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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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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: In this paper, a stochastic search method is proposed for finding a global solution to the discrete optimization problem in which the objective function must be estimated by Monte Carlo simulation, and it is shown under mild conditions that the Markov chain is strongly ergodic.
Abstract: In this paper a stochastic search method is proposed for finding a global solution to the stochastic discrete optimization problem in which the objective function must be estimated by Monte Carlo simulation. Although there are many practical problems of this type in the fields of manufacturing engineering, operations research, and management science, there have not been any nonheuristic methods proposed for such discrete problems with stochastic infrastructure. The proposed method is very simple, yet it finds a global optimum solution. The method exploits the randomness of Monte Carlo simulation and generates a sequence of solution estimates. This generated sequence turns out to be a nonstationary Markov chain, and it is shown under mild conditions that the Markov chain is strongly ergodic and that the probability that the current solution estimate is global optimum converges to one. Furthermore, the speed of convergence is also analyzed.

204 citations

Journal ArticleDOI
TL;DR: Stochastic mathematical programs with equilibrium constraints (SMPEC), which generalize MPEC models by explicitly incorporating possible uncertainties in the problem data to obtain robust solutions to hierarchical problems, are introduced.

204 citations

Journal ArticleDOI
TL;DR: A stochastic model predictive control-based energy management strategy using the vehicle location, traveling direction, and terrain information of the area for HEVs running in hilly regions with light traffic is proposed and shown that the developed method can help maintaining the battery SoC within its boundaries and achieve good energy consumption performance.
Abstract: The energy efficiency of parallel hybrid electric vehicles (HEVs) can degrade significantly when the battery state-of-charge (SoC) reaches its boundaries. The road grade has a great influence on the HEV battery charging and discharging processes, and therefore the HEV energy management can be benefited from the road grade preview. In real-world driving, the road grade ahead can be considered as a random variable because the future route is not always available to the HEV controller. This brief proposes a stochastic model predictive control-based energy management strategy using the vehicle location, traveling direction, and terrain information of the area for HEVs running in hilly regions with light traffic. The strategy does not require a determined route being known in advance. The road grade is modeled as a Markov chain and stochastic HEV fuel consumption and battery SoC models are developed. The HEV energy management problem is formulated as a finite-horizon Markov decision process and solved using stochastic dynamic programming. The proposed method is evaluated in simulation and compared with an equivalent consumption minimization strategy and the dynamic programming results. It is shown that the developed method can help maintaining the battery SoC within its boundaries and achieve good energy consumption performance.

204 citations

Journal ArticleDOI
Jon M. Conrad1
TL;DR: In this paper, the authors present a general-purpose computer program for solving dynamic programming problems in agriculture and natural resource management, which is based on the Lagrangian derived from the Discrete Maximum Principle.
Abstract: I Introduction.- 1 The Management of Agricultural and Natural Resource Systems.- 1.1 The Nature of Agricultural and Natural Resource Problems.- 1.2 Management Techniques Applied to Resource Problems.- 1.2.1 Farm management.- 1.2.2 Forestry management.- 1.2.3 Fisheries management.- 1.3 Control Variables in Resource Management.- 1.3.1 Input decisions.- 1.3.2 Output decisions.- 1.3.3 Timing and replacement decisions.- 1.4 A Simple Derivation of the Conditions for Intertemporal Optimality.- 1.4.1 The general resource problem without replacement.- 1.4.2 The general resource problem with replacement.- 1.5 Numerical Dynamic Programming.- 1.5.1 Types of resource problem.- 1.5.2 Links with simulation.- 1.5.3 Solution procedures.- 1.5.4 Types of dynamic programming problem.- 1.6 References.- 1.A Appendix: A Lagrangian Derivation of the Discrete Maximum Principle.- 1.B Appendix: A Note on the Hamiltonian Used in Control Theory.- II The Methods of Dynamic Programming.- 2 Introduction to Dynamic Programming.- 2.1 Backward Recursion Applied to the General Resource Problem.- 2.2 The Principle of Optimality.- 2.3 The Structure of Dynamic Programming Problems.- 2.4 A Numerical Example.- 2.5 Forward Recursion and Stage Numbering.- 2.6 A Simple Crop-irrigation Problem.- 2.6.1 The formulation of the problem.- 2.6.2 The solution procedure.- 2.7 A General-Purpose Computer Program for Solving Dynamic Programming Problems.- 2.7.1 An introduction to the GPDP programs.- 2.7.2 Data entry using DPD.- 2.7.3 Using GPDP to solve the least-cost network problem.- 2.7.4 Using GPDP to solve the crop-irrigation problem.- 2.8 References.- 3 Stochastic and Infinite-Stage Dynamic Programming.- 3.1 Stochastic Dynamic Programming.- 3.1.1 Formulation of the stochastic problem.- 3.1.2 A stochastic crop-irrigation problem.- 3.2 Infinite-stage Dynamic Programming for Problems With Discounting.- 3.2.1 Formulation of the problem.- 3.2.2 Solution by value iteration.- 3.2.3 Solution by policy iteration.- 3.3 Infinite-stage Dynamic Programming for Problems Without Discounting.- 3.3.1 Formulation of the problem.- 3.3.2 Solution by value iteration.- 3.3.3 Solution by policy iteration.- 3.4 Solving Infinite-stage Problems in Practice.- 3.4.1 Applications to agriculture and natural resources.- 3.4.2 The infinite-stage crop-irrigation problem.- 3.4.3 Solution to the crop-irrigation problem with discounting.- 3.4.4 Solution to the crop-irrigation problem without discounting.- 3.5 Using GPDP to Solve Stochastic and Infinite-stage Problems.- 3.5.1 Stochastic problems.- 3.5.2 Infinite-stage problems.- 3.6 References.- 4 Extensions to the Basic Formulation.- 4.1 Linear Programming for Solving Stochastic, Infinite-stage Problems.- 4.1.1 Linear programming formulations of problems with discounting.- 4.1.2 Linear programming formulations of problems without discounting.- 4.2 Adaptive Dynamic Programming.- 4.3 Analytical Dynamic Programming.- 4.3.1 Deterministic, quadratic return, linear transformation problems.- 4.3.2 Stochastic, quadratic return, linear transformation problems.- 4.3.3 Other problems which can be solved analytically.- 4.4 Approximately Optimal Infinite-stage Solutions.- 4.5 Multiple Objectives.- 4.5.1 Multi-attribute utility.- 4.5.2 Risk.- 4.5.3 Problems involving players with conflicting objectives.- 4.6 Alternative Computational Methods.- 4.6.1 Approximating the value function in continuous form.- 4.6.2 Alternative dynamic programming structures.- 4.6.3 Successive approximations around a nominal control policy.- 4.6.4 Solving a sequence of problems of reduced dimension.- 4.6.5 The Lagrange multiplier method.- 4.7 Further Information on GPDP.- 4.7.1 The format for user-written data files.- 4.7.2 Redimensioning arrays in FDP and IDP.- 4.8. References.- 4.A Appendix: The Slope and Curvature of the Optimal Return Function Vi{xi}.- III Dynamic Programming Applications to Agriculture.- 5 Scheduling, Replacement and Inventory Management.- 5.1 Critical Path Analysis.- 5.1.1 A farm example.- 5.1.2 Solution using GPDP.- 5.1.3 Selected applications.- 5.2 Farm Investment Decisions.- 5.2.1 Optimal tractor replacement.- 5.2.2 Formulation of the problem without tax.- 5.2.3 Formulation of the problem with tax.- 5.2.4 Discussion.- 5.2.5 Selected applications.- 5.3 Buffer Stock Policies.- 5.3.1 Stochastic yields: planned production and demand constant.- 5.3.2 Stochastic yields and demand: planned production constant.- 5.3.3 Planned production a decision variable.- 5.3.4 Selected applications.- 5.4 References.- 6 Crop Management.- 6.1 The Crop Decision Problem.- 6.1.1 States.- 6.1.2 Stages.- 6.1.3 Returns.- 6.1.4 Decisions.- 6.2 Applications to Water Management.- 6.3 Applications to Pesticide Management.- 6.4 Applications to Crop Selection.- 6.5 Applications to Fertilizer Management.- 6.5.1 Optimal rules for single-period carryover functions.- 6.5.2 Optimal rules for a multiperiod carryover function.- 6.5.3 A numerical example.- 6.5.4 Extensions.- 6.6 References.- 7 Livestock Management.- 7.1 Livestock Decision Problems.- 7.2 Livestock Replacement Decisions.- 7.2.1 Types of problem.- 7.2.2 Applications to dairy cows.- 7.2.3 Periodic revision of estimated yield potential.- 7.3 Combined Feeding and Replacement Decisions.- 7.3.1 The optimal ration sequence: an example.- 7.3.2 Maximizing net returns per unit of time.- 7.3.3 Replacement a decision option.- 7.4 Extensions to the Combined Feeding and Replacement Problem.- 7.4.1 The number of livestock.- 7.4.2 Variable livestock prices.- 7.4.3 Stochastic livestock prices.- 7.4.4 Ration formulation systems.- 7.5 References.- 7.A Appendix: Yield Repeatability and Adaptive Dynamic Programming.- 7.A.1 The concept of yield repeatability.- 7.A.2 Repeatability of average yield.- 7.A.3 Expected yield given average individual and herd yields.- 7.A.4 Yield probabilities conditional on recorded average yields.- IV Dynamic Programming Applications to Natural Resources.- 8 Land Management.- 8.1 The Theory of Exhaustible Resources.- 8.1.1 The simple theory of the mine.- 8.1.2 Risky possession and risk aversion.- 8.1.3 Exploration.- 8.2 A Pollution Problem.- 8.2.1 Pollution as a stock variable.- 8.2.2 A numerical example.- 8.3 Rules for Making Irreversible Decisions Under Uncertainty.- 8.3.1 Irreversible decisions and quasi-option value.- 8.3.2 A numerical example.- 8.3.3 The discounting procedure.- 8.4 References.- 9 Forestry Management.- 9.1 Problems in Forestry Management.- 9.2 The Optimal Rotation Period.- 9.2.1 Deterministic problems.- 9.2.2 Stochastic problems.- 9.2.3 A numerical example of a combined rotation and protection problem.- 9.3 The Optimal Rotation and Thinning Problem.- 9.3.1 Stage intervals.- 9.3.2 State variables.- 9.3.3 Decision variables.- 9.3.4 Objective function.- 9.4 Extensions.- 9.4.1 Allowance for distributions of tree sizes and ages.- 9.4.2 Alternative objectives.- 9.5 References.- 10 Fisheries Management.- 10.1 The Management Problem.- 10.2 Modelling Approaches.- 10.2.1 Stock dynamics.- 10.2.2 Stage return.- 10.2.3 Developments in analytical modelling.- 10.3 Analytical Dynamic Programming Approaches.- 10.3.1 Deterministic results.- 10.3.2 Stochastic results.- 10.4 Numerical Dynamic Programming Applications.- 10.4.1 An application to the southern bluefin tuna fishery.- 10.4.2 A review of applications.- 10.5 References.- V Conclusion.- 11 The Scope for Dynamic Programming Applied to Resource Management.- 11.1 Dynamic Programming as a Method of Conceptualizing Resource Problems.- 11.2 Dynamic Programming as a Solution Technique.- 11.3 Applications to Date.- 11.4 Expected Developments.- 11.5 References.- Appendices.- A1 Coding Sheets for Entering Data Using DPD.- A2 Program Listings.- A2.1 Listing of DPD.- A2.2 Listing of FDP.- A2.3 Listing of IDP.- A2.4 Listing of DIM.- Author Index.

204 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532