Journal articles: 'Two-stage stochastic programming problems'

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Ahmed, Hashnayne. "Formulation of Two-Stage Stochastic Programming with Fixed Recourse." Britain International of Exact Sciences (BIoEx) Journal 1, no. 1 (2019): 18–21. http://dx.doi.org/10.33258/bioex.v1i1.23.

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Stochastic Programming is an asset for the next world researchers due to its uncertainty calculations, which has been skipped in deterministic world experiments as it includes complicated calculations. Two-stage stochastic programming concerns two time period decisions based on some random parameters obtained from past experience or some sort of survey. The objective function for formulating two-stage stochastic programming with fixed recourse includes two parts: first-stage forecast and second-stage fixed decisions based on the experiment results. The constraints are similar to the normal optimization techniques rather some adjustments of requirements and technology assets. The fixed recourse decisions are sort of decisions from the deterministic world. Formulation techniques of two-stage stochastic programming with fixed recourse may be used for further complications arises in stochastic programming like complete recourse problems, multi-stage problems, etc. And that’s why Two-stage stochastic programming with fixed recourse is called the primary model for stochastic programming.

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Vogel, Silvia. "Necessary optimality conditions for two-stage stochastic programming problems." Optimization 16, no. 4 (1985): 607–16. http://dx.doi.org/10.1080/02331938508843056.

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Barik, S. K., M. P. Biswal, and D. Chakravarty. "Two-stage stochastic programming problems involving multi-choice parameters." Applied Mathematics and Computation 240 (August 2014): 109–14. http://dx.doi.org/10.1016/j.amc.2014.03.036.

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Arpón, Sebastián, Tito Homem-de-Mello, and Bernardo K. Pagnoncelli. "An ADMM algorithm for two-stage stochastic programming problems." Annals of Operations Research 286, no. 1-2 (2019): 559–82. http://dx.doi.org/10.1007/s10479-019-03471-0.

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Fábián, Csaba I., and Zoltán Szőke. "Solving two-stage stochastic programming problems with level decomposition." Computational Management Science 4, no. 4 (2006): 313–53. http://dx.doi.org/10.1007/s10287-006-0026-8.

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Barik, S. K., M. P. Biswal, and D. Chakravarty. "Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables." Advances in Operations Research 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/279181.

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Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highlights the possible risk involved in the decision-making tool. A numerical example is presented to demonstrate the proposed solution procedure.

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WANG, MAILI, KEVIN LANSEY, and DIANA YAKOWITZ. "AN APPROXIMATE METHOD FOR SOLVING STOCHASTIC TWO-STAGE PROGRAMMING PROBLEMS." Engineering Optimization 33, no. 3 (2001): 279–302. http://dx.doi.org/10.1080/03052150108940921.

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Barik, Suresh Kumar, Mahendra Prasad Biswal, and Debashish Chakravarty. "Two-stage stochastic programming problems involving interval discrete random variables." OPSEARCH 49, no. 3 (2012): 280–98. http://dx.doi.org/10.1007/s12597-012-0078-1.

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Ivanov, S. V., and A. I. Kibzun. "General Properties of Two-Stage Stochastic Programming Problems with Probabilistic Criteria." Automation and Remote Control 80, no. 6 (2019): 1041–57. http://dx.doi.org/10.1134/s0005117919060043.

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Tang, Hengyong, and Yufang Zhao. "L-shaped algorithm for two stage problems of stochastic convex programming." Journal of Applied Mathematics and Computing 13, no. 1-2 (2003): 261–75. http://dx.doi.org/10.1007/bf02936091.

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Leövey, H., and W. Römisch. "Quasi-Monte Carlo methods for linear two-stage stochastic programming problems." Mathematical Programming 151, no. 1 (2015): 315–45. http://dx.doi.org/10.1007/s10107-015-0898-x.

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Rao, P. Tirupathi, D. Flora Evangil, and K. Madhavi. "Stochastic Programming on Optimal Drug Administration for Two Stage Cancer Treatment Problems." International Journal of Green Computing 3, no. 1 (2012): 1–10. http://dx.doi.org/10.4018/jgc.2012010101.

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Either Continuous drug administration or continuous drug vacation for long spells of cancer chemotherapy is not suggestible. Similarly the quantum of administered drug dose either above the required level or below the wanted level is also not advised. Effective drug administration has to consider the optimal threshold limits on the drug administration/drug vacation times; upper and lower limits of drug quantity; along with the suitable number of drug administration/drug vacation cycles; and the number of spells within the cycle of drug usage/stoppage. This paper develops an optimization programming problem for designing drug administration strategies for a cancer patient under chemotherapy. This study will help in exploring the decision parameters at the targeted objectives. Optimal decisions on drug dosage level, drug administration period, drug vacation period, number of drug administration cycles; number of drugs applied within a cycle, etc., can be obtained with the model. Sensitivity analysis is carried out for understanding the model behavior. This work has a scope for developing health care Decision Support Systems.

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Lu, Hongwei, Guohe Huang, and Li He. "Inexact rough-interval two-stage stochastic programming for conjunctive water allocation problems." Journal of Environmental Management 91, no. 1 (2009): 261–69. http://dx.doi.org/10.1016/j.jenvman.2009.08.011.

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Tönissen, Denise D., Joachim J. Arts, and Zuo-Jun Max Shen. "A column-and-constraint generation algorithm for two-stage stochastic programming problems." TOP 29, no. 3 (2021): 781–98. http://dx.doi.org/10.1007/s11750-021-00593-2.

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AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

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Tometzki, Thomas, and Sebastian Engell. "Hybrid Evolutionary Optimization of Two-Stage Stochastic Integer Programming Problems: An Empirical Investigation." Evolutionary Computation 17, no. 4 (2009): 511–26. http://dx.doi.org/10.1162/evco.2009.17.4.17404.

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In this contribution, we consider decision problems on a moving horizon with significant uncertainties in parameters. The information and decision structure on moving horizons enables recourse actions which correct the here-and-now decisions whenever the horizon is moved a step forward. This situation is reflected by a mixed-integer recourse model with a finite number of uncertainty scenarios in the form of a two-stage stochastic integer program. A stage decomposition-based hybrid evolutionary algorithm for two-stage stochastic integer programs is proposed that employs an evolutionary algorithm to determine the here-and-now decisions and a standard mathematical programming method to optimize the recourse decisions. An empirical investigation of the scale-up behavior of the algorithms with respect to the number of scenarios exhibits that the new hybrid algorithm generates good feasible solutions more quickly than a state of the art exact algorithm for problem instances with a high number of scenarios.

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Tong, Xiaojiao, Liu Yang, Xiao Luo, and Bo Rao. "A stochastic dual dynamic programming method for two-stage distributionally robust optimization problems." Optimization Methods and Software 35, no. 5 (2020): 1002–21. http://dx.doi.org/10.1080/10556788.2020.1811705.

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Zhenevskaya, I. D., and A. V. Naumov. "The Decomposition Method for Two-Stage Stochastic Linear Programming Problems with Quantile Criterion." Automation and Remote Control 79, no. 2 (2018): 229–40. http://dx.doi.org/10.1134/s0005117918020030.

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Ketabchi, Saeed, and Malihe Behboodi-Kahoo. "Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/735916.

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The augmented Lagrangian method can be used for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The augmented Lagrangian objective function of a stochastic linear problem is not twice differentiable which precludes the use of a Newton method. In this paper, we apply the smoothing techniques and a fast Newton-Armijo algorithm for solving an unconstrained smooth reformulation of this problem. Computational results and comparisons are given to show the effectiveness and speed of the algorithm.

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Mohd Noh, Norshela, Arifah Bahar, and Zaitul Marlizawati Zainuddin. "Scenario Based Two-Stage Stochastic Programming Approach for the Midterm Production Planning of Oil Refinery." MATEMATIKA 34, no. 3 (2018): 45–55. http://dx.doi.org/10.11113/matematika.v34.n3.1138.

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Recently, oil refining industry is facing with lower profit margin due to uncertainty. This causes oil refinery to include stochastic optimization in making a decision to maximize the profit. In the past, deterministic linear programming approach is widely used in oil refinery optimization problems. However, due to volatility and unpredictability of oil prices in the past ten years, deterministic model might not be able to predict the reality of the situation as it does not take into account the uncertainties thus, leads to non-optimal solution. Therefore, this study will develop two-stage stochastic linear programming for the midterm production planning of oil refinery to handle oil price volatility. Geometric Brownian motion (GBM) is used to describe uncertainties in crude oil price, petroleum product prices, and demand for petroleum products. This model generates the future realization of the price and demands with scenario tree based on the statistical specification of GBM using method of moment as input to the stochastic programming. The model developed in this paper was tested for Malaysia oil refinery data. The result of stochastic approach indicates that the model gives better prediction of profit margin.

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Chen, Youhua Frank. "Fractional programming approach to two stochastic inventory problems." European Journal of Operational Research 160, no. 1 (2005): 63–71. http://dx.doi.org/10.1016/j.ejor.2003.06.020.

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Tang, Chunming, Bo He, and Zhenzhen Wang. "Modified Accelerated Bundle-Level Methods and Their Application in Two-Stage Stochastic Programming." Mathematics 8, no. 2 (2020): 265. http://dx.doi.org/10.3390/math8020265.

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The accelerated prox-level (APL) and uniform smoothing level (USL) methods recently proposed by Lan (Math Program, 149: 1–45, 2015) can achieve uniformly optimal complexity when solving black-box convex programming (CP) and structure non-smooth CP problems. In this paper, we propose two modified accelerated bundle-level type methods, namely, the modified APL (MAPL) and modified USL (MUSL) methods. Compared with the original APL and USL methods, the MAPL and MUSL methods reduce the number of subproblems by one in each iteration, thereby improving the efficiency of the algorithms. Conclusions of optimal iteration complexity of the proposed algorithms are established. Furthermore, the modified methods are applied to the two-stage stochastic programming, and numerical experiments are implemented to illustrate the advantages of our methods in terms of efficiency and accuracy.

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Zhao, Yi, Qingwan Xue, Zhichao Cao, and Xi Zhang. "A Two-Stage Chance Constrained Approach with Application to Stochastic Intermodal Service Network Design Problems." Journal of Advanced Transportation 2018 (December 24, 2018): 1–18. http://dx.doi.org/10.1155/2018/6051029.

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Compared with traditional freight transportation, intermodal freight transportation is more competitive which can combine the advantages of different transportation modes. As a consequence, operational research on intermodal freight transportation has received more attention and developed rapidly, but it is still a young research field. In this paper, a stochastic intermodal service network design problem is introduced in a sea-rail transportation system, which considers stochastic travel time, stochastic transfer time, and stochastic container demand. Given candidate train and ship services, we develop a two-stage chance constrained programming model for this problem with the objective of minimising the expected total cost. The first stage allows for the selection of operated services, while the second stage focuses on the determination of intermodal container routes where capacity and on-time delivery chance constraints are presented. A hybrid heuristic algorithm, incorporating sample average approximation and ant colony optimisation, is employed to solve this model. The proposed model is applied to a realistic intermodal sea-rail network, which demonstrates the performance of the model and algorithm as well as the influence of stochasticity on transportation plans. Hence, the proposed methodology can improve effectively the performance of intermodal service network design scheme under stochastic conditions and provide managerial insights for decision-makers.

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Averbakh, I. L. "An iterative decomposition method in single-stage stochastic integer-programming problems." USSR Computational Mathematics and Mathematical Physics 30, no. 5 (1990): 133–39. http://dx.doi.org/10.1016/0041-5553(90)90171-n.

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Ameri, Mahmoud, Armin Jarrahi, Farshad Haddadi, and Mohammad Hasan Mirabimoghaddam. "A Two-Stage Stochastic Model for Maintenance and Rehabilitation Planning of Pavements." Mathematical Problems in Engineering 2019 (January 9, 2019): 1–15. http://dx.doi.org/10.1155/2019/3971791.

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Pavement maintenance and rehabilitation (M&R) plan for maintaining the pavement quality in an acceptable level has direct influence on the required budget. Deterministic budgeting is an unrealistic assumption, so, in this study, a two-stage stochastic model using integer programming is developed to address uncertainty in budgeting. Another aim of this study is to develop an executive model that considers a broad range of parameters at network level maintenance and rehabilitation planning. While having too many details in planning problems makes them more complicated, some restrictions called “technical constraints” were considered to reduce solution time of solving procedure as well as improve M&R activities assignment efficiency. Comparing results of the stochastic model with a deterministic model for a case study revealed that the two-stage stochastic model led to increased total cost compared to the deterministic one due to considering probability in budgeting. However, the developed model provides several M&R plans that are compatible with budget variation.

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Hashemi Doulabi, Hossein, Gilles Pesant, and Louis-Martin Rousseau. "Vehicle Routing Problems with Synchronized Visits and Stochastic Travel and Service Times: Applications in Healthcare." Transportation Science 54, no. 4 (2020): 1053–72. http://dx.doi.org/10.1287/trsc.2019.0956.

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This paper, for the first time, studies vehicle routing problems with synchronized visits (VRPS) and stochastic travel and service times. In addition to considering a home healthcare scheduling problem, we introduce an operating room scheduling problem with stochastic durations as a novel application of VRPS. We formulate VRPS with stochastic times as a two-stage stochastic integer programming model that, unlike the deterministic models in the VRPS literature, does not have any big-M constraints. This advantage comes at the cost of a large number of second-stage integer variables. We prove that the integrality constraints on second-stage variables can be relaxed, and therefore, we can apply the L-shaped algorithm and its branch-and-cut implementation to solve the problem. We enhance the model by developing valid inequalities and a lower bounding functional. We analyze the subproblems of the L-shaped algorithm and devise a specialized algorithm for them that is significantly faster than standard linear programming algorithms. Computational results show that the branch-and-cut algorithm optimally solves stochastic home healthcare scheduling instances with 15 patients and 10%–30% of synchronized visits. It also finds solutions with an average optimality gap of 3.57% for instances with 20 patients. Furthermore, the branch-and-cut algorithm optimally solves stochastic operating room scheduling problems with 20 surgeries.

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Suparni, Herman Mawengkang, Opim Salim Sitompul, and Saib Suwilo. "Developing Reduced Gradient Approach for Solving Multi-Stage Stochastic Nonlinear Programs." Journal of Computational and Theoretical Nanoscience 17, no. 7 (2020): 3194–99. http://dx.doi.org/10.1166/jctn.2020.9160.

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An increasing number of practical scenarios continue to experience problems associated with multistage stochastic programming. This study proposes a decomposition method through which they can be a successful solution to multi-stage stochastic nonlinear programs. The proposed method entails the scenario analysis method. The proposed method also performs its role via search direction generation in such a way that sets of quadratic programming sub-issues are solved in a parallel way, especially when the size is significant lower, compared to the case involving original problems at the respective iterations. Relative to the dual multiplier derivation, which focuses on non-anticipativity constraints, the proposed system advocates for the introduction of generalized reduced gradient approaches.

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Lee, Hyunwoo, Seokhyun Chung, Taesu Cheong, and Sang Song. "Accounting for Fairness in a Two-Stage Stochastic Programming Model for Kidney Exchange Programs." International Journal of Environmental Research and Public Health 15, no. 7 (2018): 1491. http://dx.doi.org/10.3390/ijerph15071491.

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Kidney exchange programs, which allow a potential living donor whose kidney is incompatible with his or her intended recipient to donate a kidney to another patient in return for a kidney that is compatible for their intended recipient, usually aims to maximize the number of possible kidney exchanges or the total utility of the program. However, the fairness of these exchanges is an issue that has often been ignored. In this paper, as a way to overcome the problems arising in previous studies, we take fairness to be the degree to which individual patient-donor pairs feel satisfied, rather than the extent to which the exchange increases social benefits. A kidney exchange has to occur on the basis of the value of the kidneys themselves because the process is similar to bartering. If the matched kidneys are not of the level expected by the patient-donor pairs involved, the match may break and the kidney exchange transplantation may fail. This study attempts to classify possible scenarios for such failures and incorporate these into a stochastic programming framework. We apply a two-stage stochastic programming method using total utility in the first stage and the sum of the penalties for failure in the second stage when an exceptional event occurs. Computational results are provided to demonstrate the improvement of the proposed model compared to that of previous deterministic models.

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Lin, Shu-Cheng, Han-Wen Tuan, and Peterson Julian. "An Improvement for Fuzzy Stochastic Goal Programming Problems." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/8605652.

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We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.

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Fekete, Krešimir, Srete Nikolovski, Zvonimir Klaić, and Ana Androjić. "Optimal Re-Dispatching of Cascaded Hydropower Plants Using Quadratic Programming and Chance-Constrained Programming." Energies 12, no. 9 (2019): 1604. http://dx.doi.org/10.3390/en12091604.

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Stochastic production from wind power plants imposes additional uncertainty in power system operation. It can cause problems in load and generation balancing in the power system and can also cause congestion in the transmission network. This paper deals with the problems of congestion in the transmission network, which are caused by the production of wind power plants. An optimization model for corrective congestion management is developed. Congestions are relieved by re-dispatching several cascaded hydropower plants. Optimization methodology covers the optimization period of one day divided into the 24 segments for each hour. The developed optimization methodology consists of two optimization stages. The objective of the first optimization stage is to obtain an optimal day-ahead dispatch plan of the hydropower plants that maximizes profit from selling energy to the day-ahead electricity market. If such a dispatch plan, together with the wind power plant production, causes congestion in the transmission network, the second optimization stage is started. The objective of the second optimization stage is the minimization of the re-dispatching of cascaded hydropower plants in order to avoid possible congestion. The concept of chance-constrained programming is used in order to consider uncertain wind power production. The first optimization stage is defined as a mixed-integer linear programming problem and the second optimization stage is defined as a quadratic programming (QP) problem, in combination with chance-constrained programming. The developed optimization model is tested and verified using the model of a real-life power system.

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Hedar, Abdel-Rahman, Amira A. Allam, and Wael Deabes. "Memory-Based Evolutionary Algorithms for Nonlinear and Stochastic Programming Problems." Mathematics 7, no. 11 (2019): 1126. http://dx.doi.org/10.3390/math7111126.

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In this paper, we target the problems of finding a global minimum of nonlinear and stochastic programming problems. To solve this type of problem, we propose new approaches based on combining direct search methods with Evolution Strategies (ESs) and Scatter Search (SS) metaheuristics approaches. First, we suggest new designs of ESs and SS with a memory-based element called Gene Matrix (GM) to deal with those type of problems. These methods are called Directed Evolution Strategies (DES) and Directed Scatter Search (DSS), respectively, and they are able to search for a global minima. Moreover, a faster convergence can be achieved by accelerating the evolutionary search process using GM, and in the final stage we apply the Nelder-Mead algorithm to find the global minimum from the solutions found so far. Then, the variable-sample method is invoked in the DES and DSS to compose new stochastic programming techniques. Extensive numerical experiments have been applied on some well-known functions to test the performance of the proposed methods.

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Mitra, Sumit, Pablo Garcia-Herreros, and Ignacio E. Grossmann. "A cross-decomposition scheme with integrated primal–dual multi-cuts for two-stage stochastic programming investment planning problems." Mathematical Programming 157, no. 1 (2016): 95–119. http://dx.doi.org/10.1007/s10107-016-1001-y.

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Placido dos Santos, Felipe Silva, and Fabricio Oliveira. "An enhanced L-Shaped method for optimizing periodic-review inventory control problems modeled via two-stage stochastic programming." European Journal of Operational Research 275, no. 2 (2019): 677–93. http://dx.doi.org/10.1016/j.ejor.2018.11.053.

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Kato, Kosuke, Masatoshi Sakawa, and Hideki Katagiri. "Interactive fuzzy programming for two-level stochastic linear programming problems through expectation and variance models." International Journal of Knowledge-based and Intelligent Engineering Systems 13, no. 3-4 (2009): 111–18. http://dx.doi.org/10.3233/kes-2009-0179.

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Mahmutoğulları, Ali İrfan, Özlem Çavuş, and M. Selim Aktürk. "Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR." European Journal of Operational Research 266, no. 2 (2018): 595–608. http://dx.doi.org/10.1016/j.ejor.2017.10.038.

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Wang, Kai, and Alexandre Jacquillat. "A Stochastic Integer Programming Approach to Air Traffic Scheduling and Operations." Operations Research 68, no. 5 (2020): 1375–402. http://dx.doi.org/10.1287/opre.2020.1985.

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Air traffic management measures comprise tactical operating procedures to minimize delay costs and strategic scheduling interventions to control overcapacity scheduling. Although interdependent, these problems have been treated in isolation. This paper proposes an integrated model of scheduling and operations in airport networks that jointly optimizes scheduling interventions and ground-holding operations across airports networks under operating uncertainty. It is formulated as a two-stage stochastic program with integer recourse. To solve it, we develop an original decomposition algorithm with provable solution quality guarantees. The algorithm relies on new optimality cuts—dual integer cuts—that leverage the reduced costs of the dual linear programming relaxation of the second-stage problem. The algorithm also incorporates neighborhood constraints, which shift from exploration to exploitation at later stages. We also use a scenario generation approach to construct representative scenarios from historical records of operations—using integer programming. Computational experiments show that our algorithm yields near-optimal solutions for the entire U.S. National Airspace System network. Ultimately, the proposed approach enhances airport demand management models through scale integration (by capturing network-wide interdependencies) and scope integration (by capturing interdependencies between scheduling and operations).

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Kato, Kosuke, Hideki Katagiri, Masatoshi Sakawa, and Jingtao Wang. "Interactive fuzzy programming based on a probability maximization model for two-level stochastic linear programming problems." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 89, no. 2 (2005): 33–42. http://dx.doi.org/10.1002/ecjc.20166.

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Sakawa, Masatoshi, and Hideki Katagiri. "INTERACTIVE FUZZY PROGRAMMING BASED ON FRACTILE CRITERION OPTIMIZATION MODEL FOR TWO-LEVEL STOCHASTIC LINEAR PROGRAMMING PROBLEMS." Cybernetics and Systems 41, no. 7 (2010): 508–21. http://dx.doi.org/10.1080/01969722.2010.511547.

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Liu, Zhenfang, Yang Zhou, Gordon Huang, and Bin Luo. "Risk Aversion Based Inexact Stochastic Dynamic Programming Approach for Water Resources Management Planning under Uncertainty." Sustainability 11, no. 24 (2019): 6926. http://dx.doi.org/10.3390/su11246926.

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In this study, a dual interval robust stochastic dynamic programming (DIRSDP) method is developed for planning water resources management systems under uncertainty. As an extension of the existing interval stochastic dynamic programming (ISDP) method, DIRSDP can deal with two-stage stochastic programming (TSP)-based planning problems associated with dynamic features, input uncertainties, and multistage concerns. Compared with other optimization methods dealing with uncertainties, the developed DIRSDP method has advantages in addressing uncertainties with complex presentations and reflecting decision makers’ risk-aversion attitudes within its optimization process. Parameters in the DIRSDP model can be represented as probability distributions as well as single and/or dual intervals. Decision makers’ risk-aversion attitudes can be reflected through restricting the deviation of the recourse costs to a tolerance level. Water-allocation plans can then be developed based on the analysis of tradeoffs between the system benefit and solution robustness. The developed method is applied to a case of water resources management planning. The solutions are reasonable, indicating applicability of the developed methodology.

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Novikov, Artem. "About a regional development model that takes into account environmental problems with budgeting uncertainty." E3S Web of Conferences 265 (2021): 04028. http://dx.doi.org/10.1051/e3sconf/202126504028.

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Raw-materials base (hereinafter RMB) is one of the largest industries for financial investments in Russia. There are various mathematical descriptions for the development of regions with resource-based economy. Earlier in [1] the researchers considered the model based on bilevel integer stochastic programming problems with Boolean variables. This paper proposes a new approach to public-private partnership modelling, including a bilevel linear stochastic programming problem. This model assumes that budget constraints of the state and the investor can vary in a random manner with a specific probability distribution. We put forward two methods to solve this problem: problem’s reduction to the deterministic bilevel one and formulation of deterministic problems sequence with help of Monte Carlo methods. In order to solve deterministic problems of integer programming, we suggest two approaches: direct enumeration and heuristic “Game” approach. The numerical experiments for proposed algorithms validation are conducted on the basis of actual data of Zabaykalsky Krai development. Multiple input parameters of the model vary in these experiments. Finally, we present a brief analysis of the obtained solutions to the stochastic linear programming problems with Boolean variables.

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WANG, Jingtao, Kosuke KATO, Hideki KATAGIRI, and Masatoshi SAKAWA. "Interactive fuzzy programming based on a variance minimization model considering expectations for two-level stochastic linear programming problems." Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 16, no. 6 (2004): 561–70. http://dx.doi.org/10.3156/jsoft.16.561.

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Shao, Jian, Bu Han Zhang, Wei Si Deng, Kai Min Zhang, Bing Jie Jin, and Teng Yu Ge. "A Stochastic Programming Method for Unit Commitment of Wind Integrated Power System." Advanced Materials Research 732-733 (August 2013): 1390–95. http://dx.doi.org/10.4028/www.scientific.net/amr.732-733.1390.

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This paper presents a stochastic programming method that can assess the impact of wind generation uncertainties on unit comment (UC) problem. To model the uncertainty of wind genration, scenarios of wind speed are generated based on the known probability interval of forecasted wind speed and a scenario reduction technique limits the number of scenarios. The UC problem is modeled as a stochastic programming problem based on chance-constrained programming, and is decomposed into two embedded optimization sub-problems: the unit on/off status schedule problem and the load economic dispatch problem. Discrete particle swarm optimization (DPSO) and the equal incremental principle are used to solve the stochastic UC problem. The numerical results indicate that the proposed stochastic model is more suitable for wind integrated system with uncertainty.

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Qin, Yichen, Hoi-Lam Ma, Felix T. S. Chan, and Waqar Ahmed Khan. "A scenario-based stochastic programming approach for aircraft expendable and rotable spare parts planning in MRO provider." Industrial Management & Data Systems 120, no. 9 (2020): 1635–57. http://dx.doi.org/10.1108/imds-03-2020-0131.

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PurposeThis paper aims to build a novel model and approach that assist an aircraft MRO procurement and overhaul management problems from the perspective of aircraft maintenance service provider, in order to ensure its smoothness maintenance activities implementation. The mathematical model utilizes the data related to warehouse inventory management, incoming customer service planning as well as risk forecast and control management at the decision-making stage, which facilitates to alleviate the negative impact of the uncertain maintenance demands on the MRO spare parts inventory management operations.Design/methodology/approachA stochastic model is proposed to formulate the problem to minimize the impact of uncertain maintenance demands, which provides flexible procurement and overhaul strategies. A Benders decomposition algorithm is proposed to solve large-scale problem instances given the structure of the mathematical model.FindingsCompared with the default branch-and-bound algorithm, the computational results suggest that the proposed Benders decomposition algorithm increases convergence speed.Research limitations/implicationsThe results among the same group of problem instances suggest the robustness of Benders decomposition in tackling instances with different number of stochastic scenarios involved.Practical implicationsExtending the proposed model and algorithm to a decision support system is possible, which utilizes the databases from enterprise's service planning and management information systems.Originality/valueA novel decision-making model for the integrated rotable and expendable MRO spare parts planning problem under uncertain environment is developed, which is formulated as a two-stage stochastic programming model.

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Hasuike, Takashi, Hideki Katagiri, and Hiroaki Ishii. "Multiobjective Random Fuzzy Linear Programming Problems Based on the Possibility Maximization Model." Journal of Advanced Computational Intelligence and Intelligent Informatics 13, no. 4 (2009): 373–79. http://dx.doi.org/10.20965/jaciii.2009.p0373.

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Two multiobjective random fuzzy programming problems considered based on the possibility maximization model using possibilistic and stochastic programming are not initially well defined due to the random variables and fuzzy numbers included. To solve them analytically, probability criteria are set for objective functions and chance constraints are introduced. Taking into account the decision maker’s subjectivity and the original plan’s flexibility, a fuzzy goal is introduced for each objective function. The original problems are then changed into deterministic equivalent problems to make the possibility fractile optimization problem equivalent to a linear programming problem. The possibility maximization problem for probability is changed into a nonlinear programming problem, and an analytical solution is constructed extending previous solution approaches.

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Ryan, Kevin, Shabbir Ahmed, Santanu S. Dey, Deepak Rajan, Amelia Musselman, and Jean-Paul Watson. "Optimization-Driven Scenario Grouping." INFORMS Journal on Computing 32, no. 3 (2020): 805–21. http://dx.doi.org/10.1287/ijoc.2019.0924.

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Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. We develop an approach that improves on these bounds by reinforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into groups. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve the bound by optimizing a proxy metric based on information obtained from evaluating a subset of candidate feasible solutions. We show that the proposed grouping problem is NP-hard in general, identify a polynomially solvable case, and present two formulations for solving the problem: a matching formulation for a special case and a mixed-integer programming formulation for the general case. We use the proposed grouping scheme as a preprocessing step for a particular scenario decomposition algorithm and demonstrate its effectiveness in solving standard test instances of two-stage 0–1 stochastic programs. Using this approach, we are able to prove optimality for all previously unsolved instances of a standard test set. Additionally, we implement this scheme as a preprocessing step for PySP, a publicly available and widely used implementation of progressive hedging, and compare this grouping approach with standard grouping approaches on large-scale stochastic unit commitment instances. Finally, the idea is extended to propose a finitely convergent algorithm for two-stage stochastic programs with a finite feasible region.

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Sennott, Linn I. "COMPUTING AVERAGE OPTIMAL CONSTRAINED POLICIES IN STOCHASTIC DYNAMIC PROGRAMMING." Probability in the Engineering and Informational Sciences 15, no. 1 (2001): 103–33. http://dx.doi.org/10.1017/s0269964801151089.

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A stochastic dynamic program incurs two types of cost: a service cost and a quality of service (delay) cost. The objective is to minimize the expected average service cost, subject to a constraint on the average quality of service cost. When the state space S is finite, we show how to compute an optimal policy for the general constrained problem under weak conditions. The development uses a Lagrange multiplier approach and value iteration. When S is denumerably infinite, we give a method for computation of an optimal policy, using a sequence of approximating finite state problems. The method is illustrated with two computational examples.

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Keutchayan, Julien, David Munger, and Michel Gendreau. "On the Scenario-Tree Optimal-Value Error for Stochastic Programming Problems." Mathematics of Operations Research 45, no. 4 (2020): 1572–95. http://dx.doi.org/10.1287/moor.2019.1043.

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Stochastic programming problems generally lead to large-scale programs if the number of random outcomes is large or if the problem has many stages. A way to tackle them is provided by scenario-tree generation methods, which construct approximate problems from a reduced subset of outcomes. However, it is well known that the number of scenarios required to keep the approximation error within a given tolerance grows rapidly with the number of random parameters and stages. For this reason, to limit the fast growth of complexity, scenario-tree generation methods tailored to problems must be developed. These will use more information about the problem than just the underlying probability distributions; namely, they will also take into account the objective function and the constraints. In this paper, we develop a general framework to build problem-driven scenario trees. We do so by studying how the optimal-value error arises as a sum of lower-level errors made at each node of the tree. We show how these small but numerous node errors depend on the specific features of the problem and how they can be controlled by designing scenario trees with appropriate branching structures and discretization points and weights. We illustrate our approach on two examples.

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Sudtachat, Kanchala. "Transportation and Production Lot-size for Sugarcane under Uncertainty of Machine Capacity." MATEC Web of Conferences 167 (2018): 02007. http://dx.doi.org/10.1051/matecconf/201816702007.

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The integrated transportation and production lot size problems is important effect to total cost of operation system for sugar factories. In this research, we formulate a mathematic model that combines these two problems as two stage stochastic programming model. In the first stage, we determine the lot size of transportation problem and allocate a fixed number of vehicles to transport sugarcane to the mill factory. Moreover, we consider an uncertainty of machine (mill) capacities. After machine (mill) capacities realized, in the second stage we determine the production lot size and make decision to hold units of sugarcane in front of mills based on discrete random variables of machine (mill) capacities. We investigate the model using a small size problem. The results show that the optimal solutions try to choose closest fields and lower holding cost per unit (at fields) to transport sugarcane to mill factory. We show the results of comparison of our model and the worst case model (full capacity). The results show that our model provides better efficiency than the results of the worst case model.

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Anatolievna Burdina, Anna, Marina Nikolaevna Kaloshina, Elena Timofeevna Manaenkova, Anna Alexandrovna Nehrest, and Tatyana Mikhailovna Rogulenko. "Development of Optimization Model of Budget Allocation for Promotion of Unmanned Aerial Vehicles." International Journal of Engineering & Technology 7, no. 4.38 (2018): 91. http://dx.doi.org/10.14419/ijet.v7i4.38.24329.

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This article discusses manufacturers of unmanned aerial vehicles, convex and stochastic programming, quantile optimization in economy are reviewed. Problem of budget allocation for promotion of engineering products is defined and solved in two variants: deterministic formulation, when a company is new and has not its own statistic data, and, otherwise, stochastic formulation. These problems were solved using methods of optimization theory and theory of stochastic systems such as simplex method, successive quadratic programming, and confidence method. Optimization model of budget allocation for promotion of unmanned aerial vehicles has been developed which optimizes budget for innovative engineering products.

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Suo, Meiqin, Fuhui Du, Yongping Li, Tengteng Kong, and Jing Zhang. "An Inexact Inventory Theory-Based Water Resources Distribution Model for Yuecheng Reservoir, China." Mathematical Problems in Engineering 2020 (October 31, 2020): 1–13. http://dx.doi.org/10.1155/2020/6273513.

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In this study, an inexact inventory theory-based water resources distribution (IIWRD) method is advanced and applied for solving the problem of water resources distribution from Yuecheng Reservoir to agricultural activities, in the Zhanghe River Basin, China. In the IIWRD model, the techniques of inventory model, inexact two-stage stochastic programming, and interval-fuzzy mathematics programming are integrated. The water diversion problem of Yuecheng Reservoir is handled under multiple uncertainties. Decision alternatives for water resources allocation under different inflow levels with a maximized system benefit and satisfaction degree are provided for water resources management in Yuecheng Reservoir. The results show that the IIWRD model can afford an effective scheme for solving water distribution problems and facilitate specific water diversion of a reservoir for managers under multiple uncertainties and a series of policy scenarios.

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Amoozad Mahdiraji, Hannan, Seyed Hossein Razavi Hajiagha, Shide Sadat Hashemi, and Edmundas Kazimieras Zavadskas. "Bi-objective mean–variance method based on Chebyshev inequality bounds for multi-objective stochastic problems." RAIRO - Operations Research 52, no. 4-5 (2018): 1201–17. http://dx.doi.org/10.1051/ro/2018018.

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Multi-objective programming became more and more popular in real world decision making problems in recent decades. There is an underlying and fundamental uncertainty in almost all of these problems. Among different frameworks of dealing with uncertainty, probability and statistic-based schemes are well-known. In this paper, a method is developed to find some efficient solutions of a multi-objective stochastic programming problem. The method composed a process of transforming the stochastic multi-objective problem to a bi-objective equivalent using the concept of Chebyshev inequality bounds and then solving the obtained problem with a fuzzy set based approach. Application of the proposed method is examined on two numerical examples and the results are compared with different methods. These comparisons illustrated that the results are satisfying.

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Journal articles on the topic 'Two-stage stochastic programming problems'

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