Progressive hedging as a meta-heuristic applied to stochastic lot-sizing

Haugen, Kjetil K.; Løkketangen, Arne; Woodruff, David L.

doi:10.1016/s0377-2217(00)00116-8

Cited by 60 publications

(32 citation statements)

References 8 publications

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“…The samples, in which the maximum distances are increased to 600 of their minimum levels, (350 ), lead to less expected total cost in all cases and less opened facilities in some cases. For instance, in low impact events (0.05) six facilities (4,6,7,8,9, and 10) are opened when maximum distance is restricted to 350 . However, the number of opened facilities is reduced to five (3,6,7,9, and 10) when maximum distance is increased to 400 .…”

Section: Resultsmentioning

confidence: 99%

“…The proposed mathematical formulation is a two-stage stochastic mixed integer programming (SMIP) model, which is addressed as NP hard problems [6]. In many situations, parameters of the optimization problems cannot be known with certainty [5,7,8,9,10], in such cases stochastic programming (SP) methodologies are one of the strategies to apply. In two-stage stochastic programming, first-stage decisions are made in the existence of uncertainty for future scenarios.…”

Section: Introductionmentioning

confidence: 99%

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A stochastic location and allocation model for critical items to response large-scale emergencies: A case of Turkey

Çelik

Aydın

Gümüş

2016

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This paper aims to decide on the number of facilities and their locations, procurement for pre and post-disaster, and allocation to mitigate the effects of large-scale emergencies. A two-stage stochastic mixed integer programming model is proposed that combines facility location-prepositioning, decisions on pre-stocking levels for emergency supplies, and allocation of located distribution centers (DCs) to affected locations and distribution of those supplies to several demand locations after large-scale emergencies with uncertainty in demand. Also, the use of the model is demonstrated through a case study for prepositioning of supplies in probable large-scale emergencies in the eastern and southeastern Anatolian sides of Turkey. The results provide a framework for relief organizations to determine the location and number of DCs in different settings, by using the proposed model considering the main parameters, as; capacity of facilities, probability of being affected for each demand points, severity of events, maximum distance between a demand point and distribution center. Keywords:Emergency response facility location large scale emergencies two stage stochastic programming AMS Classification 2010:91B70, 90B06

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A stochastic location and allocation model for critical items to response large-scale emergencies: A case of Turkey

Çelik

Aydın

Gümüş

2016

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…One example is progressive hedging, also known as scenario aggregation; see, e.g., (Birge, 1997;Kall and Wallace, 1994) for a tutorial treatment and (Haugen et al, 2001) for an application to lot-sizing with setup costs. Another manufacturing application of scenario aggregation is proposed in (Jönsson et al, 1993).…”

Section: Split Variable Model Formulationmentioning

confidence: 99%

Stochastic Programming Models for Manufacturing Applications

Alfieri

Brandimarte

2005

Design of Advanced Manufacturing Systems

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Stochastic programming models have been proposed for capacity planning problems in different environments, including energy, telecommunication networks, distribution networks, and manufacturing systems. In this chapter we give an introductory tutorial to stochastic linear programming models, with emphasis on modeling techniques, rather than specialized solution methods. We consider two-stage and multi-stage stochastic programming models with recourse for manufacturing related applications, such as production planning and capacity planning with uncertainty on demand. We stress the importance of proper model formulation from two points of view: the first one is building strong mixed-integer formulations; the second one is generating scenario trees in order to suitably represent uncertainty while keeping them to a manageable size. We also compare the stochastic programming approach to traditional dynamic programming and to robust optimization.

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“…Due to the model uncertainty, approximation methods are applied to reformulate the lot-sizing models for performing deterministic mixed integer programming (MIP) in the literature. Haugen et al [9] generated subproblems for each scenario solved heuristically to capture the nature of demand uncertainty and specify a reasonable number of representative scenarios. Brandimarte [10] modeled the demand uncertainty through generating scenario trees.…”

Section: Introductionmentioning

confidence: 99%

Fix‐and‐Optimize and Variable Neighborhood Search Approaches for Stochastic Multi‐Item Capacitated Lot‐Sizing Problems

Song

et al. 2017

Mathematical Problems in Engineering

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We discuss stochastic multi-item capacitated lot-sizing problems with and without setup carryovers (also known as link lot size), S-MICLSP and S-MICLSP-L. The two models are motivated from a real-world steel enterprise. To overcome the nonlinearity of the models, a piecewise linear approximation method is proposed. We develop a new fix-and-optimize (FO) approach to solve the approximated models. Compared with the existing FO approach(es), our FO is based on the concept of " -degreeconnection" for decomposing the problems. Furthermore, we also propose an integrative approach combining our FO and variable neighborhood search (FO-VNS), which can improve the solution quality of our FO approach by diversifying the search space. Numerical experiments are performed on the instances following the nature of realistic steel products. Our approximation method is shown to be efficient. The results also show that the proposed FO and FO-VNS approaches significantly outperform the recent FO approaches, and the FO-VNS approaches can be more outstanding on the solution quality with moderate computational effort.

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Progressive hedging as a meta-heuristic applied to stochastic lot-sizing

Cited by 60 publications

References 8 publications

A stochastic location and allocation model for critical items to response large-scale emergencies: A case of Turkey

A stochastic location and allocation model for critical items to response large-scale emergencies: A case of Turkey

Stochastic Programming Models for Manufacturing Applications

Fix‐and‐Optimize and Variable Neighborhood Search Approaches for Stochastic Multi‐Item Capacitated Lot‐Sizing Problems

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