Parallel Makespan Calculation for Flow Shop Scheduling Problem with Minimal and Maximal Idle Time

In this paper, a flow shop scheduling problem with minimal and maximal machine idle time with the goal of minimizing makespan is considered. The mathematical model of the problem is presented. A generalization of the prefix sum, called the job shift scan, for computing required shifts for overlapping jobs is proposed. A work-efficient algorithm for computing the job shift scan in parallel for the PRAM model with n processors is proposed and its time complexity of O(logn) is proven. Then, an algorithm for computing the makespan in time O(mlogn) in parallel using the prefix sum and job shift scan is proposed. Computer experiments on GPU were conducted using the CUDA platform. The results indicate multi-thread GPU vs. single-thread GPU speedups of up to 350 and 1000 for job shift scan and makespan calculation algorithms, respectively. Multi-thread GPU vs. single-thread CPU speedups up to 4.5 and 14.7, respectively, were observed as well. The experiments on the Taillard-based problem instances using a simulated annealing solving method and employing the parallel makespan calculation show that the method is able to perform many more iterations in the given time limit and obtain better results than the non-parallel version.

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A Bee Colony Algorithm based Solver for Flow Shop Scheduling Problem

JOIV International Journal on Informatics Visualization ◽

10.30630/joiv.5.2.491 ◽

2021 ◽

Vol 5 (2) ◽

Author(s):

Yosua Halim ◽

Cecilia Esti Nugraheni

Keyword(s):

Processing Time ◽

Flow Shop ◽

Flow Shop Scheduling ◽

Food Sources ◽

Scheduling Problem ◽

Total Processing Time ◽

Shop Scheduling ◽

Bee Colony ◽

Problem Instances ◽

Parameter Values

Flow Shop Scheduling (FSS) is scheduled to involve n jobs and m machines in the same process sequence, where each machine processes precisely one job in a certain period. In FSS, when a machine is doing work, other machines cannot do the same job simultaneously. The solution to this problem is the job sequence with minimal total processing time. Many algorithms can be used to determine the order in which the job is performed. In this paper, the algorithm used to solve the flow shop scheduling problem is the bee colony algorithm. The bee colony algorithm is an algorithm that applies the metaheuristic method and performs optimization according to the workings of the bee colony. To measure the performance of this algorithm, we conducted some experiments by using Taillard's Benchmark as problem instances. Based on experiments that have been carried out by changing the existing parameter values, the size of the bee population, the number of iterations, and the limit number of bees can affect the candidate solutions obtained. The limit is a control parameter for a bee when looking for new food sources. The more the number of bees, the more iterations, and the limit used, the better the final time of the sequence of work. The bee colony algorithm can reach the upper limit of the Taillard case in some cases in the number of machines 5 and 20 jobs. The more the number of machines and jobs to optimize, the worse the total processing time.

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Alternative Heuristic Algorithm for Flow Shop Scheduling Problem

Operations Management Research and Cellular Manufacturing Systems - Advances in Logistics, Operations, and Management Science ◽

10.4018/978-1-61350-047-7.ch013 ◽

2013 ◽

pp. 277-297

Author(s):

Vladimír Modrák ◽

R. Sudhakra Pandian ◽

Pavol Semanco

Keyword(s):

Heuristic Algorithm ◽

Flow Shop ◽

Idle Time ◽

Flow Shop Scheduling ◽

Scheduling Problem ◽

Scheduling Problems ◽

Shop Scheduling ◽

Permutation Flow Shop Scheduling ◽

Realistic Situation ◽

Permutation Flow Shop

In this chapter an alternative heuristic algorithm is proposed that is assumed for a deterministic flow shop scheduling problem. The algorithm is addressed to an m-machine and n-job permutation flow shop scheduling problem for the objective of minimizing the make-span when idle time is allowed on machines. This chapter is composed in a way that the different scheduling approaches to solve flow shop scheduling problems are benchmarked. In order to compare the proposed algorithm against the benchmarked, selected heuristic techniques and genetic algorithm have been used. In realistic situation, the proposed algorithm can be used as it is without any modification and come out with acceptable results.

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