Makespan minimization with OR-precedence constraints

Abstract We consider a variant of the NP-hard problem assigning jobs to machines minimize completion time last job. Usually, precedence constraints are given by partial order on set jobs, and each job requires all its predecessors be completed before it can start. In this paper, we different type relation that has not been discussed as extensively is called OR-precedence. for start, require at least one completed—in contrast predecessors. Additionally, assume release date which must prove simple List Scheduling algorithm due Graham (Bell Syst Tech J 45(9):1563–1581, 1966) an approximation guarantee 2 show obtaining factor $$4/3 - \varepsilon $$ 4 / 3 - ε NP-hard. Further, present polynomial-time solves optimality if preemptions allowed. The latter result in classical where preemptive already Our generalizes previous results unit processing subject OR-precedence constraints, but without dates. running our $$O(n^2)$$ O ( n 2 ) arbitrary times reduced O ( n ) times, number jobs. performance guarantees presented here match best-known ones special cases coincide.