Mathematical programming formulations for approximate simulation of multistage production systems

Alfieri, Arianna; Matta, Andrea

doi:10.1016/j.ejor.2011.12.044

Cited by 36 publications

(19 citation statements)

References 18 publications

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“…The approach is based on a simple idea: decomposing the complete model in many simpler submodels that can be solved in a shorter time. As explained before, the proposed approach can be applied to mathematical programming models for simulation for a specific class of DESs, the main characteristic of which is the use of static rules for dispatching entities and the fixed, and known in advance, sequence of entities moving through the system (Alfieri and Matta 2012a). This class of DESs is large and contains several systems that are relevant in practice such as production lines, supply chains, assembly systems, etc.…”

Section: Approachmentioning

confidence: 99%

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A time-based decomposition algorithm for fast simulation with mathematical programming models

Alfieri

Matta

2012

Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC)

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Mathematical programming has been proposed in the literature as an alternative technique to simulate a special class of Discrete Event Systems. Several are the benefits of using a mathematical programming model for simulating but the non-linear computational time (in the number of simulated entities) needed for the solution of the models can be a huge barrier to its use in long simulations. This paper proposes a time-based decomposition algorithm that splits the mathematical programming model into a number of submodels to be solved sequentially so as to exploit the super-additivity of many non-linear functions and make the mathematical programming approach viable also for long run simulations. The number of needed submodels is the solution of an optimization problem that minimizes the expected time to solve all the submodels. The main result is that in this way the solution time becomes a linear function of the number of simulated entities.

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Section: Approachmentioning

confidence: 99%

“…Among such benefits, the possibility of easily applying sensitivity analysis and the fast convergence to a near optimal solution, when the objective function is changed to optimize some system parameters, are the most relevant ones. This last issue has been recently investigated by Alfieri and Matta (2012a).…”

Section: Introductionmentioning

confidence: 97%

A time-based decomposition algorithm for fast simulation with mathematical programming models

Alfieri

Matta

2012

Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC)

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“…The MP model may have integer variables which highly increase the computational burden. To overcome this difficulty, Alfieri and Matta [57] propose approximate representations for simulation, based on time buffers. In [58], the authors apply a time-based decomposition algorithm to further reduce the computational effort.…”

Section: Methods Related To S-omentioning

confidence: 99%

Hybrid simulation–optimization methods: A taxonomy and discussion

Figueira¹,

Almada-Lobo²

2014

Simulation Modelling Practice and Theory

217

104

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The possibilities of combining simulation and optimization are vast and the appropriate design highly depends on the problem characteristics. Therefore, it is very important to have a good overview of the different approaches. The taxonomies and classifications proposed in the literature do not cover the complete range of methods and overlook some important criteria. We provide a taxonomy that aims at giving an overview of the full spectrum of current simulation-optimization approaches. Our study may guide researchers who want to use one of the existing methods, give insights into the cross-fertilization of the ideas applied in those methods and create a standard for a better communication in the scientific community. Future reviews can use the taxonomy here described to classify both general approaches and methods for specific application fields.

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“…For example, Helber et al (2011) discuss how linear programming can be used to analyze and optimize stochastic flow lines. Alfieri and Matta (2012a) give mathematical programming formulations for simulation of multi-stage production systems. Alfieri and Matta (2012b) analyze pull-controlled single-product serial production systems with the same approach.…”

Section: Introductionmentioning

confidence: 99%

Mathematical programming representations of the dynamics of continuous-flow production systems

Tan¹

2014

IIE Transactions

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This study presents a mathematical programming representation of discrete-event systems with a continuous time and mixed continuous-discrete state space. In particular, continuous material flow production systems are considered. A mathematical programming representation is used to generate simulated sample realizations of the system and also to optimize control parameters. The mathematical programming approach has been used in the literature for performance evaluation and optimization of discrete material flow production systems. In order to show the applicability of the same approach to continuous material flow systems, this article focuses on optimal production flow rate control problems for a continuous material flow system with an unreliable station and deterministic demand. These problems exhibit most of the dynamics observed in various continuous flow productions systems: flow dynamics, machine failures and repairs, changing flow rates due to system status, and control. Moreover, these problems include decision variables related to the control policies and different objective functions. By analyzing the backlog, lost sales, and production and subcontracting rate control problems, it is shown that a mixed-integer linear programming formulation with a linear objective function and linear constraints can be developed to determine the simulated performance of the system. The optimal value of the control policy that optimizes an objective function that includes the estimated expected inventory carrying and backlog cost and also the revenue through sales can also be determined by solving a quadratic integer program with a quadratic objective function and linear constraints. As a result, it is shown that the mathematical programming representation is also a viable method for performance evaluation and optimization of continuous material production systems.

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Mathematical programming formulations for approximate simulation of multistage production systems

Cited by 36 publications

References 18 publications

A time-based decomposition algorithm for fast simulation with mathematical programming models

A time-based decomposition algorithm for fast simulation with mathematical programming models

Hybrid simulation–optimization methods: A taxonomy and discussion

Mathematical programming representations of the dynamics of continuous-flow production systems

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