This article revises and improves on a Dual Type Method (DTM), developed by Prekopa. (Prekopa, A. (1990). Dual method for the solution of a one-stage stochastic programming problem with random RHS obeying a discrete p...
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This article revises and improves on a Dual Type Method (DTM), developed by Prekopa. (Prekopa, A. (1990). Dual method for the solution of a one-stage stochastic programming problem with random RHS obeying a discrete probability distribution, ZOR-Methods and Models of Operations Research , 34 , 441-461), in two ways. The first one allows us, in each iteration, to perform the largest step toward the optimum. The second one consists of exploiting the structure of the working basis , which has to be inverted in each iteration, and updating its inverse in product form, as it is usual in case of the standard dual method. The improved method has been implemented. A report on its performance on the solution of some stochastic programming problems is also presented.
Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions,...
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Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established.
This paper proposes the portfolio stochastic programming (PSP) model and the stagewise portfolio stochastic programming (SPSP) model for investing in stocks in the Taiwan stock market. The SPSP model effectively reduc...
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This paper proposes the portfolio stochastic programming (PSP) model and the stagewise portfolio stochastic programming (SPSP) model for investing in stocks in the Taiwan stock market. The SPSP model effectively reduces the computational resources needed to solve the PSP model. Additionally, the conditional value at risk (CVaR) is used as a risk meastire in the models. In each period of investment, 200 scenarios are generated to solve the SPSP model. The experimental data set consists of the 50 listed companies with the greatest market capitalization in the Taiwan stock exchange, and the experimental interval began on January 3, 2005 and ended on December 31, 2014, consisting of 2484 trading periods (days) in total. The experimental results show that the SPSP model is insensitive to small variation of the portfolio size and the historical period for estimating statistics. The portfolio size of the SPSP model can be set with two cases: M = M-c and M <= M-c. When M = M-c, the M invested target stocks have been predetermined. When M <= M-c, a set of M-c candidate stocks are given, but the M real target stocks have not been decided. The average annualized returns are 13.09% and 12.06% for the two portfolio settings, respectively, which are higher than that of the buy-and-hold (BAH) rule (9.95%). In addition, because the CVaR is considered, both portfolio settings of the SPSP model exhibit higher Sharpe and Sortino ratios than the BAH rule, indicating that the SPSP model provides a higher probability to earn a positive return. The superior predictive ability test is performed to illustrate that the SPSP model can avoid the data-snooping problem. (C) 2016 Elsevier Ltd. All rights reserved.
Remarkable progress has been made in the development of algorithmic procedures and the availability of software for stochastic programming problems. However, some fundamental questions have remained unexplored. This p...
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Remarkable progress has been made in the development of algorithmic procedures and the availability of software for stochastic programming problems. However, some fundamental questions have remained unexplored. This paper identifies the more challenging open questions in the field of stochastic programming. Some are purely technical in nature, but many also go to the foundations of designing models for decision making under uncertainty.
This paper presents a new approach to Differential Evolution algorithm for solving stochastic programming problems, named DESP. The proposed algorithm introduces a new triangular mutation rule based on the convex comb...
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This paper presents a new approach to Differential Evolution algorithm for solving stochastic programming problems, named DESP. The proposed algorithm introduces a new triangular mutation rule based on the convex combination vector of the triangle and the difference vector between the best and the worst individuals among the three randomly selected vectors. The proposed novel approach to mutation operator is shown to enhance the global and local search capabilities and to increase the convergence speed of the new algorithm compared with conventional DE. DESP uses Deb's constraint handling technique based on feasibility and the sum of constraint violations without any additional parameters. Besides, a new dynamic tolerance technique to handle equality constraints is also adopted. Two models of stochastic programming (SP) problems are considered: Linear stochastic Fractional programming Problems and Multi-objective stochastic Linear programming Problems. The comparison results between the DESP and basic DE, basic particle swarm optimization (PSO), Genetic Algorithm (GA) and the available results from where it is indicated that the proposed DESP algorithm is competitive with, and in some cases superior to, other algorithms in terms of final solution quality, efficiency and robustness of the considered problems in comparison with the quoted results in the literature. (C) 2016 Production and hosting by Elsevier B.V. on behalf of Faculty of Computers and Information, Cairo University.
Most of the operations management literature assumes that a firm can always finance production decisions at an optimal level or borrow at a constant interest rate;however, operational decisions are constrained by limi...
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Most of the operations management literature assumes that a firm can always finance production decisions at an optimal level or borrow at a constant interest rate;however, operational decisions are constrained by limited capital and often critically depend on external financing. This paper proposes an integrated corporate planning model, which extends the forecasting-based discount dividend pricing method into an optimization-based valuation framework to make production and financial decisions simultaneously for a firm facing marker uncertainty. We also develop an efficient algorithm to solve the resulting integer stochastic programming model with nonlinear constraints. Compared with traditional valuation and planning models, our method yields higher equity valuations, indicating that valuation without considering contingent decisions is inherently inaccurate. (C) 2006 Wiley Periodicals, Inc.
This paper addresses the capital budgeting problem under uncertainty. In particular, we propose a multistage stochastic programming model aimed at selecting and managing a project portfolio. The dynamic uncertain evol...
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This paper addresses the capital budgeting problem under uncertainty. In particular, we propose a multistage stochastic programming model aimed at selecting and managing a project portfolio. The dynamic uncertain evolution of each project value is modelled by a scenario tree over the planning horizon. The model allows the decision maker to revise decisions by decommitting from a given project if it shows a negative performance. Risk is explicitly assessed by defining a mean-risk objective function, where the conditional value at risk is used. A customized branch-and-bound method is also introduced for solving the proposed model. Extensive computational experiments have been carried out to validate the model effectiveness, also in comparison with other possible benchmark policies. The numerical results collected by solving randomly generated instances with the proposed branch-and-bound approach seems to be encouraging.
Traditionally, two variants of the L-shaped method based on Benders' decomposition principle are used to solve two-stage stochastic programming problems: the aggregate and the disaggregate version. In this study w...
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Traditionally, two variants of the L-shaped method based on Benders' decomposition principle are used to solve two-stage stochastic programming problems: the aggregate and the disaggregate version. In this study we report our experiments with a special convex programming method applied to the aggregate master problem. The convex programming method is of the type that uses an oracle with on-demand accuracy. We use a special form which, when applied to two-stage stochastic programming problems, is shown to integrate the advantages of the traditional variants while avoiding their disadvantages. On a set of 105 test problems, we compare and analyze parallel implementations of regularized and unregularized versions of the algorithms. The results indicate that solution times are significantly shortened by applying the concept of on-demand accuracy. (C) 2014 Elsevier B.V. All rights reserved.
stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast quantity of literature on the subject has appeared. De...
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stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast quantity of literature on the subject has appeared. Developments in the theory of computational complexity allow us to establish the theoretical complexity of a variety of stochastic programming problems studied in this literature. Under the assumption that the stochastic parameters are independently distributed, we show that two-stage stochastic programming problems are #P-hard. Under the same assumption we show that certain multi-stage stochastic programming problems are PSPACE-hard. The problems we consider are non-standard in that distributions of stochastic parameters in later stages depend on decisions made in earlier stages.
As a critical way to realize the optimal allocation of water environment capacity resources in the basin, emission rights trading faces multiple uncertainties, making it extremely hard and challenging to formulate app...
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As a critical way to realize the optimal allocation of water environment capacity resources in the basin, emission rights trading faces multiple uncertainties, making it extremely hard and challenging to formulate appropriate decisions and plans. Therefore, this study uses interval two-stage stochastic programming (ITSP) method to model the emission rights trading process with multiple uncertainties. It can promote the secondary optimal allocation of the emission rights between the demander and the supplier after the initial allocation. Externalities caused by environmental problems are internalized through the form of emission rights trading, thereby reducing the transaction costs and promoting the coordination and integrity of water pollution control among governments in a basin. Finally, the Yellow River basin is taken as an example for case analysis. The results show that the net revenue of emission rights system in the transaction status is better than that in the non-transaction status, and the average gap of net income reaches [171.031, 193.056] billion yuan. Under different reduction policies, the average water pollutant emission reduction in transaction status is [451.15, 628.34] thousand tons, which is generally less than [516.57, 670.05] thousand tons in non-transaction status. As policies get stricter and assimilative capacity of water bodies dwindles, reduction shrinks, leading to higher risks and economic loss from being unable to meet the discharge demand. When reduction policies are relatively loose and assimilative capacity is high, emission rights trading volume peaks. At this time, the trading volume of COD reached [29.05, 40.76] thousand tons, and that of NH3-N reached [3.74, 4.31] thousand tons. All these findings will offer insights for decision-makers on how to strike a balance between economic benefits and emission rights trading plans in the Yellow River basin.
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