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We present a method to solve two-stage stochastic linear programming problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a discrete problem with one scenario for each element of the partition (subregions of the uncertainty space). Fixing first-stage variables, we formulate a second-stage subproblem for each element, and exploiting information from the dual of these problems, we provide conditions that the partition must satisfy to obtain an optimal solution. These conditions provide guidance on how to refine the partition, iteratively approaching an optimal solution. The results from computational experiments show how the method automatically refines the partition of the uncertainty space in the regions of interest for the problem. Our algorithm is a generalization of the adaptive partition-based method presented by Song and Luedtke for discrete distributions, extending its applicability to more general cases. [ABSTRACT FROM AUTHOR]

In this research, we apply a scenario aggregation approach to solving the supply chain contract model formulated by two-stage stochastic programming problem. The supply chain contract can achieve the coordination between the buyer and the supplier. We formulate the stochastic programming model for a quantity-flexibility contract. The scenario aggregation method called the progressive hedging method is used to solve this problem. Experimental results show the convergence behaviour of the algorithm and the sensitivity of parameters. [ABSTRACT FROM AUTHOR]

This paper presents a stochastic model for the long- term solution of security-constrained unit commitment (SCUC). The proposed approach could be used by vertically integrated utilities as well as the ISOs in electricity markets. In this model, random disturbances, such as outages of generation units and transmission lines as well as load forecasting inaccuracies, are modeled as scenario trees using the Monte Carlo simulation method. For dual optimization, coupling constraints among scenarios are relaxed and the optimization problem is decomposed into deterministic long-term SCUC subproblems. For each deterministic long-term SCUC, resource constraints represent fuel and emission constraints (in the case of vertically integrated utilities) and energy constraints (in the case of electricity markets). Lagrangian relaxation is used to decompose subproblems with long-term SCUC into tractable short-term MIP-based SCUC subproblems without resource constraints. Accordingly, penalty prices (Lagrangian multipliers) are signals to coordinate the master problem and small-scale subproblems. Computational requirements for solving scenario-based optimization models depend on the number of scenarios in which the objective is to minimize the weighted-average generation cost over the entire scenario tree. In large scale applications, the scenario reduction method is introduced for enhancing a tradeoff between calculation speed and accuracy of long-term SCUC solution. Numerical simulations indicate the effectiveness of the proposed approach for solving the stochastic security-constrained unit commitment. [ABSTRACT FROM AUTHOR]

Recently, airlines and aircraft manufacturers have realized the benefits of the emerging concept of dynamic capacity allocation, and have initiated advanced decision support systems to assist them in this respect. Strategic airline fleet planning is one of the major issues addressed through such systems. We present background research connected with the dynamic allocation concept, which accounts explicitly for the stochastic nature of passenger demand in the fleet composition problem. We address this problem through a scenario aggregation-based approach and present results on representative case studies based on realistic data. Our investigations establish clear benefits of a stochastic approach as compared with deterministic formulations, as well as its implementation feasibility using state-of-the-art optimization software. [ABSTRACT FROM AUTHOR]

The development of fast, robust and reliable computational tools capable of addressing process management under uncertain conditions is an active topic in the current literature, and more precisely for the process systems engineering one. Particularly, scenario reduction strategies have emerged as an alternative to overcome the traditional issues associated with large-scale scenario-based problems. This work proposes a novel and flexible scenario-reduction alternative that integrates data mining, graph theory and community detection concepts to represent the uncertain information as a network and identify the most efficient communities/clusters. The capabilities of the proposed approach were tested by solving a set of two-stage mixed-integer linear programming problems under uncertainty. For comparison and validation purposes, these problems were also solved using two available methods (SCENRED and OSCAR). This comparison demonstrates that the results obtained by using the proposed approach are at least as good or better, in terms of quality and accuracy, than the results obtained bu using SCENRED and OSCAR. Additionally, the practical advantage of the proposed parameter definition rule is demonstrated as a way to overcome the limitations of the current alternatives (i.e. arbitrary user-defined parameters). [ABSTRACT FROM AUTHOR]