Heuristics based on partial enumeration for the unrelated parallel processor scheduling problem

The classical deterministic scheduling problem of minimizing the makespan on unrelated parallel processors is known to be NP-hard in the strong sense. Given the mixed integer linear model with binary decision variables, this paper presents heuristic algorithms based on partial enumeration. Basically, they consist in the construction of mixed integer subproblems, considering the integrality of some subset of variables, formulated using the information obtained from the solution of the linear relaxed problem. Computational experiments are reported for a collection of test problems, showing that some of the proposed algorithms achieve better solutions than other relevant approximation algorithms published up to now.