Exact and heuristic algorithms for the parallel machine total completion time scheduling problem with dual resources, ready times, and sequence-dependent setup times

Abstract

This paper considers a dual resource constrained scheduling problem prevalent in high-capital cost manufacturing industry such as the photolithography area in the semiconductor industry. Specifically, the problem consists of assigning jobs to parallel machines that use common and constrained auxiliary resources such as lithography lens. Very often these auxiliary resources require heavy capital investment and setup times further complicates an already complex dual resource constrained scheduling problem. This paper advocates for the use of deterministic scheduling theory for the design and development of more efficient scheduling strategies. An Integer Programming (IP) model, a heuristic and a hybrid model were developed to schedule identical parallel machines with shared, constrained, auxiliary resources, with sequence-dependent setups, and job release dates with the goal of minimizing the sum of completion times.An IP model primed with a heuristic can add value to practitioners looking to solve real world resource constrained parallel machine scheduling problems with sequence-dependent setups. It is extremely important to control problem instance size and time horizon in order to obtain near-optimal or efficient solutions within acceptable run times. The proposed heuristic provides an initial feasible solution for the IP model which reduces the space search by decreasing the time horizon and eliminates the time needed to find an initial feasible solution. A tighter formulation is also proposed by reducing the time horizon formulation.