Abstract
In this paper it is presented an improvement of the branch and bound algorithm for the permutation flow shop problem with blocking-in-process and setup times with the objective of minimizing the total flow time and tardiness, which is known to be NP-Hard when there are two or more machines involved. With that objective in mind, a new machine-based lower bound that exploits some structural properties of the problem. A database with 27 classes of problems, varying in number of jobs (n) and number of machines (m) was used to perform the computational experiments. Results show that the algorithm can deal with most of the problems with less than 20 jobs in less than one hour. Thus, the method proposed in this work can solve the scheduling of many applications in manufacturing environments with limited buffers and separated setup times.
Highlights
In a flow shop scheduling problem, a number of jobs must be processed on each of the m machines
This paper aims to evaluate the quality of the proposed lower bounds; the initial solution is at first defined as a very high value, called big M, and is updated every time a smaller feasible solution is obtained
The computational tests performed to evaluate the effectiveness of the proposed lower bounds (LB) are described
Summary
In a flow shop scheduling problem, a number of jobs must be processed on each of the m machines. The permutation constraint means that all jobs must be processed on every machine in the same exact sequence, all machines can process no more than one job at a time, and interruptions are not accepted. The blocking constraint with zero buffer represents the lack of intermediate queues between machines, which blocks a machine in case a job finishes its processing on it and the machine is still processing another job. The total tardiness represents the time exceeded at the end of a task in relation to its due date. When not met, this criterion can result in contractual fines, increasing the total cost, in addition to the loss of reliability, a factor that results in loss of customers and damage to the company's reputation
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