A two-stage flow shop batch-scheduling problem with the option of using Not-All-Machines (original) (raw)
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A two-stage flow shop scheduling with a critical machine and batch availability
We study a two-stage flowshop, where each job is processed on the first (critical) machine, and then continues to one of two second-stage (dedicated) machines. We assume identical (but machine-dependent) job processing times. Jobs are processed on the critical machine in batches, and a setup time is required when starting a new batch. The setting assumes batch-availability, i.e., jobs become available for the second stage only when their entire batch is completed on the critical machine. We consider three objective functions: minimum makespan, minimum total load, and minimum weighted flow-time. Polynomial time dynamic programming algorithms are introduced, which are numerically shown to be able to solve problems of medium size in reasonable time. A heuristic for makespan minimization is presented and shown numerically to be both accurate and efficient..
Mathematical and Computer Modelling, Vol. 29, 1999, 101 - 126.
In this paper, we propose different heuristic algorithms for flow shop scheduling problems, where the jobs are partitioned into groups or families. Jobs of the same group can be processed together in a batch but the maximal number of jobs in a batch is limited. A setup is necessary before starting the processing of a batch, where the setup time depends on the group of the jobs. In this paper, we consider the case when the processing time of a batch is given by the maximum of the processing times of the operations contained in the batch. As objective function we consider the makespan as well as the weighted sum of completion times of the jobs. For these problems, we propose and compare various constructive and iterative algorithms. We derive suitable neighbourhood structures for such problems with batch setup times and describe iterative algorithms that are based on different types of local search algorithms. Except for standard metaheuristics, we also apply multilevel procedures which use different neighbourhoods within the search. The algorithms developed have been tested in detail on a large collection of problems with up to 120 jobs.
Approximation algorithms for two-machine flow shop scheduling with batch setup times
Mathematical Programming, 1998
In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n log n) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3.
Flow shop scheduling problem with limited machine availability: A heuristic approach
International Journal of Production Economics, 2006
This paper addresses the flow shop scheduling problem with limited machine availability. In such a problem, n jobs has to be scheduled on m machines under the makespan criterion and under the assumption that the machines are not available during the whole planning horizon. Since the makespan minimization is strongly NP-hard, we propose a heuristic approach to approximately solve the problem that consists in scheduling the jobs two by two according to an input sequence, and using a polynomial algorithm. This algorithm is an extension of the geometric approach developed for the two-job shop scheduling problem. r
Realistic two-stage flowshop batch scheduling problems with transportation capacity and times
Applied Mathematical Modelling, 2012
This paper investigates single-batch and batch-single flow shop scheduling problem taking transportation among machines into account. Both transportation capacity and transportation times are explicitly considered. While the single processing machine processes one job at a time, the batch processing machine processes a batch of jobs simultaneously. The batch processing time is the longest processing times of jobs assigned to that batch. Each problem is formulated as a mixed integer programming model to find optimal makespan. Lower bounds and heuristic algorithms are proposed and computational experiments are carried out to verify their effectiveness.
Flow shop scheduling with two batch processing machines and nonidentical job sizes
The International Journal of Advanced Manufacturing Technology, 2009
A batch processing machine can process several jobs simultaneously. In this research, we consider the problem of a two-stage flow shop with two batch processing machines to minimize the makespan. We assume that the processing time of a batch is the longest processing time among all the jobs in that batch and the sizes of the jobs are nonidentical. There is a limitation on batch sizes and the sum of job sizes in a batch must be less than or equal to the machine capacity. Since this problem is strongly nondeterministic polynomial time hard, we propose two heuristic algorithms. The first one is knowledge-based and the other is based on the batch first fit heuristic proposed previously. To further enhance the solution quality, two different simulated annealing (SA) algorithms based on the two constructive heuristics is also developed. Since heuristic methods for this problem has not been proposed previously, a lower bound is developed for evaluating the performance of the proposed methods. Several test problems have been solved by SAs and lower bound method and the results are compared. Computational studies show that both algo-rithms provide good results but the first SA (ARSA) algorithm considerably outperforms the second one (FLSA). In addition, the results of ARSA algorithm, optimal solutions, and lower bounds are compared for several small problems. The comparisons show that except for one instance, the ARSA could find the optimal solutions and the proposed lower bound provides small gaps comparing with the optimal solutions.
Two-Machine Flowshop Batching and Scheduling
Annals of Operations Research, 2005
We consider in this paper a two-machine flowshop scheduling problem in which the first machine processes jobs individually while the second machine processes jobs in batches. The forming of each batch on the second machine incurs a constant setup time. The objective is to minimize the makespan. This problem was previously shown to be NP-hard in the ordinary sense. In this paper, we first present a strong NP-hardness result of the problem. We also identify a polynomially solvable case with either anticipatory or non-anticipatory setups. We then establish a property that an optimal solution for the special case is a lower bound for the general problem. To obtain near-optimal solutions for the general problem, we devise some heuristics. The lower bound is used to evaluate the quality of the heuristic solutions. Results of computational experiments reveal that the heuristics produce solutions with small error ratios. They also suggest that the lower bound is close to the optimal solution.
Scheduling a two-stage flowshop under makespan constraint
Mathematical and Computer …, 2006
We consider selecting and sequencing jobs in a two stage flowshop so that the selected jobs are completed before a specified time limit (such as the end of a shift). The objective is to maximize the weighted (reward) sum of the selected jobs. We show that the problem is NP-hard, and present two procedures to find an optimum solution. The first procedure uses dynamic programming, and the second uses mixed integer programming. The integer programming formulation exploits special properties of the problem and solves large instances of the problem. We also develop heuristics and provide worst case performance guarantees. An improvement procedure is also developed. Extensive computational testing shows that our heuristics, when used jointly with the improvement procedure, yield excellent results (providing solutions within 3% of the optimum in an average sense) for both balanced and unbalanced shops.
This paper investigates a difficult scheduling problem on a specialized two-stage hybrid flow shop with multiple processors that appears in semiconductor manufacturing industry, where the first and second stages process serial jobs and parallel batches, respectively. The objective is to seek job-machine, job-batch, and batch-machine assignments such that makespan is minimized, while considering parallel batch, release time, and machine eligibility constraints. We first propose a mixed integer programming (MIP) formulation for this problem, then gives a heuristic approach for solving larger problems. In order to handle real world large-scale scheduling problems, we propose an efficient dispatching rule called BFIFO that assigns jobs or batches to machines based on first-in-first-out principle, and then give several reoptimization techniques using MIP and local search heuristics involving interchange, translocation and transposition among assigned jobs. Computational experiments indicate our proposed re-optimization techniques are efficient. In particular, our approaches can produce good solutions for scheduling up to 160 jobs on 40 machines at both stages within 10 min.
Journal of marine science and technology, 2006
In this paper, we consider a two-stage flowshop scheduling problem with a function constraint on alternative machines. The objective is to minimize the makespan. We show that the proposed problem is NP-hard and provide some heuristic algorithms and computational experiments. In addition, from the experimental results, the modification of Johnson's rule combined with the First-Fit rule is the best heuristic algorithm of the proposed heuristic algorithms.