Abstract
In this paper, we investigate a general algorithm for converting the 0–1 integer linear programming problem (0-1IP) into an optimal transition firing sequence problem (OFSP) of a Petri net (PN). The general 0-1IP can be visualized graphically and then analyzed using the PN theory after application of our proposed conversion algorithm. The proposed algorithm is applied to a traveling salesman problem, a vehicle routing problem and an automated guided vehicles (AGV) routing problem. A PN reduction technique is employed to reduce the size of the PN. Valid inequalities are derived using reachability analysis of the converted PN model. These inequalities are imposed on the original 0-1IP. Computational results show that the total computational time for solving an AGVRP with the valid inequalities derived using the reachability analysis is significantly reduced.
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