Monte Carlo (importance) sampling within a benders decomposition algorithm for stochastic linear programs

Infanger, Gerd

doi:10.1007/bf02060936

Cited by 179 publications

(120 citation statements)

References 20 publications

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“…Objective function values are computed for the candidate solutions using the own samples of each algorithm and compared to the optimal objective function value that is computed for the exact optimal solution based on a large sample of 150,000 realizations. As we can see from Figure 7, the standard deviations of the objective functions are smaller for APS samples, which is in line with the importance sampling results of Parpas et al (2013) andInfanger (1993). Furthermore, based on the MAPE, the optimality gap for APS approach is also consistently found to be smaller compared with the SAA approach.…”

Section: Performance Resultssupporting

confidence: 79%

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Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

2014

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I n this paper, we develop a simulation-based approach for two-stage stochastic programs with recourse.We construct an augmented probability model with stochastic shocks and decision variables. Simulating from the augmented probability model solves for the expected recourse function and the optimal first-stage decision. Markov chain Monte Carlo methods, together with ergodic averaging, provide a framework to compute the optimal solution. We illustrate our methodology via the two-stage newsvendor problem with unimodal and bimodal continuous uncertainty. Finally, we present performance comparisons of our algorithm and the sample average approximation method.

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Section: Performance Resultssupporting

confidence: 79%

“…The proposal distribution is designed to place more weight in the region of high Q x values, thus providing a more efficient estimate of E Q x . Proposals for g are described as additive (Infanger 1993) or multiplicative (Dantzig and Thapa 1997) functions.…”

Section: Simulation-based Stochastic Programmingmentioning

confidence: 99%

Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

2014

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“…For illustration purposes we describe in detail the results of applying the methodology to the test problem APLlP, which is a small electric power expansion planning problem with uncertainty in three demands and in the availability of two generators; see hfanger (1992) [31]. The master problem has 3 rows and 3 columns and each second-stage scenario has 6 rows and 9 columns.…”

Section: Testmentioning

confidence: 99%

“…The approach by Dantzig and Glynn (1990) [lo] and Infanger (1992) [31] combines Benders decomposition and Monte Carlo importance sampling for solving stochastic linear programs. Importance sampling serves as a variance-reduction technique and in practice often results in accurate estimates being obtained' with only small sample sizes.…”

Section: Introductionmentioning

confidence: 99%

A Probabilistic Lower Bound for Two-Stage Stochastic Programs

Dantzig

Infanger

2010

International Series in Operations Research &Amp; Management Science

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“…For stochastic linear programs, i.e. when the secondstage problem is linear, the convexity of the second-stage value function along with this decomposability property has been exploited to develop a number of decomposition-based algorithms [4,11,13,19,25] as well as gradient-based algorithms [8,23].…”

Section: Computational Challengesmentioning

confidence: 99%

Dynamic Capacity Acquisition and Assignment under Uncertainty

Ahmed

Garcia

2003

Annals of Operations Research

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Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-andbound strategy for the problem. Encouraging preliminary computational results are provided.

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Monte Carlo (importance) sampling within a benders decomposition algorithm for stochastic linear programs

Cited by 179 publications

References 20 publications

Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

A Probabilistic Lower Bound for Two-Stage Stochastic Programs

Dynamic Capacity Acquisition and Assignment under Uncertainty

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