A two-stage flow shop scheduling with a critical machine and batch availability (original) (raw)
Related papers
A two-stage flow shop batch-scheduling problem with the option of using Not-All-Machines
International Journal of Production Economics, 2013
ABSTRACT The decision whether to use all the available machines in the shop becomes very relevant when the capacity exceeds the demand. In such cases, it might be optimal to use only a subset of the machines. We study this option in a two-stage flowshop environment. Jobs are assumed to be identical, and are processed in batches, where a machine-dependent setup time is required when starting a new batch. The objective function is minimum makespan. We introduce an exact efficient dynamic programming algorithm, which is shown numerically to be able to solve medium size instances in very reasonable time. For the solution of large instances, we propose an asymptotically optimal heuristic procedure and a lower bound on the makespan value, which produce extremely small optimality gaps.
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.
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
Scheduling of a two-machine flowshop with availability constraints on the first machine
International Journal of Production Economics, 2006
We treat the problem of scheduling n immediately available jobs in a flowshop composed of two machines in series with the objective of minimizing the makespan, when it is known that there shall be an interruption in machine availability on the first machine. We also consider two types of processing regimes: “stop resume” and “stop restart”. We present efficient dynamic
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.
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.
Computers Operations Research, 2009
This paper considers the problem of scheduling a two-stage flowshop that consists of a common critical machine in stage one and two independent dedicated machines in stage two. All the jobs require processing first on the common critical machine. Each job after completing its critical operation in stage one will proceed to the dedicated machine of its type for further processing in stage two. The objective is to minimize the weighted sum of stage-two machine completion times. We show that the problem is strongly NP-hard, and develop an O(n 3 ) polynomial time algorithm to solve the special case where the sequences of both types of jobs are given. We also design an approximation algorithm with a tight performance ratio of 4 3 for the general case.
A Flowshop Scheduling Problem With Transportation Times and Capacity Constraints
2010
Although there are numerous methodologies and research studies on machine scheduling, most of the literature assumes that there is an unlimited number of transporters to deliver jobs from one machine to another for further processing and that transportation times can be neglected. These two assumptions are not applicable if one intends to generate an accurate schedule for the shop floor. In this research, a flowshop scheduling problem with two machines, denoted as M1 and M2, and a single transporter with capacity c is considered. The main focus is on the development of a dynamic programming algorithm to generate a schedule that minimizes the makespan. The transporter takes t 1 time units to travel with at least one job from machine M1 to machine M2, and t 2 time units to return empty to machine M1. When the processing times for all n jobs on machine M1 are constant, denoted as p j1 ≡p 1 ,
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.