finally, a finite termination algorithm is obtained that solves two classes of stochastic simple integer recourse problems.

Journal ArticleDOI
TL;DR: A stochastic dynamic programming model is developed to evaluate the optimal trade-offs across prevention and appraisal costs, and the costs of failure and shows that it may not be optimal for quality improvement efforts to target products that have the highest defective levels, largest direct costs or consume the maximum capital resources.
Abstract: We build a model to measure and account for the cost of quality. We incorporate the impact of quality on lead time variance and on service reliability and demand. Quality costs are a joint and nonlinear function of various parameters of the manufacturing process. Our model shows that it may not be optimal for quality improvement efforts to target products that have the highest defective levels, largest direct costs or consume the maximum capital resources. A stochastic dynamic programming model is developed to evaluate the optimal trade-offs across prevention and appraisal costs, and the costs of failure.

Journal ArticleDOI
TL;DR: An algorithm for solving nonlinear, two-stage stochastic problems with network recourse based on the framework of row-action methods that permits the massively parallel solution of all the scenario subproblems concurrently and achieves computing rates of 276 MFLOPS.
Abstract: We develop an algorithm for solving nonlinear, two-stage stochastic problems with network recourse. The algorithm is based on the framework of row-action methods. The problem is formulated by replicating the first-stage variables and then adding nonanticipativity side constraints. A series of independent deterministic network problems are solved at each step of the algorithm, followed by an iterative step over the nonanticipativity constraints. The solution point of the iterates over the nonanticipativity constraints is obtained analytically. The row-action nature of the algorithm makes it suitable for parallel implementations. A data representation of the problem is developed that permits the massively parallel solution of all the scenario subproblems concurrently. The algorithm is implemented on a Connection Machine CM-2 with up to 32K processing elements and achieves computing rates of 276 MFLOPS. Very large problems-8,192 scenarios with a deterministic equivalent nonlinear program with 868,367 constraints and 2,474,017 variables-are solved within a few minutes. We report extensive numerical results regarding the effects of stochasticity on the efficiency of the algorithm.

Journal ArticleDOI
TL;DR: The resulting Stochastic, Multiobjective Shortest Path (SMOSP) algorithm has important application in hazardous materials transportation in the Albany-Schenectady-Troy area of New York State.

Journal ArticleDOI
TL;DR: A stochastic programming model for the management of large portfolios of mortgage-backed securities (abbreviated: MBS) is presented, whereby portfolio decisions made here-and-now are influenced by uncertain information about the future.
Abstract: We present a stochastic programming model for the management of large portfolios of mortgage-backed securities (abbreviated: MBS). It is a two-stage, multiperiod model, whereby portfolio decisions made here-and-now are influenced by uncertain information about the future. In particular, we consider uncertainty in both the prepayment activity of the MBSs in the portfolio, as well as uncertainty about the future reinvestment rates. A simulation procedure is used to generate interest rate paths and prepayment behavior, and the stochastic program can be extremely large. Solution of the resulting large-scale programs is particularly challenging. We show that with massively parallel computing technology, the proposed models are indeed solvable. Empirical results on a Connection Machine CM-2 are reported.

Journal ArticleDOI
TL;DR: The central result asserts that, under a strong-convexity condition for the expected recourse in the unperturbed problem, optimal tenders behave Holder-continuous with respect to a Wasserstein metric.
Abstract: Quantitative continuity of optimal solution sets to convex stochastic programs with (linear) complete recourse and random right-hand sides is investigated when the underlying probability measure varies in a metric space. The central result asserts that, under a strong-convexity condition for the expected recourse in the unperturbed problem, optimal tenders behave Holder-continuous with respect to a Wasserstein metric. For linear stochastic programs this carries over to the Hausdorff distance of optimal solution sets A general sufficient condition for the crucial strong-convexity assumption is given and verified for recourse problems with separable and nonseparable objectives.

Journal ArticleDOI
TL;DR: Stochastic programming techniques are adapted and further developed for applications to discrete event systems where the sample path of the system depends discontinuously on control parameters, which could make the computation of estimates of the gradient difficult.
Abstract: In this paper, stochastic programming techniques are adapted and further developed for applications to discrete event systems. We consider cases where the sample path of the system depends discontinuously on control parameters (e.g. modeling of failures, several competing processes), which could make the computation of estimates of the gradient difficult. Methods which use only samples of the performance criterion are developed, in particular finite differences with reduced variance and concurrent approximation and optimization algorithms. Optimization of the stationary behavior is also considered. Results of numerical experiments and convergence results are reported.

Book
01 Jan 1993
TL;DR: Equilibrium models of mathematical economy numerical optimization methods and software convex programming methods of optimal complexity polynomial algorithms in linear programming decomposition of optimization systems.
Abstract: Equilibrium models of mathematical economy numerical optimization methods and software convex programming methods of optimal complexity polynomial algorithms in linear programming decomposition of optimization systems modern apparatus of non-smooth optimization discrete programming models and methods analysis of inconsistent mathematical programming problems multiobjective problems optimization in order scales extremal problems in infinite-dimensional spaces.

Journal ArticleDOI
TL;DR: A decomposition algorithm for this procedure is presented that efficiently solves problems with large-scale deterministic equivalents of up to 66,000 variables.
Abstract: This paper presents a method for finding optimal flows in a dynamic network with random inputs into the system and congestion limits on flow. This model has been used in deterministic settings to represent dynamic traffic assignment and job shop routing. This paper builds on the deterministic results to show that a globally optimal solution in the stochastic problem may be obtained by a sequence of linear optimizations. A decomposition algorithm for this procedure is presented that efficiently solves problems with large-scale deterministic equivalents of up to 66,000 variables.

Book ChapterDOI
01 Jan 1993
TL;DR: This chapter presents stochastic programming with recourse model that explicitly treats uncertainties regarding demand, fuel costs, and environmental restrictions.
Abstract: Publisher Summary This chapter focuses on the mathematical programming decomposition methods that allow large-scale models to be broken down into manageable sub-models, and then systematically reassembled. These methods show considerable promise for time critical scheduling applications, especially when the methods have been adapted for and implemented on parallel computers. The mathematical programming models fall into several categories: linear programming, network optimization, mixed integer programming, nonlinear programming, dynamic programming, multiple criteria optimization, and stochastic programming. The linear programming model assumes that all transformation activities are linear and additive. Network optimization models determine monthly production plans for tools and tool/machine combinations. Nonlinear mixed integer programming models for capacity expansion planning of electric utilities have received considerable attention. The chapter presents stochastic programming with recourse model that explicitly treats uncertainties regarding demand, fuel costs, and environmental restrictions.


Journal ArticleDOI
TL;DR: In this paper, a stochastic dynamic programming model is introduced to determine the economic optimal replacement policy in swine breeding herds, which maximizes the present value of expected annual net returns from sows present in the herd and from subsequent replacement gilts over a given planning horizon.