Catastrophic health events are natural or man-made incidents that create casualties in numbers that overwhelm the response capabilities of healthcare systems. Proper response planning for such events requires communit...
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Catastrophic health events are natural or man-made incidents that create casualties in numbers that overwhelm the response capabilities of healthcare systems. Proper response planning for such events requires community-based surge solutions such as the location of alternative care facilities and ways to improve coordination by considering triage and the movement of self-evacuees. In this paper, we construct a three-stage stochastic programming model to locate alternative care facilities and allocate casualties in response to catastrophic health events. Our model integrates casualty triage and the movement of self-evacuees in a systemic response framework that treats uncertainties involved in such large-scale events as probabilistically distributed scenarios. Solution times being instrumental to the practicality of the model, we propose an algorithm, based on Benders decomposition, to generate good solutions fast. We derive new valid inequalities, which we add to the Benders decomposition master problem to reduce the number of weak feasibility cuts generated. Because our algorithm can also be ineffective if the number of scenarios is large, we propose a two-stage approximation model that attempts to guess good third-stage solutions without third-stage decision variables and constraints. Our model, algorithm, and two-stage approximation are implemented in the case study of an earthquake situation in California based on the realistic ShakeOut Scenario data.
One of the important objectives of supply chain S&OP (Sales and Operations Planning) is the profitable alignment of customer demand with supply chain capabilities through the coordinated planning of sales, product...
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One of the important objectives of supply chain S&OP (Sales and Operations Planning) is the profitable alignment of customer demand with supply chain capabilities through the coordinated planning of sales, production, distribution, and procurement. In the make-to-order manufacturing context considered in this paper, sales plans cover both contract and spot sales, and procurement plans require the selection of supplier contracts. S&OP decisions also involve the allocation of capacity to support sales plans. This article studies the coordinated contract selection and capacity allocation problem, in a three-tier manufacturing supply chain, with the objective to maximize the manufacturer's profitability. Using a modeling approach based on stochastic programming with recourse, we show how these S&OP decisions can be made taking into account economic, market, supply, and system uncertainties. The research is based on a real business case in the Oriented Strand Board (OSB) industry. The computational results show that the proposed approach provides realistic and robust solutions. For the case considered, the planning method elaborated yields significant performance improvements over the solutions obtained from the mixed integer programming model previously suggested for S&OP.
In stochastic programming, statistics, or econometrics, the aim is in general the optimization of a criterion function that depends on a decision variable theta and reads as an expectation with respect to a probabilit...
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In stochastic programming, statistics, or econometrics, the aim is in general the optimization of a criterion function that depends on a decision variable theta and reads as an expectation with respect to a probability P. When this function cannot be computed in closed form, it is customary to approximate it through an empirical mean function based on a random sample. On the other hand, several other methods have been proposed, such as quasi-Monte Carlo integration and numerical integration rules. In this paper, we propose a general approach for approximating such a function, in the sense of epigraphical convergence, using a sequence of functions of simpler type which can be expressed as expectations with respect to probability measures P-n that, in some sense, approximate P. The main difference with the existing results lies in the fact that our main theorem does not impose conditions directly on the approximating probabilities but only on some integrals with respect to them. In addition, the P-n's can be transition probabilities, i.e., are allowed to depend on a further parameter, xi, whose value results from deterministic or stochastic operations, depending on the underlying model. This framework allows us to deal with a large variety of approximation procedures such as Monte Carlo, quasi-Monte Carlo, numerical integration, quantization, several variations on Monte Carlo sampling, and some density approximation algorithms. As by-products, we discuss convergence results for stochastic programming and statistical inference based on dependent data, for programming with estimated parameters, and for robust optimization;we also provide a general result about the consistency of the bootstrap for M-estimators.
This paper is concerned with power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming...
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This paper is concerned with power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. We propose an L-shaped algorithm to solve the problem.
This paper is devoted to the analysis of the effectiveness of the use of arable land. This is an issue, which is important for national-level decision makers. The particular calculations are carried out for Hungary, b...
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This paper is devoted to the analysis of the effectiveness of the use of arable land. This is an issue, which is important for national-level decision makers. The particular calculations are carried out for Hungary, but similar analysis can be made for each country having several parts with different geographical conditions. In general the structure of the use of arable land has been developed in an evolutionary manner in each country. This paper is devoted to the evaluation of the effectiveness of this structure. Some main crops must be included in the analysis such that the land used for their production is a high percentage in the total arable land of the country. From agricultural point of view the question to be answered is whether or not the same level of supply is achievable with high probability on a smaller area. As the agriculture is affected by stochastic factors via the weather, no supply can be guaranteed up to 100 per cent. Thus each production structure provides the required supply only with a certain probability. One inequality corresponding to each crop must be satisfied at the same time with a prescribed probability. The main theoretical difficulty here is that the inequalities are not independent from one another from stochastic point of view as the yields of the crops are highly correlated. The problem is modeled by a chance constrained stochastic programming model such that the stochastic variables are on the left-hand side of the inequalities, while the right-hand sides are constants. Kataoka was the first in 1963 who solved a similar problem with a single inequality in the probabilistic constraint. The mathematical analysis of the present problem is using the results of Kataoka. This problem is solved numerically via discretization. Numerical results for the optimal structure of the production are presented for the case of Hungary. It is shown that a much higher probability, i.e. a more safe supply, can be achieved on a smaller area than what
The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multista...
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The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multistage stochastic programming problems in arborescent form (i.e. formulated with implicit non-anticipativity constraints on a scenario tree). The objective function of the problem can be either linear or nonlinear, while we require that the constraints are linear and involve only variables from two adjacent periods (current and lag 1). The approach is built on the following steps. First, reformulate the stochastic programming problem into an optimal control one. Second, apply a discrete version of Pontryagin maximum principle to obtain optimality conditions. Third, discuss and rearrange these conditions to obtain a decomposition that acts both at a time stage level and at a nodal level. To obtain the solution of the original problem we aggregate the solutions of subproblems through an enhanced mean valued fixed point iterative scheme.
We present a new approach to asset allocation with transaction costs. A multiperiod stochastic Linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by ...
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We present a new approach to asset allocation with transaction costs. A multiperiod stochastic Linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by the model that balances expected return and risk. Utilizing portfolio protection and dynamic hedging, an investment portfolio similar to an option-like payoff structure on the initial investment portfolio is characterized. The relative changes in the expected terminal wealth, worst case payoff, and risk aversion, are studied theoretically and illustrated using a numerical example. This model dominates a static mean-variance model when the optimal portfolios are evaluated by the Sharpe ratio.
Sovereign states issue fixed and floating securities to fund their public debt. The value of such portfolios strongly depends on the fluctuations of the term structure of interest rates. This is a typical example of p...
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Sovereign states issue fixed and floating securities to fund their public debt. The value of such portfolios strongly depends on the fluctuations of the term structure of interest rates. This is a typical example of planning under uncertainty, where decisions have to be taken on the base of the key stochastic economic factors underneath the model. We propose a multistage stochastic programming model to select portfolios of bonds, where the aim of the decision maker is to minimize the cost of the decision process. At the same time, we bound the conditional Value-at-Risk, a measure of risk which accounts for the losses of the tail distribution. We build an efficient frontier to trade-off the optimal cost versus the conditional Value-at-Risk and analyze the results obtained.
We consider expected return, Conditional Value at Risk, and liquidity criteria in a multi-period portfolio optimization setting modeled by stochastic programming. We aim to identify a preferred solution of the decisio...
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We consider expected return, Conditional Value at Risk, and liquidity criteria in a multi-period portfolio optimization setting modeled by stochastic programming. We aim to identify a preferred solution of the decision maker (DM) by obtaining information on her/his preferences. We use a weighted Tchebycheff program to generate representative sets of solutions. Our approach models the stochasticity of market movements by stochastic programming. Working with multiple scenario trees, we construct confidence ellipsoids around representative solutions, and present them to the DM for her/him to make a choice. With each iteration of the approach, an increasingly concentrated set of ellipsoids around the DM's choices are generated. The procedure is demonstrated with tests performed using stocks traded on Borsa Istanbul.
This paper develops a stochastic programming model that integrates the most recent regulation rules of the Spanish peninsular system for bilateral contracts in the day-ahead optimal bid problem. Our model allows a pri...
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This paper develops a stochastic programming model that integrates the most recent regulation rules of the Spanish peninsular system for bilateral contracts in the day-ahead optimal bid problem. Our model allows a price-taker generation company to decide the unit commitment of the thermal and combined cycle programming units, the economic dispatch of the bilateral contract between all the programming units and the optimal sale bid by observing the Spanish peninsular regulation. The model was solved using real data of a typical generation company and a set of scenarios for the Spanish market price. The results are reported and analyzed.
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