Showing papers on "Stochastic programming published in 1997"

State-of-the-Art-Survey—Stochastic Programming: Computation and Applications

Abstract: Although decisions frequently have uncertain consequences, optimal-decision models often replace those uncertainties with averages or best estimates. Limited computational capability may have motivated this practice in the past. Recent computational advances have, however, greatly expanded the range of optimal-decision models with explicit consideration of uncertainties. This article describes the basic methodology for these stochastic programming models, recent developments in computation, and several practical applications.

Improved Fashion Buying with Bayesian Updates

Abstract: We focus on the problem of buying fashion goods for the “big book” of a catalogue merchandiser. This company also owns outlet stores and thus has the opportunity, as the season evolves, to divert inventory originally purchased for the big book to the outlet store. The obvious questions are: (1) how much to order originally, and (2) how much to divert to the outlet store as actual demand is observed. We develop a model of demand for an individual item. The model is motivated by data from the women's designer fashion department and uses both historical data and buyer judgement. We build a stochastic dynamic programming (DP) model of the fashion buying problem that incorporates the model of demand. The DP model is used to derive the structure of the optimal inventory control policy. We then develop an updated Newsboy heuristic that is intuitively appealing and easily implemented. When this heuristic is compared to the optimal solution for a wide variety of scenarios, we observe that it performs very well. Si...

Decomposition methods in stochastic programming

Abstract: Stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review basic ideas of cutting plane methods, augmented Lagrangian and splitting methods, and stochastic decomposition methods for convex polyhedral multi-stage stochastic programming problems.

Approximate dynamic programming for sensor management

Abstract: This paper studies the problem of dynamic scheduling of multi-mode sensor resources for the problem of classification of multiple unknown objects. Because of the uncertain nature of the object types, the problem is formulated as a partially observed Markov decision problem with a large state space. The paper describes a hierarchical algorithm approach for efficient solution of sensor scheduling problems with large numbers of objects, based on a combination of stochastic dynamic programming and nondifferentiable optimization techniques. The algorithm is illustrated with an application involving classification of 10,000 unknown objects.

Uncertainty and the management of mallard harvests

Abstract: Those charged with regulating waterfowl harvests must cope with random environmental variations, incomplete control over harvest rates, and uncertainty about biological mechanisms operative in the population. Stochastic dynamic programming can be used effectively to account for these uncertainties if the probabilities associated with uncertain outcomes can be estimated. To use this approach managers must have clearly-stated objectives, a set of regulatory options, and a mathematical description of the managed system. We used dynamic programming to derive optimal harvest strategies for mallards (Anas platyrhynchos) in which we balanced the competing objectives of maximizing long-term cumulative harvest and achieving a specified population goal. Model-specific harvest strategies, which account for random variation in wetland conditions on the breeding grounds and for uncertainty about the relation between hunting regulations and harvest rates, are provided and compared. We also account for uncertainty in population dynamics with model probabilities, which express the relative confidence that alternative models adequately describe population responses to harvest and environmental conditions. Finally, we demonstrate how the harvest strategy thus derived can "evolve" as model probabilities are updated periodically using comparisons of model predictions and estimates of population size. J. WILDL. MANAGE. 61(1):202-216

Learning automata and stochastic optimization

Abstract: Stochastic optimization.- On learning automata.- Unconstrained optimization problems.- Constrained optimization problems.- Optimization of nonstationary functions.

Universal alignment probabilities and subset selection for ordinal optimization

Abstract: We examine in this paper the subset selection procedure in the context of ordinal optimization introduced in Ref. 1. Major concepts including goal softening, selection subset, alignment probability, and ordered performance curve are formally introduced. A two-parameter model is devised to calculate alignment probabilities for a wide range of cases using two different selection rules: blind pick and horse race. Our major result includes the suggestion of quantifiable subset selection sizes which are universally applicable to many simulation and modeling problems, as demonstrated by the examples in this paper.

A multiparametric programming approach for linear process engineering problems under uncertainty

Abstract: In this paper, a parametric programming approach is proposed for the analysis of linear process engineering problems under uncertainty. A novel branch and bound algorithm is presented for the solut...

Distributions with given marginals and moment problems

Abstract: Preface. Optimal Bounds on the Average of a Rounded-off Observation in the Presence of a Single Moment Condition G.A. Anastassio. The Complete Solution of a Rounding Problem Under Two Moment Conditions T. Rychlik. Methods of Realization of Moment Problems with Entropy Maximization V. Girardin. Matrices of Higher Moments: Some Problems of Representation E. Kaarik. The Method of Moments in Tomography and Quantum Mechanics L.B. Klebanov, S.T. Rachev. Moment Problems in Stochastic Geometry V. Benes. Frechet Classes and Nonmonotone Dependence M. Scarsini, M. Shaked. Comonotonicity, Rank-Dependent Utilities and a Search Problem A. Chateauneuf, et al. A Stochastic Ordering Based on a Decomposition of Kendall's Tau P. Caperaa, et al. Maximum Entropy Distributions with Prescribed Marginals and Normal Score Correlations M.J.W. Jansen. On Bivariate Distributions with Polya-Aeppli or Luders-Delaporte Marginals V.E. Piperigou. Boundary Distributions with Fixed Marginals E.-M. Tiit, H.-L. Helemae. On Approximations of Copulas X. Li, et al. Joint Distributions of Two Uniform Random Variables When the Sum and Difference are Independent G. Dall'Aglio. Diagonal Copulas R.B. Nelsen, G.A. Fredricks. Copulas Constructed from Diagonal Sections G.A. Fredricks, R.B. Nelsen. Continuous Scaling on a Bivariate Copula C.M. Cuadras, J. Fortiana. Representation of Markov Kernels by Random Mappings Under Order Conditions H.G. Kellerer. How to Construct a Two- Dimensional Random Vector with a Given Conditional Structure J. Stepan. Strassen's Theorem for Group-Valued Charges A. Hirshberg, R.M. Shortt. The Lancaster's Probabilities on R2 and Their Extreme Points G. Letac. On Marginalization, Collapsibility andPrecollapsibility M. Studeny. Moment Bounds for Stochastic Programs in Particular for Recourse Problems J. Dupacova. Probabilistic Constrained Programming and Distributions with Given Marginals T. Szantai. On an e-solution of Minimax Problem in Stochastic Programming V. Kankova. Bounds for Stochastic Programs -- Nonconvex Case T. Visek. Artificial Intelligence, the Marginal Problem and Inconsistency R. Jirousek. Inconsistent Marginal Problem on Finite Sets O. Kriz. Topics in the Duality for Mass Transfer Problems V.L. Levin. Generalising Monotonicity C.S. Smith, M. Knott. On Optimal Multivariate Couplings L. Ruschendorf, L. Uckelmann. Optimal Couplings Between One-Dimensional Distributions L. Uckelmann. Duality Theorems for Assignments with Upper Bounds D. Ramachandran, L. Ruschendorf. Bounding the Moments of an Order Statistics if Each k-Tuple is Independent J.H.B. Kemperman. Subject Index.

Minimax Regret Strategies for Greenhouse Gas Abatement: Methodology and Application

Abstract: Classical stochastic programming has already been used with large-scale LP models for long-term analysis of energy-environment systems. We propose a Minimax Regret formulation suitable for large-scale linear programming models. It has been experimentally verified that the minimax regret strategy depends only on the extremal scenarios and not on the intermediate ones, thus making the approach computationally efficient. Key results of minimax regret and minimum expected value strategies for Greenhouse Gas abatement in the Province of Quebec, are compared.

Dependent-Chance Programming: A Class of Stochastic Optimization

Abstract: This paper provides a theoretical framework of dependent-chance programming, as well as dependent-chance multiobjective programming and dependent-chance goal programming which are new types of stochastic optimization A stochastic simulation based genetic algorithm is also designed for solving dependent-chance programming models

Mathematical Programming for Industrial Engineers

Abstract: Linear programming integer programming graph theory and networks dynamic programming nonlinear programming multiobjective programming stochastic programming heuristic methods.

An aggregate stochastic dynamic programming model of multireservoir systems

Abstract: We present a new method of determining an operating policy for a multireservoir system in which the operating policy for a reservoir is determined by solving a stochastic dynamic programming model consisting of that reservoir and a two-dimensional representation of the rest of the system The method is practical for systems with many reservoirs because the time required to determine an operating policy only increases quadratically with the number of reservoirs in the system and because the operating policy for a reservoir is a function of few variables We apply the method to examples of multireservoir systems with between 3 and 17 reservoirs and show that the operating policies determined are very close to optimal

Value of seasonal flow forecasts in Bayesian stochastic programming

Abstract: This paper presents a Bayesian Stochastic Dynamic Programming (BSDP) model to investigate the value of seasonal flow forecasts in hydropower generation. The proposed BSDP framework generates monthly operating policies for the Skagit Hydropower System (SHS), which supplies energy to the Seattle metropolitan area. The objective function maximizes the total benefits resulting from energy produced by the SHS and its interchange with the Bonneville Power Administration. The BSDP-derived operating policies for the SHS are simulated using historical monthly inflows, as well as seasonal flow forecasts during 60 years from January 1929 through December 1988. Performance of the BSDP model is compared with alternative stochastic dynamic programming models. To illustrate the potential advantage of using the seasonal flow forecasts and other hydrologic information, the sensitivity of SHS operation is evaluated by varying (1) the reservoir capacity; (2) the energy demand; and (3) the energy price. The simulation results demonstrate that including the seasonal forecasts is beneficial to SHS operation.

Using fuzzy numbers in linear programming

Abstract: Managers, decision makers, and experts dealing with optimization problems often have a lack of information on the exact values of some parameters used in their problems. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve these problems. This paper studies a linear programming (LP) problem in which all its elements are defined as fuzzy sets. Special cases of this general model are found and reproduced, and it is shown that they coincide with the particular problems proposed in the literature by different authors and distinct approaches. Solution methods are also provided. They show how it is possible to address and solve linear programming problems with data given in a qualitative form, instead of the usual quantitative and precise way.

Application of stochastic global optimization algorithms to practical problems

Abstract: We describe global optimization problems from three different fields representing many-body potentials in physical chemistry, optimal control of a chemical reactor, and fitting a statistical model to empirical data. Historical background for each of the problems as well as the practical significance of the first two are given. The problems are solved by using eight recently developed stochastic global optimization algorithms representing controlled random search (4 algorithms), simulated annealing (2 algorithms), and clustering (2 algorithms). The results are discussed, and the importance of global optimization in each respective field is focused.

Optimization and Persistence

Abstract: Most optimization-based decision support systems are used repeatedly with only modest changes to input data from scenario to scenario. Unfortunately, optimization (mathematical programming) has a well-deserved reputation for amplifying small input changes into drastically different solutions. A previously optimal solution, or a slight variation of one, may still be nearly optimal in a new scenario and managerially preferable to a dramatically different solution that is mathematically optimal. Mathematical programming models can be stated and solved so that they exhibit varying degrees of persistence with respect to previous values of variables, constraints, or even exogenous considerations. We use case studies to highlight how modeling with persistence has improved managerial acceptance and describe how to incorporate persistence as an intrinsic feature of any optimization model.

Optimal production planning in a stochastic manufacturing system with long-run average cost

Abstract: This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach that the Hamilton–Jacobi–Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.

Optimal Stochastic Multicrop Seasonal and Intraseasonal Irrigation Control

Abstract: Optimal seasonal multicrop irrigation water allocation and optimal stochastic intraseasonal (daily) irrigation scheduling are carried out using a two-stage decomposition approach based on a stochastic dynamic programming methodology. In the first stage the optimal seasonal water and acreage allocation among several crops or fields is defined using deterministic dynamic programming with the objective of maximizing total benefits from all the crops. The optimization is based on seasonal crop production functions. Seasonal crop production functions are obtained using single-crop stochastic dynamic programming, which incorporates the physics of soil moisture depletion and the stochastic properties of precipitation. In the second stage optimal intraseasonal irrigation scheduling is performed using a single-crop stochastic dynamic programming algorithm, conditional on the optimal seasonal water allocation of stage one. Optimal daily irrigation decision functions are obtained as a function of root-zone soil moisture content and the currently available irrigation water. The methodology is applied to a case study characterized by four crops in which both the optimal irrigation applications and the optimal acreage for each crop are determined.

On a stochastic knapsack problem and generalizations

Abstract: We consider an integer stochastic knapsack problem (SKP) where the weight of each item is deterministic, but the vector of returns for the items is random with known distribution. The objective is to maximize the probability that a total return threshold is met or exceeded. We study several solution approaches. Exact procedures, based on dynamic programming (DP) and integer programming (IP), are developed for returns that are independent normal random variables with integral means and variances. Computation indicates that the DP is significantly faster than the most efficient algorithm to date. The IP is less efficient, but is applicable to more general stochastic IPs with independent normal returns. We also develop a Monte Carlo approximation procedure to solve SKPs with general distributions on the random returns. This method utilizes upper- and lower-bound estimators on the true optimal solution value in order to construct a confidence interval on the optimality gap of a candidate solution.

Scalable parallel Benders decomposition for stochastic linear programming

Abstract: We develop a scalable parallel implementation of the classical Benders decomposition algorithm for two-stage stochastic linear programs. Using a primal-dual, path-following algorithm for solving the scenario subproblems we develop a parallel implementation that alleviates the difficulties of load balancing. Furthermore, the dual and primal step calculations can be implemented using a data-parallel programming paradigm. With this approach the code effectively utilizes both the multiple, independent processors and the vector units of the target architecture, the Connection Machine CM-5. The, usually limiting, master program is solved very efficiently using the interior point code LoQo on the front-end workstation. The implementation scales almost perfectly with problem and machine size. Extensive computational testing is reported with several large problems with up to 2 million constraints and 13.8 million variables.

A stochastic dynamic programming model for the management of the saiga antelope

Abstract: A stochastic dynamic programming model for the optimal management of the saiga antelope is presented. The optimal hunting mortality rate and proportion of adult males in the harvest are found as functions of the size and structure of the saiga population before hunting. The effects of stochastic climatic variation on the population are taken into account in this model. It is shown that key assumptions must be made about the effects of the breeding sex ratio on female fecundity, and about whether poaching is occurring. If incorrect assumptions are made about either of these factors, the calculated optimal strategy can become severely suboptimal. A simple suboptimal decision rule that takes the population size and structure into account is shown to be more able to buffer against these factors than the optimal strategy, which has proved too complicated for analytical solution. The model predictions are robust to parameter changes.

Robust Investment Model for Long Range Capacity Expansion of Chemical Processing Networks under Uncertain Demand Forecast Scenarios

Abstract: The problem of long-range capacity expansion planning for chemical processing networks under uncertain demand forecast scenarios is addressed. This optimization problem involves capacity expansion timing and sizing of each chemical processing unit to maximize the expected net present value while considering the deviation of net present values and the excess capacity over a given time horizon. A multiperiod mixed integer nonlinear programming optimization model that is both solution and model robust for any realization of demand scenarios is developed using the two-stage stochastic programming modeling framework. Two example problems are considered to illustrate the effectiveness of the model. Especially, the use of the model is illustrated on a real problem arising from investment planning in Korean petrochemical industry.