Showing papers on "Stochastic programming published in 1982"
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TL;DR: In this paper, the authors present a survey of dynamic programming models for water resource problems and examine computational techniques which have been used to obtain solutions to these problems, including aqueduct design, irrigation system control, project development, water quality maintenance, and reservoir operations analysis.
Abstract: The central intention of this survey is to review dynamic programming models for water resource problems and to examine computational techniques which have been used to obtain solutions to these problems. Problem areas surveyed here include aqueduct design, irrigation system control, project development, water quality maintenance, and reservoir operations analysis. Computational considerations impose severe limitation on the scale of dynamic programming problems which can be solved. Inventive numerical techniques for implementing dynamic programming have been applied to water resource problems. Discrete dynamic programming, differential dynamic programming, state incremental dynamic programming, and Howard's policy iteration method are among the techniques reviewed. Attempts have been made to delineate the successful applications, and speculative ideas are offered toward attacking problems which have not been solved satisfactorily.
524 citations
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TL;DR: The bi-level linear case is addressed in detail and the reformulated optimization problem is linear save for a complementarity constraint of the form 〈u, g〉 = 0.
493 citations
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TL;DR: Borders on the value of the stochastic solution are presented, that is, the potential benefit from solving the stoChastic program over solving a deterministic program in which expected values have replaced random parameters.
Abstract: Stochastic linear programs have been rarely used in practical situations largely because of their complexity. In evaluating these problems without finding the exact solution, a common method has been to find bounds on the expected value of perfect information. In this paper, we consider a different method. We present bounds on the value of the stochastic solution, that is, the potential benefit from solving the stochastic program over solving a deterministic program in which expected values have replaced random parameters. These bounds are calculated by solving smaller programs related to the stochastic recourse problem.
310 citations
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TL;DR: In this paper, a stochastic linear programming formulation of a firm's short-term financial planning problem is presented, which allows a more realistic representation of the uncertainties fundamental to this problem than previous models.
Abstract: This paper presents a stochastic linear programming formulation of a firm's short term financial planning problem. This framework allows a more realistic representation of the uncertainties fundamental to this problem than previous models. In addition, using Wets's algorithm for linear simple recourse problems, this formulation has approximately the same computational complexity as the mean approximation i.e., the deterministic program obtained by replacing all random elements by their means. Using this formulation we empirically investigate the effects of differing distributions and penalty costs. We conclude that even with symmetric penalty costs and distributions the mean model is significantly inferior to the stochastic linear programming formulation. Thus we are able to demonstrate that ignoring the stochastic components in linear programming formulations can be very costly without having significant computational savings.
108 citations
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TL;DR: Under suitable convexity and integrability assumptions, for the stochastic programming problem with recourse statements, error bounds are proved very easily and lower bounds for approximations using discrete random vectors are proved.
Abstract: Under suitable convexity and integrability assumptions, for the stochastic programming problem with recourse statements are proved very easily, which have been shown until now only for stochastic linear programming. In particular, this includes lower bounds for approximations using discrete random vectors. Until now unpublished, even for the linear ease, are error bounds, which are proved here under different assumptions. Computational experiences are reported. Finally, some improvements are suggested which may reduce the computation time.
82 citations
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TL;DR: In this article, a general technique for the characterization of optimal plans resulting from stochastic dynamic programming is presented. But the analysis of many problems in economics requires the consideration of both time and uncertainty, and a frequent criticism of the application of this technique to economic decision problems is that although solutions are shown to exist they are not adequately characterized.
66 citations
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56 citations
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TL;DR: In this article, a group preventive replacement problem is formulated in continuous time for a multicomponent system having identical elements and the dynamic programming equation is obtained in the framework of the theory of optimal control of jump processes.
Abstract: A group preventive replacement problem is formulated in continuous time for a multicomponent system having identical elements. The dynamic programming equation is obtained in the framework of the theory of optimal control of jump processes. For a discrete time version of the model, the numerical computation of optimal and suboptimal strategies of group preventive replacement are done. A monotonicity property of the Bellman functional (or cost-to-go function) is used to reduce the size of the computational problem. Some counterintuitive properties of the optimal strategy are apparent in the numerical results obtained.
48 citations
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TL;DR: Results are presented from the application of the method to control the alfalfa weevil by a combination of insecticide applications, early harvesting, and biological control provided by a parasite.
Abstract: A procedure is presented for calculating optima integration and timing of biological, chemical and cultural methods for control of a univoltine pest population in a random environment. The procedure describes a system of high dimension by two nested models: a stochastic dynamic programming problem with four state variables and a more detailed differential equation model describing the effect of management and weather on population demography and crop yield. A computational algorithm is presented which reduces computation requirements for the population model from about 1013 operations to 106 operations for a typical example. Results are presented from the application of the method to control the alfalfa weevil by a combination of insecticide applications, early harvesting, and biological control provided by a parasite.
38 citations
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TL;DR: A simplified description of a new computing procedure for goal programming problems with minor modifications based on Baumol's simplex method, which appears to be more efficient than goal programming methods which are in common use.
Abstract: A simplified description of a new computing procedure for goal programming problems is provided, together with a step-by-step solution of an illustrative example. The procedure is based on Baumol's simplex method for solving linear programming problems with minor modifications. The proposed computational method appears to be more efficient than goal programming methods which are in common use.
35 citations
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TL;DR: In this paper, a model for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period is presented.
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TL;DR: In this article, the authors introduce stochastic features into a facility location model to describe both the total demand for facilities and the trip pattern of the customers, and explore the usefulness of such tools in formulating and solving problems of this type.
01 Jan 1982
TL;DR: In this article, the authors show that simple heuristics have strong properties of asymptotically optimal behavior for hierarchical vehicle routing problems, where the objective is to minimize the sum of the acquisition cost and the length of the longest route assigned to any vehicle.
Abstract: Hierarchical vehicle routing problems, in which the decision to acquire a number of vehicles has to be based on imperfect (probabilistic) information about the location of future customers, allow a natural formulation as two-stage stochastic programming problems, where the objective is to minimize the sum of the acquisition cost and the length of the longest route assigned to any vehicle. For several versions of this difficult optimization problem, we show that simple heuristics have strong properties of asymptotically optimal behavior.
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TL;DR: In this paper, the optimization procedures used in the Tennessee Valley Authority (TVA) HYDROSIM model are described, where a linear programming procedure for implementing preemptive priority constraints and a nonlinear search procedure for minimizing the power cost function are described.
Abstract: The optimization procedures used in the Tennessee Valley Authority (TVA) HYDROSIM model are described. Scheduling of the TVA operated reservoir system poses a stochastic, nonlinear, multireservoir problem with both nonviolable (physical) and violable (operating) constraints. A linear programming procedure for implementing the preemptive priority constraints and a nonlinear search procedure for minimizing the power cost function are described. A guide development program based on stochastic dynamic programming is also described.
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01 Jan 1982TL;DR: 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.
Abstract: This paper surveys recent results for stochastic discrete programming models of hierarchical planning problems. Practical problems of this nature typically involve a sequence of decisions over time at an increasing level of detail and with increasingly accurate information. These may be modelled by multistage stochastic programmes whose lower levels (later stages) are stochastic versions of familiar 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.
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01 Jan 1982
TL;DR: In this paper, the authors present an optimization condition and its application to Parametric Semi-Infinite Optimization (PINO) for point-to-set-mappings and the rate of convergence of corresponding algorithms.
Abstract: 1: Mathematical Programming and Optimal Control Theory.- An Optimality Condition and its Application to Parametric Semi-Infinite Optimization.- The Choice of a Parameter in a Penalty Method.- Recent Results on ?-Conjugation and Nonconvex Optimization.- On Quantitative Stability of Point-to-Set-Mappings and the Rate of Convergence of Corresponding Algorithms.- On the Penalization Method in Convex Stochastic Programming.- A New Algorithm of Solving the Flow - Shop Problem.- On Dynamic Traffic Assignment.- On an Approximation Problem of Mechanical Structural Optimization.- Optimal Daily Scheduling of the Electricity Production in Hungary.- Power Distribution Planning and the Application of Linear Mixed-Integer Programming.- Optimal Flood Control by Reservoir Systems Using the Reduced Gradient Method.- Instant Optimization of Hydro Energy Storage Plants.- Dynamic Programming in Power System Extension Planning.- Some New Multicriteria Approaches.- Equilibrium Selection in a Wage Bargaining Situation with Incomplete Information.- Planning and Forecast Horizons in a Simple Wheat Trading Model.- Intertemporal Reversales of Environmental and Macroeconomic Policies.- Optimal Control of Concave Economic Models with two Control Instruments.- Optimal Control with Switching Dynamics.- Dynamic Systems with Several Decision-Makers.- Optimal Bimodal Harvest Policies in Age-Specific Bioeconomic Models.- Growth Rates, Optimal Harvesting and Related Topics in the Mass Rearing of Tsetse Flies.- The Release of Partly Fertile Males or Females in the Application of the Sterile-Insect Technique: Mathematical Analysis of the Hard-Release Strategy.- 2: Stochastic Models.- New Developments in Optimal Control of Queueing Systems.- Estimation and Control in a GI|M|1-System.- On Discriminating among Stochastic Models - A Survey.- Increasing the Work-Safety in Nuclear Power Plants through the Use of Preventive Maintenance Policies.- Recent Developments in Econometrics.- Slight Misspecifications of Linear Systems.- Local Sensitivity Analysis and Matrix Derivatives.- Analysis and Forecasting of Demand for Electricity Using Time Series Analysis.- Short Term Load Predication in Electric Power Systems.- Interactive Short-Term Load Forecasting.- Predicting the Demand for Electricity - An Application of Transfer Function Analysis.- Problems Associated with the Design of a Reliability Model in Electricity Industry.
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01 Jan 1982
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TL;DR: In this article, a two-stage stochastic programming approach is used for a cost-oriented project scheduling model, where completion-time estimates for the activity-completion-times are computed in such a way that, in order to meet a prescribed time-constraint for the project completion time, the expected costs for performing the activities according to the computed time-schedule are minimized.
Abstract: If for a project (described by a non-empty set of activities, a relation on this set of activities the transitive closure of which is a strict order, and activity-completion-times assigned to the single activities) the activity-completion-times are assumed to be random variables a two-stage stochastic programming approach can be used for a cost-oriented project scheduling model. Completion-time estimates for the activity-completion-times are computed in such a way that, in order to meet a prescribed time-constraint for the project-completion-time, the expected costs for performing the activities according to the computed time-schedule are minimized. An example is included for illustration.
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TL;DR: In this article, the authors present a method which allows the quadratic programming formulation of the elastoplastic analysis to be reformulated as an equivalent quadratically programming problem which has significantly fewer variables than the original formulation.
Abstract: Two important problems in the area of engineering plasticity are limit load analysis and elastoplastic analysis. It is well known that these two problems can be formulated as linear and quadratic programming problems, respectively (Refs. 1–2). In applications, the number of variables in each of these mathematical programming problems tends to be large. Consequently, it is important to have efficient numerical methods for their solution. The purpose of this paper is to present a method which allows the quadratic programming formulation of the elastoplastic analysis to be reformulated as an equivalent quadratic programming problem which has significantly fewer variables than the original formulation. Indeed, in Section 4, we will present details of an example for which the original quadratic programming formulation required 297 variables and for which the equivalent formulation presented here required only two variables. The method is based on a characterization of the entire family of optimal solutions for a linear programming problem.
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01 Dec 1982
TL;DR: It is shown how to treat the problems of time optimization and cost optimization of STEOR networks (GERT networks with only nodes of the “stochastic exclusive-or” type) within the scope of Markov decision processes and the related dynamic programming techniques.
Abstract: We show how to treat the problems of time optimization and cost optimization of STEOR networks (GERT networks with only nodes of the “stochastic exclusive-or” type) within the scope of Markov decision processes and present the related dynamic programming techniques.
01 Jan 1982
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TL;DR: Using discrete time models for the ocean acoustic detection process formulated in earlier papers, this work solves the problem for a finite horizon of observations using several alternative objective and reward/penalty functions.
Abstract: Stochastic dynamic programming techniques are used to formulate and solve the problem of tracking two independent and stationary targets with one sensor in order to maximize a certain measure of performance. At any point in time, the sensor, usually a passive sonar array, can be allocated to only one of the two targets. Assuming the fluctuation process in the ocean to be governed by a phase‐random multipath law, the sensor ’’holds’’ the target when ρ, the root‐mean‐square pressure at the receiver, is above a user‐specified threshold. Using discrete time models for the ocean acoustic detection process formulated in earlier papers, we solve the problem for a finite horizon of observations using several alternative objective and reward/penalty functions. Delays of user‐specified magnitude in ’’switching’’ from one target to the other are also incorporated in our algorithms. Examples using both real and simulated data are presented and discussed. Finally, future research directions are suggested.
01 Dec 1982
TL;DR: A hybrid approach is presented, combining generalized goal programming and generalized networks, for the modeling of truly large-scale problems of such a type, via a multiobjective integer mathematical programming model.
Abstract: : A large number of real world problems may be characterized via a multiobjective integer mathematical programming model. However, the solution to truly large-scale problems of such a type has been a difficult task. In this paper, we present a hybrid approach, combining generalized goal programming and generalized networks, for the modeling of such problems. Once such a model has generalized networks, for the modeling of such problems. Once such a model has been developed, it may then be possible to employ the solution procedures of generalized networks to efficiently obtain a solution - particularly if the resultant hybrid model is, fundamentally, a multiobjective generalized network. (Author)
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TL;DR: In this paper, the authors focus on finding estimates on the variation of stochastic solutions and the corresponding solution of the mean of the dynamic system in the context of random polynomials and differential equations.
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01 Jan 1982TL;DR: A new approach using stochastic programming for a cost-oriented project scheduling model is presented and a solution procedure is described which constructs a sequence of nonstochastic Fulkerson project scheduling models.
Abstract: If the activity-completion-times of a project-network are random variables the project-completion-time is a random variable the distribution function of which is difficult to obtain. Thus, efforts have been made to determine bounds for the mean and bounding distribution functions for the distribution function of the project-completion-time some results of which are shortly surveyed. Then, a new approach using stochastic programming for a cost-oriented project scheduling model is presented. Generalizing a well-known Fulkerson-approach planned execution-times for the random activity-completion-times are computed where nonconformity with the actual realizations impose compensation costs (gains). Taking into consideration a prescribed project-completion-time constraint the expected costs for performing the activities ac-cording to the planned executions-times are minimized. A solution procedure is described which constructs a sequence of nonstochastic Fulkerson project scheduling models. It is demonstrated by means of an example.
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01 Jan 1982
TL;DR: The formalization of dynamic economic problems within the framework of optimization methods took place only in the late 1960s, about 25 years after the formulation and solution of the static programming problem as mentioned in this paper.
Abstract: Publisher Summary This chapter discusses various mathematical methods for economic analysis. It discusses the evolution of optimal control theory. The formalization of dynamic economic problems within the framework of optimization methods took place only in the late 1960s, about 25 years after the formulation and solution of the static programming problem. The theory of optimal control, thus, gave rise to an important new branch of economic theory, in both its deterministic and stochastic frameworks. It has been recognized that many important dynamic economic problems can be formulated in a standard mathematical form called dynamic optimization or optimal control. This is a well-defined problem consisting of three elements: (1) the objective function, (2) the state relationships, and (3) the constraints. Dynamic optimization is a technique of finding the values of decision (or control) variables that optimize the objective function and satisfy the constraints. The state relationships that provide the structure of the problem can be viewed as the main constraints of the problem and serve as a connection between the decision and state variables. The constraints consist of additional equations or inequalities, which must be satisfied by the decision and state variables. The objective function may depend on both sets of variables, though this double dependence is often disguised in the formulation of the problem.
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TL;DR: A stochastic dynamic programming formulation is used and three theorems concerning the reduction of the dimension of the state space, the concavity of the objective function, and the functional form of the optimal releases policy with a time-varying utility function are derived.
01 Dec 1982
TL;DR: In this paper, the stability of solutions to stochastic programming problems with recourse was studied and the Lipschitz continuity of optimal solutions as well as associated Lagrange multipliers with respect to the distribution function was shown.
Abstract: In this paper we study the stability of solutions to stochastic programming problems with recourse and show the Lipschitz continuity of optimal solutions as well as the associated Lagrange multipliers with respect to the distribution function.
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TL;DR: In this article, a convex chance-constrained programming problem with linear decision variables that can be either continuous or integer and where some or all of the associated cash flows are random variables that may be statistically dependent is considered.