Lagrangean decomposition: A model yielding stronger lagrangean bounds

Guignard, Monique; Kim, Siwhan

doi:10.1007/bf02592954

“…see the work by Pinto & Grossmann 23 ) or large-scale stochastic programming problems in supply chain operations under uncertainty. 24 Lagrangean decomposition [19][20] can effectively solve large-scale supply chain planning problems with "decomposable" structures. [25][26][27][28][29] If the supply chain planning problem includes both strategic and operational decisions, bilevel decomposition 21 can be implemented to iteratively solve an upper level aggregated model and a lower level detailed model.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal Distribution-Inventory Planning of Industrial Gases. II. MINLP Models and Algorithms for Stochastic Cases

You

¹

,

Pinto²,

Grossmann

³

et al. 2011

Ind. Eng. Chem. Res.

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In this paper, we address the optimization of industrial gas distribution systems, which consist of plants and customers, as well as storage tanks, trucks and trailers. A mixedinteger linear programming (MILP) model is presented to minimize the total capital and operating cost, and to integrate short-term distribution planning decisions for the vehicle routing with long-term inventory decisions for sizing storage tanks at customer locations. In order to optimize asset allocation in the industrial gas distribution network by incorporating operating decisions, the model also takes into account the synergies among delivery schedule, tank sizes, customer locations and inventory profiles. To effectively solve large scale instances, we propose two fast computational strategies. The first approach is a two-level solution strategy based on the decomposition of the full scale MILP model into an upper level route selectiontank sizing model and a lower level reduced routing model. The second approach is based on a continuous approximation method, which estimates the operational cost at the strategic level and determines the tradeoff with the capital cost from tank sizing.Three cases studies including instances with up to 200 customers are presented to illustrate the applications of the models and the performance of the proposed solution methods.

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“…To address the computational challenge, various decomposition methods, such as Benders decomposition, 18 Lagrangean decomposition, [19][20] bilevel decomposition 21 and hierarchical decomposition 22 are proposed. Benders decomposition 18 is usually used to solve complex mixed-integer programming models arising from process planning and scheduling (e.g.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal Distribution-Inventory Planning of Industrial Gases. I. Fast Computational Strategies for Large-Scale Problems

You

¹

,

Pinto²,

Capón

³

et al. 2011

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

In this paper, we address the optimization of industrial gas distribution systems, which consist of plants and customers, as well as storage tanks, trucks and trailers. A mixedinteger linear programming (MILP) model is presented to minimize the total capital and operating cost, and to integrate short-term distribution planning decisions for the vehicle routing with long-term inventory decisions for sizing storage tanks at customer locations. In order to optimize asset allocation in the industrial gas distribution network by incorporating operating decisions, the model also takes into account the synergies among delivery schedule, tank sizes, customer locations and inventory profiles. To effectively solve large scale instances, we propose two fast computational strategies. The first approach is a two-level solution strategy based on the decomposition of the full scale MILP model into an upper level route selectiontank sizing model and a lower level reduced routing model. The second approach is based on a continuous approximation method, which estimates the operational cost at the strategic level and determines the tradeoff with the capital cost from tank sizing.Three cases studies including instances with up to 200 customers are presented to illustrate the applications of the models and the performance of the proposed solution methods.

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“…The examples were selected to feature different degrees of steady-state and dynamic nonlinear behavior, such that the complexity of solving scheduling and control problems is highlighted. We also did so hoping to justify the use of advanced decomposition optimization techniques such as Lagrangian decomposition [8] to address the scheduling and control of more complex reaction system such as polymerization reaction systems. We stress that for all the case studies all the parallel lines are equipped with identical PFRs.…”

Section: Case Studiesmentioning

confidence: 99%

Simultaneous Cyclic Scheduling and Control of Tubular Reactors: Parallel Production Lines

Flores‐Tlacuahuac

¹

,

Grossmann

²

2011

Ind. Eng. Chem. Res.

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In this work we propose a simultaneous scheduling and control optimization formulation to address both optimal steady-state production and dynamic product transitions in multiproduct tubular reactors working in several parallel production lines. Because the problem involves integer and continuous variables and the dynamic behavior of the underlying system the resulting optimization problem is cast as a Mixed-Integer Dynamic Optimization (MIDO) problem. Moreover, because spatial and temporal variations are considered when modeling the addressed systems, the dynamic systems give rise to a system of one-dimensional partial differential equations. For solving the MIDO problems we transform them into a mixed-integer nonlinear programs (MINLP). We use the method of lines for spatial discretization, whereas orthogonal collocation on finite elements was used for temporal discretization. The proposed simultaneous scheduling and control formulation is tested using three multiproduct continuous tubular reactors featuring complex nonlinear behavior.2

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Lagrangean decomposition: A model yielding stronger lagrangean bounds

Cited by 367 publications

References 14 publications

Optimal Distribution-Inventory Planning of Industrial Gases. II. MINLP Models and Algorithms for Stochastic Cases

Optimal Distribution-Inventory Planning of Industrial Gases. II. MINLP Models and Algorithms for Stochastic Cases

Optimal Distribution-Inventory Planning of Industrial Gases. I. Fast Computational Strategies for Large-Scale Problems

Simultaneous Cyclic Scheduling and Control of Tubular Reactors: Parallel Production Lines

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