Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Instead of modeling the crew scheduling problem as dete...
详细信息
Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Instead of modeling the crew scheduling problem as deterministic, we consider a stochastic crew scheduling model and devise a solution methodology for integrating disruptions in the evaluation of crew schedules. The goal is to use that information to find robust solutions that better withstand disruptions. Such an approach is important because we can proactively consider the effects of certain scheduling decisions. By identifying more robust schedules, cascading delay effects are minimized. In this paper we describe our stochastic integer programming model for the airline crew scheduling problem and develop a branching algorithm to identify expensive flight connections and find alternative solutions. The branching algorithm uses the structure of the problem to branch simultaneously on multiple variables without invalidating the optimality of the algorithm. We present computational results demonstrating the effectiveness of our branching algorithm.
Due to the interaction between the planning and operation of micro energy network, considering the operation optimization can better play the role of micro energy network. But due to the influence of various uncertain...
详细信息
Due to the interaction between the planning and operation of micro energy network, considering the operation optimization can better play the role of micro energy network. But due to the influence of various uncertainties, the deterministic programming solution may be sub-optimal. In this context, the two-stage stochastic programming of micro energy network is of great significance. In this paper, from the perspective of electric energy, the closely related P2G, storage system and fuel cell are modeled as a whole, so that the model is simplified to a certain extent. stochastic scenarios that considers multiple uncertain factors are constructed considering the correlation between electricity demand, wind speed and solar radiation intensity. And a two-stage stochastic programming model of micro energy network is established. Through the case study, the influence of P2GSS on micro energy network planning under uncertainty environment as well as the difference between stochastic programming and deterministic programming of micro energy network is analyzed. The simulation results show that P2GSS can reduce the economic cost and CO2 emission of micro energy network planning solution. Through the comparison of different planning schemes, it can provides a reference for the planning and construction of the micro-energy network.
A probabilistic constrained stochastic linear programming problem is considered, where the rows of the random technology matrix are independent and normally distributed. The quasi-concavity of the constraining functio...
详细信息
A probabilistic constrained stochastic linear programming problem is considered, where the rows of the random technology matrix are independent and normally distributed. The quasi-concavity of the constraining function needed for the convexity of the problem is ensured if the factors of the function are uniformly quasi-concave. A necessary and sufficient condition is given for that property to hold. It is also shown, through numerical examples, that such a special problem still has practical application in optimal portfolio construction. (C) 2011 Published by Elsevier B.V.
This paper addresses dynamic cell formation problem (DCFP) which has been explored vastly for several years. Although a considerable body of literature in this filed, two remarkable aspects have been significantly ign...
详细信息
This paper addresses dynamic cell formation problem (DCFP) which has been explored vastly for several years. Although a considerable body of literature in this filed, two remarkable aspects have been significantly ignored so far, as uncertainty and human-related issues. In order to compensate such a shortage, this paper develops a bi-objective stochastic model. The first objective function of the developed model seeks to minimize total cost of machine procurement, machine relocation, inter-cell moves, overtime utilization, worker hiring/laying-off, and worker moves between cells;while the second objective function maximizes labor utilization of the cellular manufacturing system. In the developed model, labor utilization, worker overtime cost, worker hiring/laying off, and worker cell assignment are considered to tackle some of the most notable human-related issues in DCFP. Considering the complexity of the proposed model, a hybrid Tabu Search-Genetic Algorithm (TS-GA) is proposed whose strength is validated to obtain optimal and near optimal solutions through conducted experimental results. (C) 2016 Elsevier Ltd. All rights reserved.
The stochastic linear programming problem with recourse has a dual block-angular structure. II can thus be handled by Benders' decomposition or by Kelley's method of cutting planes;equivalently the dual proble...
详细信息
The stochastic linear programming problem with recourse has a dual block-angular structure. II can thus be handled by Benders' decomposition or by Kelley's method of cutting planes;equivalently the dual problem has a primal block-angular structure and can be handled by Dantzig-Wolfe decomposition-the two approaches are in fact identical by duality. Here we shall investigate the use of the method of cutting planes from analytic centers applied to similar formulations. The only significant difference form the aforementioned methods is that new cutting planes (or columns, by duality) will be generated not from the optimum of the linear programming relaxation, but from the analytic center of the set of localization.
Most models for chemical production planning are based on deterministic programming approaches without considering uncertainty. This paper presents a two-stage stochastic programming model for chemical production plan...
详细信息
Most models for chemical production planning are based on deterministic programming approaches without considering uncertainty. This paper presents a two-stage stochastic programming model for chemical production planning optimization with management of purchase and inventory under economic uncertainties including prices of raw materials, product prices and demands, and uses the Monte Carlo sampling method to solve it. The expected profit is maximized taking into account raw materials costs, inventory costs, operating costs and costs of lost demand under economic uncertainties, while the production planning and purchase scheme are optimized simultaneously. The proposed model is validated by a real chemical enterprise based on GIOCIMS (Graphical I/O Chemical Industry Modeling System). The results indicate that the two-stage stochastic programming model can suggest a solution with higher expected profit and lower risk than the one suggested by deterministic programming model.
A stochastic programming formulation is developed for determining the optimal placement of gas detectors in petrochemical facilities. FLACS, a rigorous gas dispersion package, is used to generate hundreds of scenarios...
详细信息
A stochastic programming formulation is developed for determining the optimal placement of gas detectors in petrochemical facilities. FLACS, a rigorous gas dispersion package, is used to generate hundreds of scenarios with different leak locations and weather conditions. Three problem formulations are investigated: minimization of expected detection time, minimization of expected detection time including a coverage constraint, and a placement based on coverage alone. The extensive forms of these optimization problems are written in Pyomo and solved using CPLEX. A sampling procedure is used to find confidence intervals on the optimality gap and quantify the effectiveness of detector placements on alternate subsamples of scenarios. Results show that the additional coverage constraint significantly improves performance on alternate subsamples. Furthermore, both optimization-based approaches dramatically outperform the coverage-only approach, making a strong case for the use of rigorous dispersion simulation coupled with stochastic programming to improve the effectiveness of these safety systems. (C) 2012 Published by Elsevier Ltd.
Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and...
详细信息
Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics. Efficient algorithms are developed that determine optimal reduced measures approximately. Numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty. For instance, it turns out that after 50% reduction of the scenario tree the optimal reduced tree still has about 90% relative accuracy.
In this study, a risk-based interactive multi-stage stochastic programming (RIMSP) approach is proposed through incorporating the fractile criterion method and chance-constrained programming within a multistage decisi...
详细信息
In this study, a risk-based interactive multi-stage stochastic programming (RIMSP) approach is proposed through incorporating the fractile criterion method and chance-constrained programming within a multistage decision-making framework. RIMSP is able to deal with dual uncertainties expressed as random boundary intervals that exist in the objective function and constraints. Moreover, RIMSP is capable of reflecting dynamics of uncertainties, as well as the trade-off between the total net benefit and the associated risk. A water allocation problem is used to illustrate applicability of the proposed methodology. A set of decision alternatives with different combinations of risk levels applied to the objective function and constraints can be generated for planning the water resources allocation system. The results can help decision makers examine potential interactions between risks related to the stochastic objective function and constraints. Furthermore, a number of solutions can be obtained under different water policy scenarios, which are useful for decision makers to formulate an appropriate policy under uncertainty. The performance of RIMSP is analyzed and compared with an inexact multi-stage stochastic programming (IMSP) method. Results of comparison experiment indicate that RIMSP is able to provide more robust water management alternatives with less system risks in comparison with IMSP. (C) 2016 Elsevier Ltd. All rights reserved.
We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program w...
详细信息
We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the probability of future capacity requirements to be violated are simultaneously minimized. Assuming the existence of a finite number of possible future states of the world, an algorithm for the problem is elaborated. The algorithm determines all non-dominated solutions to the problem by a reduced feasible region method, solving a sequence of restricted subproblems by a cutting plane procedure. Computational results are reported for three different problem instances, one of which is a real-life problem faced by SONOFON, a Danish communications network operator.
暂无评论