Branch-and-bound algorithm for UET scheduling problem

This paper addresses the problem of scheduling unit execution time task systems on m identical machines under certain precedence constraints. The aim is to compute the minimal length nonpreemptive schedule. The problem is NP-hard if m is arbitrary and only polynomially solvable for some special cases. The Coffman-Graham algorithm solves optimally the over-interval order class. Using this result, we propose a new branch and bound algorithm to find an optimal schedule in the general case. This branch and bound algorithm is based upon a dominance rule and lower bounds including relaxation of the number of available processors and certain precedence constraints.