Solving open benchmark instances for the job-shop problem by parallel head-tail adjustments

Abstract

A fast and efficient head–tail adjustment algorithm is presented for the job‐shop scheduling problem. The main feature of this algorithm is to do the adjustments on different machines in parallel and simultaneously to propagate the results between the machines. In connection with a branching scheme this algorithm is used to improve lower and upper bounds, and to prove the optimality of solutions for benchmark problems which have been open for some time. Copyright © 2001 John Wiley & Sons, Ltd.

An extended Akers graphical method with a biased random‐key genetic algorithm for job‐shop scheduling

“…(), Demirkol et al. (), Jain (), Brinkkötter and Brucker (), Schilham (), Henning (), Nowicki and Smutnicki (), Pardalos and Shylo (), Zhang et al. (), Pardalos et al.…”

An extended Akers graphical method with a biased random‐key genetic algorithm for job‐shop scheduling

“…(), Demirkol et al. (), Jain (), Brinkkötter and Brucker (), Schilham (), Henning (), Nowicki and Smutnicki (), Pardalos and Shylo (), Zhang et al. (), Pardalos et al.…”

An Efficient Search Method for Job-Shop Scheduling Problems

“…For TD instances, the best known upper bounds (UB best ) and the best known lower bounds (LB best ) are taken from [23]. For the remaining instances, UB best and LB best are taken from [22] and updated with the improved results from [24]. 111 of the 242 instances have previously been solved to optimality, and for those unsolved instances, the mean relative deviation between the best known upper bound and the best lower bound is 7.72%.…”

Clique Search in Graphs of Special Class and Job Shop Scheduling

“…The job sequencing problem is an optimization problem [14], that is actively researched (see for example [15][16][17][18][19][20][21].) Certain products are to be produced on given machines satisfying predetermined technological order.…”

“…Nodes 18 and 19 can be deleted as node 20 dominates them. The color indices of nodes 6,7,8,9,10,11,12,14,15,16,17 are too small and so they maybe deleted. The graph G does not contain any 6-cliques.…”

An extended Akers graphical method with a biased random‐key genetic algorithm for job‐shop scheduling

“…(), Demirkol et al. (), Jain (), Brinkkötter and Brucker (), Schilham (), Henning (), Nowicki and Smutnicki (), Pardalos and Shylo (), Zhang et al. (), Pardalos et al.…”

An Efficient Search Method for Job-Shop Scheduling Problems

“…For TD instances, the best known upper bounds (UB best ) and the best known lower bounds (LB best ) are taken from [23]. For the remaining instances, UB best and LB best are taken from [22] and updated with the improved results from [24]. 111 of the 242 instances have previously been solved to optimality, and for those unsolved instances, the mean relative deviation between the best known upper bound and the best lower bound is 7.72%.…”

Clique Search in Graphs of Special Class and Job Shop Scheduling

“…The job sequencing problem is an optimization problem [14], that is actively researched (see for example [15][16][17][18][19][20][21].) Certain products are to be produced on given machines satisfying predetermined technological order.…”

“…Nodes 18 and 19 can be deleted as node 20 dominates them. The color indices of nodes 6,7,8,9,10,11,12,14,15,16,17 are too small and so they maybe deleted. The graph G does not contain any 6-cliques.…”

An extended Akers graphical method with a biased random‐key genetic algorithm for job‐shop scheduling

“…(), Demirkol et al. (), Jain (), Brinkkötter and Brucker (), Schilham (), Henning (), Nowicki and Smutnicki (), Pardalos and Shylo (), Zhang et al. (), Pardalos et al.…”

An Efficient Search Method for Job-Shop Scheduling Problems

“…For TD instances, the best known upper bounds (UB best ) and the best known lower bounds (LB best ) are taken from [23]. For the remaining instances, UB best and LB best are taken from [22] and updated with the improved results from [24]. 111 of the 242 instances have previously been solved to optimality, and for those unsolved instances, the mean relative deviation between the best known upper bound and the best lower bound is 7.72%.…”

Clique Search in Graphs of Special Class and Job Shop Scheduling

“…The job sequencing problem is an optimization problem [14], that is actively researched (see for example [15][16][17][18][19][20][21].) Certain products are to be produced on given machines satisfying predetermined technological order.…”

“…Nodes 18 and 19 can be deleted as node 20 dominates them. The color indices of nodes 6,7,8,9,10,11,12,14,15,16,17 are too small and so they maybe deleted. The graph G does not contain any 6-cliques.…”