A new duality theory is developed for a class of stochastic programs in which the probability distribution is not necessarily discrete. This provides a new framework for problems which are not necessarily bounded, are...
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A new duality theory is developed for a class of stochastic programs in which the probability distribution is not necessarily discrete. This provides a new framework for problems which are not necessarily bounded, are not required to have relatively complete recourse, and do not satisfy the typical Slater condition of strict feasibility. These problems instead satisfy a different constraint qualification called 'direction-free feasibility' to deal with possibly unbounded constraint sets, and 'calmness' of a certain finite-dimensional value function to serve as a weaker condition than strict feasibility to obtain the existence of dual multipliers. In this way, strong duality results are established in which the dual variables are finite-dimensional, despite the possible infinite-dimensional character of the second-stage constraints. From this, infinite-dimensional dual problems are obtained in the space of essentially bounded functions. It is then shown how this framework could be used to obtain duality results in the setting of mathematical finance.
Incentive-based demand response (IBDR) has been recognized as a powerful tool to mitigate supply-demand imbalance in electricity market. However, the complex uncertainties of consumers, including participation uncerta...
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Incentive-based demand response (IBDR) has been recognized as a powerful tool to mitigate supply-demand imbalance in electricity market. However, the complex uncertainties of consumers, including participation uncertainty and responsiveness uncertainty, have been a central challenge to implement IBDR programs. In this paper, a stochastic programming model for IBDR considering the complex uncertainties of consumers is proposed. The proposed model can effectively deals with the above two uncertainties. Besides, the model of energy storage unit (ESU) has been improved to cope with properly the deviation between total actual balancing power and required balancing power. Moreover, the model enhances the applicability of IBDR to be applicable to both curtailment IBDR programs and absorbing IBDR programs by adding dynamic parameters. The model is formulated as a bi-level stochastic programming problem based on uncertain programming theory, and corresponding equivalent model is also given to solve the problem effectively. Finally, simulation results verify merits of the proposed model in cutting down total cost of DRA, decreasing risk cost of DRA and reducing balancing power deviation caused by uncertainty of consumers.
As communication technologies evolve, it becomes necessary to incorporate the stochastic effect of traffic flows into network models. This paper introduces the stochastic programming (SP) methodology for characterizin...
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As communication technologies evolve, it becomes necessary to incorporate the stochastic effect of traffic flows into network models. This paper introduces the stochastic programming (SP) methodology for characterizing traffic. Two SP approaches, here-and-now (HN) and scenario tracking (ST), are described through case studies for a prototype network. A numerical optimization procedure is used to perform the simulation. It is clearly demonstrated that when the probability distributions can be estimated analytically, the HN approach can be attractive. Otherwise, the ST approach may be more appropriate. (C) 2005 Elsevier B.V. All rights reserved.
In order to achieve better system performance, the concept of an ad-hoc mobile cloud, whereby a mobile device can access resources such as processing, data or storage at other neighbouring nodes, has been proposed. Th...
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In order to achieve better system performance, the concept of an ad-hoc mobile cloud, whereby a mobile device can access resources such as processing, data or storage at other neighbouring nodes, has been proposed. The difficulty that arises with this concept is the mobility of nearby devices, i.e., a neighboring device may move out of range before it can communicate its results back to the source device. In this paper, we propose a workload assignment scheme between a source device and nearby mobile devices that takes into account the randomness of the connection time between these devices. In order to cope with this randomness, we adopt a multi-stage stochastic programming approach which is able to take posterior recourse actions to compensate for inaccurate predictions. Moreover, in order to motivate the available mobile devices to cooperate, we formulate a distributed multi-stage stochastic buyer-seller game (MSSBSG) in which different mobile devices attempt to maximize their utilities. Our results show that the stochastic programming approach outperforms several baseline schemes and the MSSBSG approach effectively promotes cooperation between mobile devices and achieves the best overall performance compared to simpler approaches that do not take stochastic operating conditions into account.
A bounding-based method is developed for estimating the expected operation cost of a multiarea electric power system in which transmission capacity limits interarea flows. Costs include the expense of power generation...
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A bounding-based method is developed for estimating the expected operation cost of a multiarea electric power system in which transmission capacity limits interarea flows. Costs include the expense of power generation and losses suffered by consumers because of supply shortfalls, averaged over random generator outage states and varying demand levels. The calculation of this expectation, termed the distribution problem, is a large-scale stochastic programming problem. Rather than solving this problem directly, lower and upper bounds to the expected cost are created using two more easily solved models. The lower bound is from a deterministic model based on the expected value of the uncertain inputs. The upper bound results from a linear program with recourse whose structure permits relatively quick solution by Benders decomposition. The Benders subproblems use probabilistic production costing, which can be viewed as a stochastic greedy algorithm, to consider random outages and demands. These bounds are iteratively tightened by partitioning realizations of the random variables into subsets based on the status of larger generators and a cluster analysis of demands. Computational examples are described and application issues addressed.
Service and manufacturing firms often attempt to mitigate demand-supply mismatch risks by deploying flexible resources that can be adapted to serve multiple demand classes. It is critical to evaluate the trade-off bet...
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Service and manufacturing firms often attempt to mitigate demand-supply mismatch risks by deploying flexible resources that can be adapted to serve multiple demand classes. It is critical to evaluate the trade-off between the cost of investing in such resources and the resulting benefits. In this paper, we show that the heavily advocated "chaining" heuristic can sometimes perform unsatisfactorily when resources are not perfectly flexible. Alternatively, we propose an integer stochastic programming formulation as an attempt to optimize the flexibility structure. Although it is intractable to compute the optimal solution exactly, we propose a Lagrangian-relaxation heuristic that generates high-quality solutions efficiently. Using computational experiments, we identify conditions under which our approach can outperform the popular chaining solution.
Capacity planning is a challenging problem in semiconductor manufacturing industry due to high uncertainties both in market and manufacturing systems, short product life cycle, and expensive capital invest. To tackle ...
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Capacity planning is a challenging problem in semiconductor manufacturing industry due to high uncertainties both in market and manufacturing systems, short product life cycle, and expensive capital invest. To tackle this problem, this paper proposes a scenario-based stochastic programming model which considers demand and capacity uncertainties via scenarios, where the overall equipment efficiency is employed to describe the uncertain capacity for the first time. Based on the decentralized structure of tool procurement, production, stockout, and inventory decision-making processes, recourse approximation strategies are presented with varying degree of information share. The computational experiments show that the resulting tool set is robust enough to cope with the changes in capacity with the expected profits being maximized for different scenarios, and the scheme can generate pretty good solutions in reasonable computational time. (C) 2008 Elsevier B.V. All rights reserved.
Considering the minimisation of an estimated second degree polynomial response surface model as a problem of stochastic programming, this article establishes the equivalent deterministic programs applying the so calle...
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Considering the minimisation of an estimated second degree polynomial response surface model as a problem of stochastic programming, this article establishes the equivalent deterministic programs applying the so called E-model, V-model, P-model and minimax methods. Similarly, after observing that some of the solutions by the techniques of stochastic programming coincide with the solution of a multiobjective optimisation problem, this paper proposes two alternative methods for the solution of the stochastic optimisation of a second degree polynomial response surface model: (i) A lexicographic method, and (ii) A method based on distances. An example is solved by means of the described techniques. (c) 2004 Elsevier B.V. All rights reserved.
A more realistic management of electric vehicle (EV) charging points requires to cope with stochastic behavior on vehicle staying patterns. This paper presents a stochastic programming model to achieve optimal managem...
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A more realistic management of electric vehicle (EV) charging points requires to cope with stochastic behavior on vehicle staying patterns. This paper presents a stochastic programming model to achieve optimal management taking into account price variation in day-ahead and intraday electricity markets, together with regulating reserve margins. In this model, first-stage decisions determine day-ahead energy purchases and sales and the upward and downward reserve margins committed. Second-stage decisions correspond to intraday markets and deal with reserve requirements and several possible scenarios for vehicle staying pattern. The design of the objective function prioritizes supplying energy to EV batteries while minimizing the net expected energy cost at the EV charging point. A case study describing a parking for 50 EVs is analyzed. The case includes household, commercial and mixed EV staying patterns with several intraday arrival and departure scenarios. Pure and hybrid EVs are included, taking into account their respective energy characteristics. Sensitivity analysis is used to show the potential energy cost savings and the impact of different non-supply penalizations. The case study considers several vehicle staying patterns, energy price profiles and discharge allowances. The model achieves energy cost reductions between 1% and 15% depending on the specific case. A model validation by simulation has been done.
This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the here and now variables which represent the capacity of the...
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This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the here and now variables which represent the capacity of the network. The main contribution is a heuristic approach which involves the formulation of the problem as a mean-field game. Every agent in the mean-field game has control over its own primal-dual dynamics and seeks consensus with neighboring agents according to a communication topology. We obtain theoretical results concerning the existence of a mean-field equilibrium. Moreover, we prove that the consensus dynamics converge such that the agents agree on the capacity of the network. Lastly, we emphasize the ways in which penalties on control and state influence the dynamics of agents in the mean-field game.
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