A computational study of branch and bound techniques for minimizing the total weighted tardiness in job shops

We present and compare a number of branch and bound algorithms for minimizing the total weighted tardiness in job shops. There are basically two types of branching schemes. The first one inserts operations in a partial schedule, while the second one fixes arcs in the disjunctive graph formulation of the problem. The bounding schemes are based on the analysis of precedence constraints, and on the solution of nonpreemptive single machine subproblems that are subject to so-called delayed precedence constraints. We obtain optimal solutions for all the instances with ten jobs and ten machines that we consider, including three tardiness versions of a well-known 10 × 10 instance introduced by Muth and Thompson in 1963.