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Showing papers on "Stochastic programming published in 1973"


Journal ArticleDOI
TL;DR: The paper presents theory dealing primarily with properties of the relevant functions that result in convex programming problems, and discusses interpretations of this theory.
Abstract: This paper considers a class of optimization problems characterized by constraints that themselves contain optimization problems. The problems in the constraints can be linear programs, nonlinear programs, or two-sided optimization problems, including certain types of games. The paper presents theory dealing primarily with properties of the relevant functions that result in convex programming problems, and discusses interpretations of this theory. It gives an application with linear programs in the constraints, and discusses computational methods for solving the problems.

477 citations


Journal ArticleDOI
TL;DR: This paper presents a staff planning and scheduling model that has specific application in the nurse-staffing process in acute hospitals, and more general application in many other service organizations in which demand and production characteristics are similar.
Abstract: This paper presents a staff planning and scheduling model that has specific application in the nurse-staffing process in acute hospitals, and more general application in many other service organizations in which demand and production characteristics are similar. The aggregate planning models that have been developed for goods-producing organizations are not appropriate for these types of service organizations. In this paper the process for staffing services is divided into three decision levels: a policy decisions, including the operating procedures for service centers and for the staff-control process itself; b staff planning, including hiring, discharge, training, and reallocation decisions; and c short-term scheduling of available staff within the constraints determined by the two previous levels. These three planning "levels" are used as decomposition stages in developing a general staffing model. The paper formulates the planning and scheduling stages as a stochastic programming problem, suggests an iterative solution procedure using random loss functions, and develops a noniterative solution procedure for a chance-constrained formulation that considers alternative operating procedures and service criteria, and permits including statistically dependent demands. The discussion includes an example application of the model and illustrations of its potential uses in the nurse-staffing process.

184 citations


Journal ArticleDOI
TL;DR: The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures on two stochastic programming decision models, where the solvability of the second stage problem only with a prescribed (high) probability is required.
Abstract: Two stochastic programming decision models are presented. In the first one, we use probabilistic constraints, and constraints involving conditional expectations further incorporate penalties into the objective. The probabilistic constraint prescribes a lower bound for the probability of simultaneous occurrence of events, the number of which can be infinite in which case stochastic processes are involved. The second one is a variant of the model: two-stage programming under uncertainty, where we require the solvability of the second stage problem only with a prescribed (high) probability. The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures.

182 citations


Journal ArticleDOI
TL;DR: In this article, a class of stochastic optimization problems characterized by non-differentiability of the objective function is examined and it is shown that, in many cases, the expected value of the target function is differentiable and thus the resulting optimization problem can be solved by using classical analytical or numerical methods.
Abstract: In this paper, we examine a class of stochastic optimization problems characterized by nondifferentiability of the objective function. It is shown that, in many cases, the expected value of the objective function is differentiable and, thus, the resulting optimization problem can be solved by using classical analytical or numerical methods. The results are subsequently applied to the solution of a problem of economic resource allocation.

122 citations


Journal ArticleDOI
TL;DR: Rules are given that enable the transformation of a0-1 polynomial programming problem into a 0-1 linear programming problem to be effected with reduced numbers of constraints.
Abstract: This paper gives rules that enable the transformation of a 0-1 polynomial programming problem into a 0-1 linear programming problem to be effected with reduced numbers of constraints. Rules are also given that provide reduced numbers of variables when the true variables of interest are not individual cross-product terms, but sums of such terms or polynomials of the form ∑xjp.

118 citations


Book ChapterDOI
TL;DR: This chapter discusses the coupling relationship between system identification and optimization and describes the analytical tools and methods for tackling the joint problem.
Abstract: Publisher Summary The modern systems approach in handling large scale problems includes the concepts of system identification and optimization. The coupling relationship between these concepts is inherent in the nature of the desired “optimal solution.” Any mathematical model consists of unknown variables and “known” parameters characterizing the system. These parameters are not known, but are estimated or determined under non-optimal conditions. The solution that is generated from such system models might be non-optimal. The identification of the system's parameters, referred to as system modeling, is essential to obtain an optimal control policy. This chapter discusses the coupling relationship between these concepts and describes the analytical tools and methods for tackling the joint problem. Mathematical models, which aim at representing real physical systems in quantitative form, have become important tools in the design, synthesis, analysis, operation, and control of complex systems.

70 citations


Journal ArticleDOI
TL;DR: In this article, a solution procedure for discrete stochastic programs with recourse linear programs under uncertainty is presented, in which the m-dimensional space in which each combination of the discrete values is a lattice point is used to delete infeasible points from the space.
Abstract: This paper presents a solution procedure for discrete stochastic programs with recourse linear programs under uncertainty. It views the m stochastic elements of the requirements vector as an m-dimensional space in which each combination of the discrete values is a lattice point. For a given second-stage basis, certain of the lattice points are feasible. A procedure is presented to delete infeasible points from the space. Thus, the aggregate probability associated with points feasible for this basis can be enumerated, and used to weight the vector of dual variables defined by the basis. Finally, the paper presents a systematic procedure for changing optimal bases so that a feasible and optimal basis is found for every lattice point.

33 citations


Journal ArticleDOI
TL;DR: A dynamic programming model with a physical equation and a stochastic recursive equation is developed to find the optimum operational policy of a single multipurpose surface reservoir.
Abstract: The main objective of this paper is to present a stockastic dynamic programming model useful in determining the optimal operating policy of a single multipurpose surface reservoir. It is the unreliability of forecasting the amount of future streamflow which makes the problem of a reservoir operation a stochastic process. In this paper the stochastic nature of the streamflow is taken into account by considering the correlation between the streamflows of each pair of consecutive time intervals. This interdependence is used to calculate the probability of transition from a given state and stage to its succeeding ones. A dynamic programming model with a physical equation and a stochastic recursive equation is developed to find the optimum operational policy. For illustrative purposes, the model is applied to a real surface water reservoir system.

32 citations


Journal ArticleDOI
TL;DR: This paper shows how a stochastic programming model for least-cost feed formulations under a probabilistic protein constraint and other linear restrictions can be solved by using an iterative quadratic programming technique.
Abstract: This paper shows how a stochastic programming model for least-cost feed formulations under a probabilistic protein constraint and other linear restrictions can be solved by using an iterative quadratic programming technique. As the least-cost plan for a given probability level must be E-σ efficient, the result thus obtained is optimal.

31 citations


Journal ArticleDOI
TL;DR: An extensive literature survey is followed by description of the basic deterministic planning model—a model emphasizing the interactive consequences of cropping pattern selection, conjunctive use of ground and surface water, and employment of wells as water table control devices.
Abstract: Certain concepts and techniques of systems analysis can assist irrigation planning in poor countries with social and physical environments different from those of industrialized nations. An extensive literature survey is followed by description of the basic deterministic planning model—a model emphasizing the interactive consequences of cropping pattern selection, conjunctive use of ground and surface water, and employment of wells as water table control devices. Stochastic parameters are introduced into the model in order to improve the model's robustness of representation of reality and in order to interpret the consequences of stochastic variability meaningfully. Various factors favor the use of the chance-constrained approach to stochastic programming. Unlike previous applications, general distribution functions, variable capacities, piecewise linear decision rules, and stochastic demands and supplies are dealt with.

23 citations


Journal ArticleDOI
TL;DR: In this paper chance-constrained programming is used to model a system of linked multipurpose reservoirs to determine an optimal operating policy for a given time sequence of minimum and maximum reservoir levels.
Abstract: In this paper chance-constrained programming is used to model a system of linked multipurpose reservoirs. The objective of the model is to determine an optimal operating policy for a given time sequence of minimum and maximum reservoir levels. The unregulated inflows into the reservoirs are assumed to be stochastic with a known distribution for each time frame. The chance-constraints, based on material balance equations, are converted to an equivalent linear deterministic constraint set. The linked system model is a natural extension of the single reservoir model. The problem of stochastic demands as well as stochastic inflows is shown to be a straightforward generalization of the stochastic inflow problem. Since the resulting constraints for these models are linear and the decision variables are deterministic rather than random variables, linear, quadratic, and even general convex objective functions can be readily handled.

01 Jan 1973
TL;DR: The STAR program is a crucial element of EPA’s research efforts; and as the STAR program has evolved, it has developed a grant-award process that in many ways exceeds those in place at other organizations that have extramural research programs.
Abstract: s or progress and final reports for any of the STAR grants are available at the NCER Web Site: http://es.epa.gov/ncer/. What Related Research Is Also Funded Under the STAR Program? NCER funds a broad range of research through extramural grants (descriptions available on the NCER Web Site above). However, there are several research areas that are closely related to the Air Research Program and as such, NCER staff coordinate in planning RFAs and monitoring research results. • The Human Health Program funds research related to improving human health risk assessment in areas such as exposure assessment, biomarkers, genetic susceptibility, and asthma. Together with the NIH, the Human Health Program funds several centers of excellence for Children’s Environmental Health Research. • The Global Change Program includes a major focus area exploring the impact of global change on air quality. The projects underway include research linking global models to regional air quality models, forecasting plausible emission scenarios for 50-100 years into the future, and improving models for important emission sources likely to have significant change over the next century. • The Economics and Decision Sciences Program supports research related to the value of reducing adverse health and ecological effects, market mechanisms, compliance decision-making, and benefits of disclosing information. • The Nanotechnology Program supports research on the environmental implications of nanotechnology, including toxicity, exposure, transport, and transformation of manufactured nanomaterials. • Mercury research in NCER includes studies on the atmospheric processes that influence the fate and behavior of mercury. • The Small Business Innovation Research (SBIR) Program was created to strengthen the role of small businesses in federally funded research and development and develop a stronger national base for technical innovation. The SBIR program has addressed issues related to air pollution measurement and control. What Have Been the Findings of Previous External Reviews of the STAR Program? The STAR Program, in general, has been reviewed a number of times (e.g., twice by Subcommittees of the BOSC, the Government Accounting Office, the Agency’s Inspector General). In 2002, NCER asked the National Research Council’s Board on Environmental Studies and Toxicology to conduct an independent assessment of the STAR program. A committee was formed and U.S. EPA Science To Achieve Results (STAR) Program 111 The PM Centers Program 2005-2010: Overviews and Abstracts charged with assessing the program’s scientific merit, its demonstrated or potential influence on policies and decisions, and other program benefits that are relevant to EPA’s mission. The committee was asked specifically to examine the program’s research priorities, research solicitations, peerreview process, current research projects, and results and dissemination of completed research in the context of other relevant research conduced or funded by EPA and in comparison with those of other basic and applied research grant programs. In preparing its report, the committee focused on three research programs: Particulate Matter, Ecologic Indicators, and Endocrine Disruptors. They issued a report, “The Measure of STAR,” in May 2003 (www.nap.edu/books/0309089387/html/) concluding: “The STAR program is a crucial element of EPA’s research efforts; and...As the STAR program has evolved, it has developed a grant-award process that in many ways exceeds those in place at other organizations that have extramural research programs.” EPA’s Science Advisory Board conducted a specific review of the STAR PM Centers research program midway through the research grants in 2002. The “Interim Review of the Particulate Matter (PM) Research Centers of the USEPA: An SAB Report” (available at http://www.epa.gov/ sab/pdf/ec02008.pdf) was favorable with major findings stating that the PM Centers have produced benefits above and beyond what might be expected from individual investigator-initiated grants and that they are likely to continue to produce such benefits through the next several years. STAR Air Research Program RFA Topic Areas and Summary of Awarded Grants 1998-2005 RFAYear RFA Topic Areas and Grant Research Area 1998 Health Effects of PM and Associated Air Pollutants (10 grants-Total) • PM and respiratory effects (7 grants) • PM and cardiovascular effects (2 grants) • PM and morbidity/mortality (1 grant) 1999 Airborne Particulate Matter Health Effects (8 grants-Total) • PM dosimetry (1 grant) • PM cardiopulmonary epidemiology (3 grants) • PM controlled exposure studies (3 grants) • Source evaluation of PM effects (1 grant) Airborne Particulate Matter Centers (5 grants-Total) – Overall Themes: • Exposure, susceptibility, and biological mechanisms • Health risks of PM components • Combustion-derived fine particle composition, exposures and health effects • Mobile source pollution and health effects • Health effects of ultrafine particles 2001 Health Effects of Particulate Matter (4 grants-Total) • Mechanisms of PM respiratory effects (3 grants) • Air pollutants and emergency room visits (1 grant) U.S. EPA Science To Achieve Results (STAR) Program 112 The PM Centers Program 2005-2010: Overviews and Abstracts 2002 Airborne PM Health Effects: Cardiovascular Mechanisms (4 grants-Total) • Diesel exposures (3 grants) • Concentrated airborne particulate and ozone (1 grant) Epidemiologic Research on Health Effects of Long-Term Exposure to Ambient PM and Other Air Pollutants (4 grants-Total) Four Cohorts: • Seventh Day Adventists (California) • Multi-Ethnic Study of Atherosclerosis (MESA) • Medicare Database • U.S. Nurses’ Health Study 2003 Measurement, Modeling, and Analysis Methods for Airborne Carbonaceous Fine PM (16 grants-Total) • Emission source estimates of primary organic aerosol and secondary organic aerosol precursors (3 grants) • Secondary organic aerosol formation mechanisms (4 grants) • Next generation receptor model (1 grant) • Advanced measurement techniques for source apportionment of organic PM (5 grants) • Differences in EC/OC measurement methods (2 grants) • Organic aerosol sampling artifacts (1 grant) Epidemiologic Research on Health Effects of Long-Term Exposure to Ambient PM and Other Air Pollutants (1 grant-Total) • MESA – Air The Role of Air Pollutants in Cardiovascular Disease (6 grants-Total) • Animal models of human disease to evaluate mechanisms (3 grants) • PM effects on regulation of heart rhythm (1 grant) • PM effects on the function of tissue lining blood vessels (2 grants) 2004 Source Apportionment of Particulate Matter (11 grants-Total) • Receptor modeling (3 grants) • Integration of receptor, source-based and inverse modeling (4 grants) • Measurement methods for molecular tracer species and identification of new molecular tracers (4 grants) 2005 Airborne Particulate Matter Centers (5 grants-Total) – Overall Theme • Linking health effects with PM from sources and components Measurement Methods for Particulate Matter Composition Attachment: Process for Selecting STAR RFA Topics and Reviewing Applications How Are the Topics for the Science To Achieve Results (STAR) Solicitations Selected? Research Coordination Teams (RCTs) • RCTs are composed of representatives from ORD’s laboratories and centers and EPA’s program and regional offices; they develop a plan for research to be done intramurally in ORD laboratories and extramurally through STAR. • The research plan is based on the EPA and the ORD Strategic Plans, as well as specific program needs identified through the RCT process. U.S. EPA Science To Achieve Results (STAR) Program 113 The PM Centers Program 2005-2010: Overviews and Abstracts • A series of criteria are used to decide whether research would best be accomplished internally at ORD or externally through grants, cooperative agreements or contracts. These criteria include: • Which organization has the most appropriate expertise? • How urgently is the research needed? What is our available in-house capacity? • Does the proposed extramural research complement the intramural program? • NCER staff work with the RCTs to write the Request for Applications (RFAs). What Is the Review Process That NCER Uses for All Assistance Applications? Peer review is the cornerstone of high-quality scientific research. Because all NCER applications are subjected to a rigorous, independent peer review, the program funds only the most scientifically meritorious research. The external peer review process is managed entirely by a separate division of NCER, preserving independence from the NCER staff who prepare RFAs and manage grants. External Peer Review • NCER staff determines the types of expertise reviewers must possess given the technical requirements of the solicitation. • Each application is reviewed and critiqued in-depth by at least three expert panelists and discussed by the full review panel. • For all applications, each principal reviewer is required to, and non-principal reviewers may elect to, provide an overall rating of Excellent, Very Good, Good, Fair, or Poor. • Ratings are tallied and averaged, and the lead principal reviewer prepares a summary evaluation that is consistent with this average rating. • Applications receiving a Very Good or Excellent are sent to ORD’s Programmatic Review Panel. Programmatic Review Panel • ORD’s Programmatic Review Panel recommends proposals on the basis of relevancy to EPA’s mission, balance of research portfolio, and capacity to complement in-house research. • ORD’s Programmatic Review Panel consists of members from ORD, Program and Regional Offices. U.S. EPA Science To Achieve Results (STAR) Program 114

Journal ArticleDOI
TL;DR: In this article, the optimal return function is shown to be convex and the admissible control region is assumed to be a continuous function of the (perfectly) observed state, and the optimal feedback controls are shown to exist within the class of Borel measurable functions of past states.
Abstract: Linear stochastic systems with convex performance criteria and convex, compact control regions are studied. The admissible control region is assumed to be a continuous function of the (perfectly) observed state. Optimal feedback controls are shown to exist within the class of Borel measurable functions of past states. In fact, they are shown to be continuous functions of the present state. Using dynamic programming the optimal return function is shown to be convex. Asymptotic results for stable systems are derived. These results are then used to explore several problems in aggregate production and work-force planning. Computational aspects of the results in the context of the smoothing problem are discussed.

Journal ArticleDOI
TL;DR: In this article, a stochastic control problem over an infinite horizon which involves a linear system and a convex cost functional is analyzed, and the convergence of the dynamic programming algorithm associated with the problem is proved.
Abstract: A stochastic control problem over an infinite horizon which involves a linear system and a convex cost functional is analyzed. We prove the convergence of the dynamic programming algorithm associated with the problem, and we show the existence of a stationary Borel measurable optimal control law. The approach used illustrates how results on infinite time reachability [1] can be used for the analysis of dynamic programming algorithms over an infinite horizon subject to state constraints.

Journal ArticleDOI
TL;DR: A stochastic programming model for evaluation of investment in irrigation reflects the complex hydrologic and economic interactions that arise from consideration of the conjunctive use of ground and surface water, the need for the provision of drainage to irrigated lands, and the use of some lands for rice cultivation.
Abstract: A stochastic programming model for evaluation of investment in irrigation is presented. The model reflects the complex hydrologic and economic interactions that arise from consideration of the conjunctive use of ground and surface water, the need for the provision of drainage to irrigated lands, and the use of some lands for rice cultivation. The implications of stochastic precipitation are discussed. Several decision rules for system operation are presented and discussed in terms of computation requirements and the possibility of field implementation. Deterministic equivalents to the probabilistic water requirement constraints are derived for zero-order, linear, and two-piece decision rules, and the model is solved with alternate assumptions regarding the form of the rules to be used. An irrigation project proposed for Bangladesh is chosen to illustrate some possible consequences for investment planning of the choice of decision rules. Decision rules in chance-constrained programming are seen as tools for effecting good approximate solutions to stochastic programming problems when used with knowledge of the technical aspects of the investment decisions to be analyzed.

Journal ArticleDOI
TL;DR: This paper presents a realistic chemical-process optimization problem in detail, and notes the fact of its equivalence to the general nonlinear programming problem.
Abstract: This paper presents a realistic chemical-process optimization problem in detail, and notes the fact of its equivalence to the general nonlinear programming problem. The eight equality constraints that arise are handled by algebraic substitution, and the resulting four-variable problem is solved by a modified form of the Davidon-Fletcher-Powell algorithm. Details of the method are presented including a FORTRAN computer program, and results of two typical cases are summarized.



Journal ArticleDOI
TL;DR: This note shows that the latest representations of the gradient is but a simple modification of the latest representation of the linear objective function without risk aversion.
Abstract: In stochastic programming with recourse the objective is to maximize the expected net payoff. This assumes implicitly no aversion to risk. With risk aversion, the objective becomes to maximize the expected concave utility of the net payoffs. Because of the special structure of the problem with risk aversion, a number of computational short cuts are possible in the mathematical program that results. All the second-stage problems can be solved as linear programs. Unfortunately, whether with or without risk aversion, it is necessary to solve the first-stage problem as a nonlinear program. This note shows that the latest representation of the gradient is but a simple modification of the latest representation of the linear objective function without risk aversion.

Journal ArticleDOI
01 Jul 1973
TL;DR: An efficient algorithm to determine the optimal sequence of measurements is presented, on the base of which a sensitivity analysis with respect to the process parameters is also carried out.
Abstract: Two kinds of problems regarding measurement optimization in stochastic decision processes, when measurements are costly or constrained not to exceed a given number, have been investigated in the last years: the first one refers to the optimum timing of observations on the state vector of the process, while the second refers to the convenience of buying information on the random actions exerted by a stochastic environment. In this paper the two problems are considered from a unified point of view. In other words, the decision maker has to determine the optimal observation policy, under the assumption that both state and random vectors are measurable. A solution based on the application of dynamic programming is discussed for a general class of multistage processes. Analytical results are then obtained for scalar linear systems with quadratic cost on state and control. In this case, an efficient algorithm to determine the optimal sequence of measurements is presented, on the base of which a sensitivity analysis with respect to the process parameters is also carried out.



Proceedings ArticleDOI
01 Dec 1973
TL;DR: The subject of this paper is the application of stochastic control theory to resource allocation under uncertainty in the context of the general problem of allocating resources to repair machines where it is possible to perform a limited number of diagnostic experiments to learn more about potential failures.
Abstract: The subject of this paper is the application of stochastic control theory to resource allocation under uncertainty. In these problems it is assumed that the results of a given allocation of resources are not known with certainty, but that a limited number of experiments can be performed to reduce the uncertainty. The problem is to develop a policy for performing experiments and allocating resources on the basis of the outcome of the experiments such that a performance index is optimized. The problem is first analyzed using the stochastic dynamic programming approach. A computationally practical algorithm for obtaining an approximate solution is then developed. This algorithm preserves the "closed-loop" feature of the dynamic programming solution in that the resulting decision policy depends both on the results of past experiments and on the statistics of the outcomes of future experiments. In other words, the present decision takes into account the value of future information. The concepts are discussed in the context of the general problem of allocating resources to repair machines where it is possible to perform a limited number of diagnostic experiments to learn more about potential failures. Illustrative numerical results are given.


Journal ArticleDOI
TL;DR: In this paper, a general equivalence between a stochastic optimal control problem and a linear-quadratic game was shown, and it was shown that a more general form of the equivalence exists which has an interesting form.
Abstract: In a recent paper an equivalence was demonstrated between a certain stochastic optimal control problem and a linear-quadratic game. In this note it is pointed out that a more general equivalence exists which has an interesting form.



Journal ArticleDOI
TL;DR: Cost optimization based on mathematical programming is described for a fixed-time-interval transshipment problem with capacity constraints on paths between warehouses and rotail outlets and this procedure is further extended to include serial and cross correlations.
Abstract: Cost optimization based on mathematical programming is described for a fixed-time-interval transshipment problem with capacity constraints on paths between warehouses and rotail outlets. Stochastic optimization is achieved by coupling deterministic linear programming with Monte Carlo simulation, and this procedure is further extended to include serial and cross correlations. In addition, posterior information may be considered by invoking the Bayes theorem. Non-linear systems are also treated.