In this paper, the optimal operation problem of smart micro-grids integrated with the pricing of Time-of-Use (TOU) demand response (DR) program is modeled as a two-stage stochastic programming problem with the aim of ...
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In this paper, the optimal operation problem of smart micro-grids integrated with the pricing of Time-of-Use (TOU) demand response (DR) program is modeled as a two-stage stochastic programming problem with the aim of minimizing the cost of MG operation and running TOU in the presence of renewable resources and incentive-based DR programs. Here, TOU as the most common type of time-based DR programs is implemented using a linear function based on the concept of self- and cross-price elasticity of load demand. In the presented model, the forecasting errors of generation of renewable resources are modeled by probability density functions. The operator of MG decides on two stages for optimal management of its network;the first stage refers to the operation of base condition of MG and the second one is pertaining to after the realization of different scenarios for generation of renewable resources. The base condition of MG refers to the situation in which the active power productions of renewables are equal to the predicted values. The proposed model is solved by Particle Swarm Optimization algorithm. A typical MG is employed to investigate and analyze the different features of the method. By varying the demand response potential of MG consumers, TOU tariffs are determined, and their impact on the results of energy and reserve cost as well as voltage and load profiles of MG are analyzed. Numerical results show the efficiency of DR in reducing costs as well as covering the uncertainty resulting from renewables.
An experiment with 480 DeKalb DK laying hens was conducted to study the effect of rations formulated with stochastic programming (STCH) or linear programming with a margin of safety (LPMS) over 12, 28-d periods. Ratio...
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An experiment with 480 DeKalb DK laying hens was conducted to study the effect of rations formulated with stochastic programming (STCH) or linear programming with a margin of safety (LPMS) over 12, 28-d periods. Rations were formulated to guarantee the requirement of methionine and lysine greater-than-or-equal-to 69%, in all rations, and Ca and P greater-than-or-equal-to either 69 or 90%. The four rations were: LPMS69 with Ca and P greater-than-or-equal-to 69%, LPMS90 with Ca and P greater-than-or-equal-to 90%, STCH69 with Ca and P greater-than-or-equal-to 69%, and STCH90 with Ca and P greater-than-or-equal-to 90%. Rations formulated with STCH were lower in cost than LPMS rations for respective probability levels. Costs per metric ton for LPMS69, LPMS90, STCH69, and STCH90 were $155.70, $157.71, $155.00, and $156.30, respectively. Compared to STCH rations, LPMS rations were overformulated in nutrients. There was no difference (P > .05) in performance for hen-housed egg production, hen-day egg production, feed er dozen eggs, mortality, egg weight, or eggshell percentage.
We consider the problem of optimal management of energy contracts, with bounds on the local (time step) amounts and global (whole period) amounts to be traded, integer constraint on the decision variables and uncertai...
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We consider the problem of optimal management of energy contracts, with bounds on the local (time step) amounts and global (whole period) amounts to be traded, integer constraint on the decision variables and uncertainty on prices only. After building a finite state Markov chain by using vectorial quantization tree method, we rely on the stochastic dual dynamic programming (SDDP) method to solve the continuous relaxation of this stochastic optimization problem. An heuristic for computing sub optimal solutions to the integer optimization problem, based on the Bellman values of the continuous relaxation, is provided. Combining the previous techniques, we are able to deal with high-dimensional state variables problems. Numerical tests applied to realistic energy markets problems have been performed.
We consider a two-stage stochastic variational inequality arising from a general convex two-stage stochastic programming problem, where the random variables have continuous distributions. The equivalence between the t...
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We consider a two-stage stochastic variational inequality arising from a general convex two-stage stochastic programming problem, where the random variables have continuous distributions. The equivalence between the two problems is shown under some moderate conditions, and the monotonicity of the two-stage stochastic variational inequality is discussed under additional conditions. We provide a discretization scheme with convergence results and employ the progressive hedging method with double parameterization to solve the discretized stochastic variational inequality. As an application, we show how the water resources management problem under uncertainty can be transformed from a two-stage stochastic programming problem to a two-stage stochastic variational inequality, and how to solve it, using the discretization scheme and the progressive hedging method with double parameterization.
Limiting flight delays during operations has become a critical research topic in recent years due to their prohibitive impact on airlines, airports, and passengers. A popular strategy for addressing this problem consi...
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Limiting flight delays during operations has become a critical research topic in recent years due to their prohibitive impact on airlines, airports, and passengers. A popular strategy for addressing this problem considers the uncertainty of day-of-operations delays and adjusts flight schedules to accommodate them in the planning stage. In this work, we present a stochastic programming model to account for uncertain future delays by adding buffers to flight turnaround times in a controlled manner. Specifically, our model adds slack to flight connection times with the objective of minimizing the expected value of the total propagated flight delay in a schedule. We also present a parallel solution framework that integrates an outer approximation decomposition method and column generation. Further, we demonstrate the scalability of our approach and its effectiveness in reducing delays with an extensive simulation study of five different flight networks using real-world data.
Several methods have been presented in the literature for the management of a pharmaceutical portfolio, i.e. selecting which clinical studies should be conducted. We compare two existing approaches that use stochastic...
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Several methods have been presented in the literature for the management of a pharmaceutical portfolio, i.e. selecting which clinical studies should be conducted. We compare two existing approaches that use stochastic programming techniques and formulate the problem as a mixed integer linear programme (MILP). The first approach will be referred to as the ROV (real option valuation) approach since values are assigned to drug development programmes using methods for real option valuation. The second approach will be referred to as the PS (project scheduling) approach as this approach focusses on the scheduling of clinical studies and is formulated similarly to the resource constrained project scheduling problem. The ROV approach treats the value of a drug development programme as stochastic whereas the PS approach treats the trial outcomes as the stochastic component of the programme. As a consequence, the two approaches may select different portfolios. An advantage of the PS approach is that a schedule for when trials are to be conducted is provided as part of the optimal solution. This advantage comes at a much increased computational burden, however.
A unified approach to stochastic feasible direction methods is developed. An abstract point-to-set map description of the algorithm is used and a general convergence theorem is proved. The theory is used to develop st...
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A unified approach to stochastic feasible direction methods is developed. An abstract point-to-set map description of the algorithm is used and a general convergence theorem is proved. The theory is used to develop stochastic analogs of classical feasible direction algorithms.
We propose a stochastic programming model as a solution for optimizing the problem of locating and allocating medical supplies used in disaster management. To prepare for natural disasters, we developed a stochastic o...
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We propose a stochastic programming model as a solution for optimizing the problem of locating and allocating medical supplies used in disaster management. To prepare for natural disasters, we developed a stochastic optimization approach to select the storage location of medical supplies and determine their inventory levels and to allocate each type of medical supply. Our model also captures disaster elaborations and possible effects of disasters by using a new classification for major earthquake scenarios. We present a case study for our model for the preparedness phase. As a case study, we applied our model to earthquake planning in Adana, Turkey. The experimental evaluations showed that the model is robust and effective.
A new decomposition method for multistage stochastic linear programming problems is proposed. A multistage stochastic problem is represented in a tree-like form and with each node of the decision tree a certain linear...
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A new decomposition method for multistage stochastic linear programming problems is proposed. A multistage stochastic problem is represented in a tree-like form and with each node of the decision tree a certain linear or quadratic subproblem is associated. The subproblems generate proposals for their successors and some backward information for their predecessors. The subproblems can be solved in parallel and exchange information in an asynchronous way through special buffers. After a finite time the method either finds an optimal solution to the problem or discovers its inconsistency. An analytical illustrative example shows that parallelization can speed up computation over every sequential method. Computational experiments indicate that for large problems we can obtain substantial gains in efficiency with moderate numbers of processors.
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is thatallscenario subproblems have to be solved at each ...
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Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is thatallscenario subproblems have to be solved at each iteration. In this paper, we introduce randomized versions of the Progressive Hedging algorithm able to produce new iterates as soon as asinglescenario subproblem is solved. Building on the relation between Progressive Hedging and monotone operators, we leverage recent results on randomized fixed point methods to derive and analyze the proposed methods. Finally, we release the corresponding code as an easy-to-use Julia toolbox and report computational experiments showing the practical interest of randomized algorithms, notably in a parallel context. Throughout the paper, we pay a special attention to presentation, stressing main ideas, avoiding extra-technicalities, in order to make the randomized methods accessible to a broad audience in the Operations Research community.
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