A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

Tang, Lixin; Xuan, Hua; Liu, Jiyin

doi:10.1016/j.cor.2005.03.028

Cited by 88 publications

(57 citation statements)

References 16 publications

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“…[172] proposes yet more mathematical models for a flexible flow line for tardiness related criteria. A regular HFS, this time with the sum of weighted completion times criterion, is approached with mathematical programming and lagrangian relaxation in [189]. The same problem and objective, but with the addition of limited buffers, is studied in [188].…”

Section: Exact Algorithmsmentioning

confidence: 99%

The hybrid flow shop scheduling problem

Ruíz

Vázquez-Rodríguez

2010

European Journal of Operational Research

680

236

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The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the Hybrid Flow Shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution.The paper discusses several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.

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Section: Exact Algorithmsmentioning

confidence: 99%

The hybrid flow shop scheduling problem

Ruíz

Vázquez-Rodríguez

2010

European Journal of Operational Research

680

236

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“…For this purpose, we apply lemma 1 which is developed by Tang et al [14] . 14), the subproblem is converted to parallel machine scheduling problem with weighted (with positive value) completion time minimization.…”

Section: Second Approach: Dominance Rulesmentioning

confidence: 99%

Lagrangian relaxation approach to minimize makespan for hybrid flow shop scheduling problem with unrelated parallel machines

Asadi-Gangraj

2017

Scientia Iranica

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This research addresses scheduling problem of n jobs on a Hybrid Flow Shop (HFS) with unrelated parallel machines in each stage. A monolithic mixed integer linear programming (MILP) model is presented to minimize the maximum completion time (makespan). As the research problem is shown to be strongly NP-hard, a Lagrangian relaxation (LR) algorithm is developed to handle the HFS scheduling problem. We design two approaches, simplification of subproblems and dominance rules, to solve the subproblems which are generated in each iteration. For evaluation purposes, numerical experiments with small and large size problems are randomly generated with up to 50 jobs and four stages. The experimental results show that the Lagrangian relaxation approaches outperform the MILP model with respect to CPU time. Furthermore, from the results, it can be conclude that the simplification of subproblems shows slightly better solutions in comparison with dominance rules to solve the subproblems.

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“…Through LR, the algorithm was able to find the optimal solution based on the "min-max" criteria for the jobshop scheduling. Tang, Xuan, and Liu [8] designed a DP algorithm for solving identical parallel machine sub-problems where jobs have negative weights. LR algorithm was used and decomposition was applied to decompose the master problem into several sub-problems so that the DP algorithm process is speeded up.…”

Section: Minimize Makespan With Lagrangian Approachmentioning

confidence: 99%

“…The Lagrangian approach has been used widely in the study of makespan minimization [8,27,36]. Velde [36] presented B&B algorithm for two-machine flow shop problem in order 14 to minimize the sum of the job completion times.…”

Section: Minimize Makespan With Lagrangian Approachmentioning

confidence: 99%

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Suhaimi

Nguyen

Damodaran

2016

Computers & Industrial Engineering

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Batch Processing Machines (BPMs) are commonly used in electronics manufacturing, semi-conductor manufacturing, and metal-working -to name a few. Scheduling these machines are not an easy task; practical considerations and the exponential number of decision variables involved impede schedulers (or decision makers) from making good decisions. This research focuses on minimizing the makespan of a set of non-identical parallel batch processing machines. In order to schedule jobs on these machines, two decisions are to be made. The first decision is to group jobs to form batches such that the machine capacity is not exceeded. The second decision is to sequence the batches formed on the machines such that the makespan is minimized. Both the decisions are intertwined as the processing time of the batch is determined by the composition of the jobs in the batch. The problem under study is shown to be NP-hard. A mathematical model from the literature is adopted to develop a solution approach which would help the decision maker to make meaningful decisions.Lagrangian Relaxation approach has been shown to be very effective in solving scheduling problems. Using this decomposition approach, the mathematical model is decomposed and a sub-gradient approach was used to update the multipliers. Two sets of constraints were relaxed to consider two Lagrangian Relaxation models. Experiments were conducted with data sets from the literature. The solution quality of the proposed approach was compared with meta-heuristic (i.e. Particle Swarm Optimization (PSO) and Random Key Genetic Algorithm (RKGA)) published in the literature and a commercial solver (i.e. IBM ILOG CPLEX). On smaller instances (i.e. 10 and 20 jobs), the proposed approach outperformed PSO and RKGA. However, the proposed approach and CPLEX report the same results. On larger instances (i.e. 50, 100 and 200 job instances) with two and four-machines, the proposed approach was better than PSO whenever the variability in the processing times were smaller. The proposed approach generally outperformed RKGA and CPLEX on larger problem instances. Out of 200 experiments conducted, the proposed approach helped to find new improved solution on 34 instances and comparable on 105 instances when compared to PSO. The PSO approach was much faster than all other approaches on larger problem instances. The experimental study clearly identifies the problem instances on which the proposed approach can find a better solution. The proposed Lagrangian Relaxation solution approach helps the schedulers to make more informed decisions. Minor modifications can be made to use the proposed solution approach for other practical considerations (e.g. job ready times, tardiness objective, etc.) The main contribution of this research is the proposed solution approach which is effective in solving a class of non-identical batch processing machine problems with better solution quality when compared to existing meta-heuristic. NORTHERN

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A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

Cited by 88 publications

References 16 publications

The hybrid flow shop scheduling problem

The hybrid flow shop scheduling problem

Lagrangian relaxation approach to minimize makespan for hybrid flow shop scheduling problem with unrelated parallel machines

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

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