TY - GEN
T1 - General conversion of integer programming problems into optimal firing sequence problem of Petri nets
AU - Kodama, Akito
AU - Nishi, Tatsushi
PY - 2016/12/27
Y1 - 2016/12/27
N2 - Given an initial marking and final marking for a Petri net model, an optimal firing sequence problem is defined as the problem to find an optimal transition firing sequence to minimize the objective function. For the purpose of analysis of general integer programming problems, we propose a Petri net representation and reachability analysis of integer programming problems. In the proposed method, an integer programming problem is converted into the optimal firing sequence problem of Petri nets. By utilizing the proposed algorithm, integer programming problems can be visualized and analyzed by the Petri net theory. We apply the proposed methodology to the scheduling problems of dual armed cluster tools. The valid inequalities are derived from the reachability analysis. Numerical results show that those valid inequalities can significantly reduce the computational time of the original integer programming problem.
AB - Given an initial marking and final marking for a Petri net model, an optimal firing sequence problem is defined as the problem to find an optimal transition firing sequence to minimize the objective function. For the purpose of analysis of general integer programming problems, we propose a Petri net representation and reachability analysis of integer programming problems. In the proposed method, an integer programming problem is converted into the optimal firing sequence problem of Petri nets. By utilizing the proposed algorithm, integer programming problems can be visualized and analyzed by the Petri net theory. We apply the proposed methodology to the scheduling problems of dual armed cluster tools. The valid inequalities are derived from the reachability analysis. Numerical results show that those valid inequalities can significantly reduce the computational time of the original integer programming problem.
UR - http://www.scopus.com/inward/record.url?scp=85009833712&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85009833712&partnerID=8YFLogxK
U2 - 10.1109/IEEM.2016.7797904
DO - 10.1109/IEEM.2016.7797904
M3 - Conference contribution
AN - SCOPUS:85009833712
T3 - IEEE International Conference on Industrial Engineering and Engineering Management
SP - 395
EP - 399
BT - 2016 International Conference on Industrial Engineering and Engineering Management, IEEM 2016
PB - IEEE Computer Society
T2 - 2016 International Conference on Industrial Engineering and Engineering Management, IEEM 2016
Y2 - 4 December 2016 through 7 December 2016
ER -