Heuristic to Minimize Makespan in Uniform Parallel Machines Scheduling Problem (original) (raw)
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Intelligent Information Management, 2010
This paper discusses an efficient heuristic to minimize the makespan of scheduling n independent jobs on m unrelated parallel machines. The problem of scheduling the jobs on the unrelated parallel machines is combinatorial in nature. Hence, the heuristic approach is inevitable for quicker solution. In this paper, a simple and efficient heuristic is designed to minimize the makespan of scheduling n independent jobs on m unrelated parallel machines. A mathematical model is also presented for this problem. A factorial experiment is used to compare the results of the proposed heuristic with that of a mathematical model by taking "Method" (Heuristic and Model) as the first factor and "Problem Size" (No. of machines X No. of Jobs: 2X5, 2X6, ……, 2X9, 3X5, 3X6, ……, 3X9, ……., 5X5, 5X6, …5X9) as the second factor. It is found that there is no significant difference between the results of the proposed heuristic and that of the mathematical model. Further, the mean percent error of the results obtained by the heuristic from the optimal results obtained by the model is 2.336 %. The heuristic gives optimal solution for 76.67 % of the problems.
Computers & Operations Research, 1994
Scope and Purpose--In several manufacturing processes, it is necessary to determine an assignment of inde~ndent jobs to identical parallel machines in order to minimize the total completion time or makespan. There has been a great deal of research on this hard combinatorial problem. One active line of research has been the design of heuristics. This paper proposes a new fast and powerful heurisrtic for this problem.
International Journal of Innovation in Enterprise System
XYZ company produce the various shape of motor spare parts product. The company has three identical parallel spot welding machines that use a random method of production scheduling, based on machine capacity without any sequence of jobs, and only use daily production targets given to operators. Based on the data, the actual scheduling of the machines has a very large completion time difference between each machine, or the machine loading is uneven. As a result, the makespan becomes longer with a value of 440000 seconds (26 days). This research aims to minimize the existing makespan by giving proposed scheduling, using the suggested algorithm method, which has a small number of iterations and has an optimal result. The method begins with the longest processing time sequence rule which is used as the upper bound for the first iteration, then continued to calculate the lower bound and machine workload. The calculation stops at the 15th iteration because the completion time value exceed...
Minimizing Makespan in Job Shop Scheduling Problem with Parallel Machines
International Journal of Industrial Engineering Production Management, 2009
In this paper the problem of job shop scheduling with parallel machines in each stages is discussed. The objective is to minimize the maximum completion time (makespan). This problem is a combination of two classic problems of job shop and parallel machines which in this case parallel machines has been used as kind of flexibility in the job shop problem. The review of literature has shown that this problem has not been discussed yet. After presenting the mathematical mode, heuristic algorithms are used for solving this NP-hard problem. Regarding this, five algorithms are presented and a lower bound is developed. Finally all these algorithms have been analyzed. According to results the proposed algorithm of H2 works better than the others when there are few jobs. As the number of jobs increases H1 is more efficient than H2 asymptotically. Also the efficiency of H3 algorithm is the worst among the rest.
Applied Soft Computing, 2011
This paper considers the identical parallel machine scheduling problem to minimize the makespan with controllable processing times, in which the processing times are linear decreasing functions of the consumed resource. The total resource consumption is limited. This problem is NP-hard even if the total resource consumption equals to zero. Two kinds of machines, critical machine and non-critical machine, are defined. Some theoretical results are provided. And then, a simulated annealing algorithm is designed to obtain the near-optimal solutions with high quality. To evaluate the performance of the proposed algorithm, we generate the random test data in our experiment to simulate the ingot preheating before hot-rolling process in steel mills. The accuracy and efficiency of the simulated annealing algorithm is tested based on the data with problem size varying from 200 jobs to 1000 jobs. By examining 10,000 randomly generated instances, the proposed simulated annealing algorithm shows an excellent performance in not only the solution quality but also the computation time.
IEEE Access
This paper examines the uniform parallel-machine scheduling problem in which the objective aims to minimize the total resource consumption (TRC) with a bounded makespan. A matheuristic is proposed to deal with this strongly NP-hard problem. The performance of the proposed matheuristic is compared with that of the state-of-the-art particle swarm optimization (PSO) meta-heuristic and the lower bound (LB) of TRC on a set of benchmark instances. Computational results show that the proposed matheuristic significantly outperforms the PSO meta-heuristic and its solution is very close to the tight LB. Given the critical need for environmental protection, this paper provides an effective and efficient algorithm for diminishing the gap between the theoretical progress of scheduling and the practical need for environmental protection. INDEX TERMS Operations research, scheduling algorithm, parallel machines, total resource consumption.
Uniform parallel machine scheduling with resource consumption constraint
Applied Mathematical Modelling, 2015
Scheduling with learning effects has become a popular topic in the past decade; however, most of the research focuses on single-machine problems. In many situations, there are machines in parallel and the skills of workers might be different due to their individual experience. In this paper, we study a uniform parallel machine problem in which the objective is to jointly find an optimal assignment of operators to machines and an optimal schedule to minimize the makespan. Two heuristic algorithms are proposed and computational experiments are conducted to evaluate their performance.
On Optimality Conditions for Job Scheduling on Uniform Parallel Machines
Advances in Computer Science for Engineering and Education II, 2019
We study three similar problems of scheduling of unrelated jobs on uniform parallel machines each having a distinct optimization criterion. In the first problem the criterion is the makespan minimization. In the second one the goal is to create a schedule, where the minimum of the completion times of the last jobs on the parallel machines is maximized (machine covering problem). In the third one the goal is to create a schedule with maximally uniform distribution of jobs among the machines. We propose the sufficient conditions of schedule optimality for these problems. First, optimality criteria for the analyzed problems were transformed into functions of makespan's lower boundary deviation. This allows to define auxiliary optimization problems of the mixedinteger programming problems class. The objective of these auxiliary problems is to determine a perfect schedule-the one that gives the perfect value of the corresponding source criterion for the given volume of jobs. Perfect value allows us to determine the sufficient conditions of schedule optimality for all three problems.
A Note on Scheduling Equal-Length Jobs on Uniform Machines
We consider a basic problem of scheduling n equal-length jobs with release times on a group of m uniform machines with the objective to minimize the maximum job completion time, the makespan. According to our understanding, the status of this problem remained open. Here we propose a fast heuristic algorithm that solves the problem.