TY - GEN

T1 - Petri net representation for 0-1 integer programming problems

AU - Kodama, Akito

AU - Nishi, Tatsushi

PY - 2014

Y1 - 2014

N2 - Petri net is a mathematical modeling tool that represents wide variety of discrete event systems. Given an initial marking and final marking for a Petri net, an optimal firing sequence problem is defined as the problem to And an optimal transition sequence to minimize the objective function. For the purpose of analysis of 0-1 integer programming problems, we propose a general algorithm to convert general 0-1 integer programming problem into an optimal firing sequence problem of Petri net. By utilizing the proposed algorithm, general 0-1 integer programming problems can be visualized and analyzed by Petri net theory. The property of solutions derived by solving the original 0-1 integer programming and the optimal firing sequence problem is discussed. The solution of 0-1 integer programming problem and that of the optimal firing sequence problem of Petri net are compared. The results show that the solutions for both problems are identical for traveling salesman problem and vehicle routing problems.

AB - Petri net is a mathematical modeling tool that represents wide variety of discrete event systems. Given an initial marking and final marking for a Petri net, an optimal firing sequence problem is defined as the problem to And an optimal transition sequence to minimize the objective function. For the purpose of analysis of 0-1 integer programming problems, we propose a general algorithm to convert general 0-1 integer programming problem into an optimal firing sequence problem of Petri net. By utilizing the proposed algorithm, general 0-1 integer programming problems can be visualized and analyzed by Petri net theory. The property of solutions derived by solving the original 0-1 integer programming and the optimal firing sequence problem is discussed. The solution of 0-1 integer programming problem and that of the optimal firing sequence problem of Petri net are compared. The results show that the solutions for both problems are identical for traveling salesman problem and vehicle routing problems.

KW - 0-1 integer programming problem

KW - discrete event systems

KW - optimal firing sequence problem

KW - Petri nets

KW - traveling salesman problem

KW - vehicle routing problems

UR - http://www.scopus.com/inward/record.url?scp=84988298068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988298068&partnerID=8YFLogxK

U2 - 10.1109/IEEM.2014.7058734

DO - 10.1109/IEEM.2014.7058734

M3 - Conference contribution

AN - SCOPUS:84988298068

T3 - IEEE International Conference on Industrial Engineering and Engineering Management

SP - 729

EP - 733

BT - IEEM 2014 - 2014 IEEE International Conference on Industrial Engineering and Engineering Management

PB - IEEE Computer Society

T2 - 2014 IEEE International Conference on Industrial Engineering and Engineering Management, IEEM 2014

Y2 - 9 December 2014 through 12 December 2014

ER -