The capacitated arc-routing problem with stochastic demands (CARPSD) is an extension of the well-known capacitated arc-routing problem (CARP) in which demands are stochastic. This leads to the possibility of route fai...
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The capacitated arc-routing problem with stochastic demands (CARPSD) is an extension of the well-known capacitated arc-routing problem (CARP) in which demands are stochastic. This leads to the possibility of route failures whenever the realized demand exceeds the vehicle capacity. This paper presents the CARPSD in the context of garbage collection. It describes an adaptive large-scale neighbourhood search heuristic for the problem. Computational results show the superiority of this algorithm over an alternative solution approach.
We consider a class of stochasticprogramming with binary recourse variables in which a fixed cost is imposed if the value of the continuous recourse variable is strictly positive. The algorithm of a branch-and-cut me...
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We consider a class of stochasticprogramming with binary recourse variables in which a fixed cost is imposed if the value of the continuous recourse variable is strictly positive. The algorithm of a branch-and-cut method to solve the problem is developed by using the property of the expected recourse function. The problem is applied to a power generating system. The numerical experiments show that the proposed algorithm is quite efficient. The mathematical programming model defined in this paper is quite useful for a variety of design and operational problems. (C) 2010 Published by Elsevier Ltd.
We consider a class of stochasticprogramming with binary recourse variables in which a fixed cost is imposed if the value of the continuous recourse variable is strictly positive. The algorithm of a branch-and-cut me...
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We consider a class of stochasticprogramming with binary recourse variables in which a fixed cost is imposed if the value of the continuous recourse variable is strictly positive. The algorithm of a branch-and-cut method to solve the problem is developed by using the property of the expected recourse function. The problem is applied to a power generating system. The numerical experiments show that the proposed algorithm is quite efficient. The mathematical programming model defined in this paper is quite useful for a variety of design and operational problems.
This paper proposes a methodology for deploying permanent Dynamic Message Signs (DMS) in a vehicular traffic network. Of particular interest is the planning problem to optimize the number of DMS to deploy in conjuncti...
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This paper proposes a methodology for deploying permanent Dynamic Message Signs (DMS) in a vehicular traffic network. Of particular interest is the planning problem to optimize the number of DMS to deploy in conjunction with Advanced Traveler Information Systems (ATIS), operating and maintenance cost of DMS, and incident-related user cost under random traffic incident situations. The optimal DMS location design problem discussed herein is formulated as a two-stage stochastic program with recourse (SPR). A Tabu search algorithm combined with dynamic traffic simulation and assignment approaches are employed to solve this problem. A case study performed on the Fort-Worth, Texas network highlights the effectiveness of the proposed framework and illustrates the affect factors such as demand, network structure, DMS response rate, and incident characteristics have on the solution. The numerical results suggest that designing and deploying DMS and ATIS jointly is more cost-effective and efficient than the sequential build-out of the two from the system management perspective. (C) 2007 Elsevier Ltd. All rights reserved.
This study presents an approach for considering a vehicle routing problem where customers' pickup demands are uncertain and require serving within some settled time windows. Customers' demands are assumed to f...
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This study presents an approach for considering a vehicle routing problem where customers' pickup demands are uncertain and require serving within some settled time windows. Customers' demands are assumed to follow given discrete probability distributions. This study proposes a nonlinear stochastic integer program with recourse to formulate the vehicle routing problem with stochastic demands and time windows (VRPTW-SD, for short). The objective of the VRPTW-SD is to minimize the total cost of the first-stage solution and expected recourse cost of the second-stage solution. The total cost of the first-stage problem includes the total travel cost for all links and the total waiting cost at all nodes. When a vehicle capacity is attained or exceeded, recourse actions are needed and recourse costs incurred in order to finish the planned route schedules. Two categories of schedule failure are introduced in this work;the recourse costs derive from the variations in travel time travel time, waiting time, and penalties of late arrival for time windows. In addition, an optimization algorithm is developed for solving the VRPTW-SD, according to the framework of the L-shaped method. Numerical results are given to demonstrate its validity.
Most of the applied models written with an algebraic modeling language involve simultaneously several dimensions such as materials, location, time or uncertainty. The information about dimensions available in the alge...
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Most of the applied models written with an algebraic modeling language involve simultaneously several dimensions such as materials, location, time or uncertainty. The information about dimensions available in the algebraic formulation is usually sufficient to retrieve different block structures from mathematical programs. These structured problems can then be solved by adequate solution techniques. To illustrate this idea we focus on stochasticprogramming problems with recourse. Taking into account both time and uncertainty dimensions of these problems, we are able to retrieve different customized structures in their constraint matrices. We applied the Structure Exploiting Tool to retrieve the structure from models built with the GAMS modeling language. The underlying mathematical programs are solved with the decomposition algorithm that applies interior point methods. The optimization algorithm is run in a sequential and in a parallel computing environment.
Passage of the 1996 Farm Bill marked a dramatic departure in federal farm policy as the longstanding deficiency payment program was replaced with non-risk responsive transition payments. In light of the departure, sub...
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In this paper we study stability of optimal solutions of stochasticprogramming problems with fixed recourse. An upper bound for the rate of convergence is given in terms of the objective functions of the associated d...
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In this paper we study stability of optimal solutions of stochasticprogramming problems with fixed recourse. An upper bound for the rate of convergence is given in terms of the objective functions of the associated deterministic problems. As an example it is shown how it can be applied to derivation of the Law of Iterated Logarithm for the optimal solutions. It is also shown that in the case of simple recourse this upper bound implies upper Lipschitz continuity of the optimal solutions with respect to the Kolmogorov-Smirnov distance between the corresponding cumulative probability distribution functions.
We introduce an upper bound on the expectation of a special class of sublinear functions of multivariate random variables defined over the entire Euclidean space without an independence assumption. The bound can be ev...
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We introduce an upper bound on the expectation of a special class of sublinear functions of multivariate random variables defined over the entire Euclidean space without an independence assumption. The bound can be evaluated easily requiring only the solution of systems of linear equations thus permitting implementations in high-dimensional space. Only knowledge on the underlying distribution means and second moments is necessary. We discuss pertinent techniques on dominating general sublinear function, by using simpler sublinear and polyhedral functions and second order quadratic functions.
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