Minimaximal Paths in Disjunctive Graphs by Direct Search

The problem of finding a minimaximal path in a disjunctive network is stated in terms of both graph theory and linear programming with mixed-integer variables. It is solved in both formulations using a “direct search” scheme with additional dynamic features, which seems to be a more efficient algorithm than those based on other methods. Although it yields an optimal solution, the algorithm can be used as such or with very few changes to find suboptimal solutions for larger problems. Computational experience on the general machine scheduling problem is described.