This paper provides a stochastic programming approach to optimally reinforce and expand the transmission network so that the impact of deliberate attacks is mitigated. The network planner selects the new lines to be b...
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This paper provides a stochastic programming approach to optimally reinforce and expand the transmission network so that the impact of deliberate attacks is mitigated. The network planner selects the new lines to be built accounting for the vulnerability of the transmission network against a set of credible intentional outages. The vulnerability of the transmission network is measured in terms of the expected load shed. An instance of the previously reported terrorist threat problem is solved to generate the set of credible deliberate attacks. The proposed model is formulated as a mixed-integer linear program for which efficient solvers are available. Results from a case study based on the IEEE Two Area Reliability Test System are provided and analyzed.
We select a city that is one of the ten major coal bases in China and analyse the prospective development of the coal industry in this region. We introduce stochastic programming (SP) to the coal industry to manage un...
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We select a city that is one of the ten major coal bases in China and analyse the prospective development of the coal industry in this region. We introduce stochastic programming (SP) to the coal industry to manage uncertainties complicating the accurate prediction of the industry's development. First, we establish a coal industry system in the region and analyse this system. Second, we set up a System Dynamic-stochastic programming (SD-SP) model based on the coal industry in the region. Third, we set up the SD-SP model with sensitivity analysis to the coal industry. Finally, we complete the simulation by importing optimum parameters and contrasting the optimisation scheme with the current programming scheme.
This paper describes an employee scheduling system for retail outlets;it is a constraint-based system that exploits forecasts and stochastic techniques to generate schedules meeting the demand for sales personnel. Unc...
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This paper describes an employee scheduling system for retail outlets;it is a constraint-based system that exploits forecasts and stochastic techniques to generate schedules meeting the demand for sales personnel. Uncertain scenarios due to fluctuating demand are taken into account to develop a stochastic operational optimization of staffing levels. Mathematically, the problem is stated as a mixed-integer linear programming problem. Simulations with store data belonging to a major Swiss retailer show the effective performance of the proposed approach. The schedule quality is assessed through comparison with a deterministic scheduling package, which has been used at several outlets in Switzerland. (C) 2015 Elsevier Ltd. All rights reserved.
This paper presents two-stage bi-objective stochastic programming models for disaster relief operations. We consider a problem that occurs in the aftermath of a natural disaster: a transportation system for supplying ...
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This paper presents two-stage bi-objective stochastic programming models for disaster relief operations. We consider a problem that occurs in the aftermath of a natural disaster: a transportation system for supplying disaster victims with relief goods must be established. We propose bi-objective optimization models with a monetary objective and humanitarian objective. Uncertainty in the accessibility of the road network is modeled by a discrete set of scenarios. The key features of our model are the determination of locations for intermediate depots and acquisition of vehicles. Several model variants are considered. First, the operating budget can be fixed at the first stage for all possible scenarios or determined for each scenario at the second stage. Second, the assignment of vehicles to a depot can be either fixed or free. Third, we compare a heterogeneous vehicle fleet to a homogeneous fleet. We study the impact of the variants on the solutions. The set of Pareto-optimal solutions is computed by applying the adaptive Epsilon-constraint method. We solve the deterministic equivalents of the two-stage stochastic programs using the MIP-solver CPLEX.
Quantitative stability of optimal values and solution sets to stochastic programming problems is studied when the Underlying probability distribution varies in some metric space of probability measures. We give condit...
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Quantitative stability of optimal values and solution sets to stochastic programming problems is studied when the Underlying probability distribution varies in some metric space of probability measures. We give conditions that imply that a stochastic program behaves stable with respect to a minimal information (m.i.) probability metric that is naturally associated with the data of the program. Canonical metrics bounding the m.i. metric are derived for specific models, namely for linear two-stage, mixed-integer two-stage and chance-constrained models. The corresponding quantitative stability results as well as some consequences for asymptotic properties of empirical approximations extend earlier results in this direction. In particular, rates of convergence in probability are derived under metric entropy conditions. Finally, we study stability properties of stable investment portfolios having minimal risk with respect to the spectral measure and stability index of the underlying stable probability distribution.
Monte Carlo methods have extensively been used and studied in the area of stochastic programming. Their convergence properties typically consider global minimizers or first-order critical points of the sample average ...
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Monte Carlo methods have extensively been used and studied in the area of stochastic programming. Their convergence properties typically consider global minimizers or first-order critical points of the sample average approximation (SAA) problems and minimizers of the true problem, and show that the former converge to the latter for increasing sample size. However, the assumption of global minimization essentially restricts the scope of these results to convex problems. We review and extend these results in two directions: we allow for local SAA minimizers of possibly nonconvex problems and prove, under suitable conditions, almost sure convergence of local second-order solutions of the SAA problem to second-order critical points of the true problem. We also apply this new theory to the estimation of mixed logit models for discrete choice analysis. New useful convergence properties are derived in this context, both for the constrained and unconstrained cases, and associated estimates of the simulation bias and variance are proposed.
Emergency Mobility Facilities (EMFs) possess the capability to relocate dynamically, providing adequate responses to fluctuations in emergent demand patterns across temporal and spatial dimensions. This study proposes...
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Emergency Mobility Facilities (EMFs) possess the capability to relocate dynamically, providing adequate responses to fluctuations in emergent demand patterns across temporal and spatial dimensions. This study proposes a two-stage stochastic programming model that integrates the EMF allocation problem and the road network design problem for disaster preparedness. The model takes into account uncertainties arising from emergency demand and road network congestion levels under various sizes and timings of disaster occurrences. The first-stage decision involves determining the fleet size of EMFs and identifying which road links' travel time should be reduced. The second-stage decision pertains to the routing and schedule of each EMF for each disaster scenario. Due to considering various sources of uncertainty, the resulting model takes the form of a non-convex mixed-integer nonlinear program (MINLP). This poses computational challenges due to the inclusion of bilinear terms, implicit expressions, and the double-layered structure in the second-stage model, along with integer decision variables. A comprehensive set of techniques is applied to solve the model efficiently. This includes employing linearization techniques, converting the second-stage model into a single-level equivalent, transforming an integer variable into multiple binary variables, and utilizing other methods to equivalently reformulate the model into a mixed-integer linear programming problem (MILP). These transformations render the model amenable to solutions using the integer L-shaped method. A simplified example clarifies the solution procedures of the model and algorithm, establishing the theoretical foundation for their practical implementation. Subsequently, to empirically demonstrate the practicality of the proposed model and algorithm, a real-world case study is conducted, effectively validating their utility.
Most studies of process flexibility design have focused on homogeneous networks, whereas production systems in practice usually differ in many aspects, such as plant efficiency and product profitability. This research...
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Most studies of process flexibility design have focused on homogeneous networks, whereas production systems in practice usually differ in many aspects, such as plant efficiency and product profitability. This research investigates the impacts of two dimensions of production system heterogeneity, plant uniformity and product similarity, on process flexibility design in unbalanced networks, where the numbers of plants and products are not equal. We model the design of flexible process structures under uncertain market demand as a two-stage stochastic programming problem and solve it by applying Benders decomposition with a set of acceleration techniques. To overcome slow convergence of the exact algorithm, we also develop an efficient optimization-based heuristic capable of obtaining solutions with optimality gaps less than 6% on average for realistic-scale production systems (e.g., with five plants and 10 types of products). Numerical results using the proposed heuristic show that flexibility designs are influenced by both dimensions of system heterogeneity, though the desired level of flexibility is more sensitive to the effect of plant uniformity than that of product similarity.
In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programmi...
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In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method possesses a nearly optimal rate of convergence if the problem is convex. We discuss a variant of the algorithm which consists of applying a postoptimization phase to evaluate a short list of solutions generated by several independent runs of the RSG method, and we show that such modification allows us to improve significantly the large-deviation properties of the algorithm. These methods are then specialized for solving a class of simulation-based optimization problems in which only stochastic zeroth-order information is available.
The paper proposes a factorial multi-stage stochastic programming (FMSP) approach to support water resources management under uncertainty. This approach was developed based on the conventional inexact multi-stage stoc...
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The paper proposes a factorial multi-stage stochastic programming (FMSP) approach to support water resources management under uncertainty. This approach was developed based on the conventional inexact multi-stage stochastic programming method. Five alternative inexact multi-stage stochastic programming algorithms in addition to the conventional algorithm were introduced and bundled to offer multiple decision options that reflect decision makers' perspectives and the complexities in system uncertainties. More importantly, factorial analysis, a multivariate inference method, was introduced into the modeling framework to analyze the potential interrelationships among a variety of uncertain parameters and their impacts on system performance. The proposed approach was applied to a water resources management case. The desired water-allocation schemes were obtained to assist in maximizing the total net benefit of the system. Multiple uncertain parameters and their interactions were examined, and those that had significant influences on system performance were identified. For example, the medium flow in the third planning period was the system objective's most influential factor. Any variation of this factor would significantly influence the acquisition of the total net benefit in the community. The significant interactions were also identified, such as the interaction between the agricultural sector's penalty and the medium flow in the third planning period. Through the analysis of multi-parameter interactions, the interrelationships among the uncertain parameters could be further revealed. (C) 2012 Elsevier Ltd. All rights reserved.
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