TY - JOUR
T1 - The no-wait two-machine flow shop scheduling problem with convex resource-dependent processing times
AU - Shabtay, Dvir
AU - Kaspi, Moshe
AU - Steiner, George
N1 - Funding Information:
This research was partially supported by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev. Partial support by the Natural Sciences and Engineering Research Council of Canada under grant 041798 is also gratefully acknowledged. We also thank the anonymous reviewers whose comments led to a substantially improved presentation for the paper.
PY - 2007/5/1
Y1 - 2007/5/1
N2 - We extend the classical no-wait two-machine flow shop scheduling problem to the case where job-processing times are controllable through the allocation of a common, limited and nonrenewable resource. Our objective is to simultaneously determine the sequence of the jobs and the resource allocation for each job on both machines in order to minimize the makespan. By using the equivalent load method to obtain the optimal resource allocation on a series-parallel graph, we reduce the problem to a sequencing one and show that it is equivalent to a new special case of the Traveling Salesman Problem (TSP). We prove that although the reduced problem forms a subclass of the TSP on permuted Monge matrices, it is still strongly NP-hard. We provide an approximation result and present three special cases which are polynomially solvable. We have also tested two different subtour-patching heuristics in large-scale computational experiments on randomly generated instances of the problem. Both heuristics produced close-to-optimal solutions in most cases.
AB - We extend the classical no-wait two-machine flow shop scheduling problem to the case where job-processing times are controllable through the allocation of a common, limited and nonrenewable resource. Our objective is to simultaneously determine the sequence of the jobs and the resource allocation for each job on both machines in order to minimize the makespan. By using the equivalent load method to obtain the optimal resource allocation on a series-parallel graph, we reduce the problem to a sequencing one and show that it is equivalent to a new special case of the Traveling Salesman Problem (TSP). We prove that although the reduced problem forms a subclass of the TSP on permuted Monge matrices, it is still strongly NP-hard. We provide an approximation result and present three special cases which are polynomially solvable. We have also tested two different subtour-patching heuristics in large-scale computational experiments on randomly generated instances of the problem. Both heuristics produced close-to-optimal solutions in most cases.
KW - Convex resource consumption function
KW - Flow shop scheduling
KW - No-wait
KW - Series-parallel graph
KW - TSP on k-root cost matrices
UR - http://www.scopus.com/inward/record.url?scp=33847713661&partnerID=8YFLogxK
U2 - 10.1080/07408170601181674
DO - 10.1080/07408170601181674
M3 - Article
AN - SCOPUS:33847713661
SN - 0740-817X
VL - 39
SP - 539
EP - 557
JO - IIE Transactions (Institute of Industrial Engineers)
JF - IIE Transactions (Institute of Industrial Engineers)
IS - 5
ER -