Synergy of Lagrangian Relaxation and Constraint Programming for Manufacturing Scheduling

Buil, Roman; Luh, Peter B.; Xiong, Bo

doi:10.1109/wcica.2006.1714526

Cited by 2 publications

(8 citation statements)

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“…LR has been used by Luh and his research team in [1], [5]- [7] and in other publications to achieve good decomposition of scheduling problems relaxing one or more sets of constraints. The formulation presented in Section II can be decomposed into partwise subproblems by just relaxing the coupling machine capacity constraints.…”

Section: Lagrangian Relaxation (Lr) Methodsmentioning

confidence: 99%

“…As presented in [5] CP is used during the iterative LR method to find feasible solution using Time Windows (TWs) constructed around the unfeasible solutions. At the end of the iterations CP is also used but with different TW.…”

Section: Lr and Cp Methodsmentioning

confidence: 99%

“…Following the formulation presented in [1] and [5], the problem is to schedule N parts on H types of machines with time horizon K to minimize a weighted tardiness and earliness criterion [6]. …”

Section: Problem Formulationmentioning

confidence: 99%

“…The problem is to minimize (1) through selecting appropriate machine types and beginning times, subject to constraints (2)- (5). Note that parts availability, precedence constraints and processing time requirements relate to individual jobs, and the objective function is also jobwise additive.…”

Section: Problem Formulationmentioning

confidence: 99%

“…A method combining LR and CP was presented in [5], and its results are better than results of the LR method by itself. This method applies CP to find feasible solutions from the unfeasible ones, at some iterations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Improvement of Lagrangian Relaxation Convergence for Production Scheduling

Buil

Piera

Luh

2012

IEEE Trans. Automat. Sci. Eng.

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Abstract-It is widely accepted that new production scheduling tools are playing a key role in flexible manufacturing systems to improve their performance by avoiding idleness machines while minimizing set-up times penalties, reducing penalties for do not delivering orders on time, etc. Since manufacturing scheduling problems are NP-hard, there is a need of improving scheduling methodologies to get good solutions within low CPU time. Lagrangian Relaxation (LR) is known for handling large-scale separable problems, however, the convergence to the optimal solution can be slow. LR needs customized parametrization, depending on the scheduling problem, usually made by an expert user. It would be interesting the use of LR without being and expertise, i.e., without difficult parameters tuning. This paper presents innovative approaches on the LR method to be able to develop a tool capable of solve scheduling problems applying the LR method without requiring a deep expertise on it. First approach is the improvement of an already existing method which use Constraint Programming (CP) to obtain better primal cost convergence. Second approach is called Extended Subgradient Information (ESGI) and it speed up the dual cost convergence. Finally, a set of step size rules for the Subgradient (SG) method are compared to choose the most appropriate rule depending on the scheduling problem. Test results demonstrate that the application of CP and ESGI approaches, together with LR and the selected step size rule depending on the problem, generates better solutions than the LR method by itself.Note to Practitioners-Production scheduling tools are one of the keys in flexible mannfacturing systems to improve its performance. These tools are usually based on optimization methods, as could be the Lagrangian Relaxation. The problems of using optimization methods are the need of time to get the solution, and the need of a high-specialized user to tune them. Therefore, optimization methods must be improved to use less time to obtain solutions and to do not need high-specialized users. This paper was motivated by these needs: reducing the CPU time when scheduling operations in production planning to permit quick replies to real-time perturbations into production processes; and making easier the use of production scheduling tools. This paper suggests new approaches for the Lagrangian Relaxation (LR) method applying Constraint Logic Programming (CLP) and improving the multipliers calcula- tion (inside the Subgradient method) during the iterations to speed up the convergence of the LR method and make it easily tuned. Thus, the CPU time to find a solution is reduced and the results show that the use of the approaches reduces the needed knowledge (about the LR method application) to correctly tune the parameters to obtain good solntions. Therefore, an industry would be able to react to perturbations in less time and without a high-specialized user.

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Section: Lagrangian Relaxation (Lr) Methodsmentioning

confidence: 99%

Section: Lr and Cp Methodsmentioning

confidence: 99%