An intelligent water drop algorithm to identical parallel machine scheduling with controllable processing times: a just-in-time approach

Identical parallel machine scheduling problem with controllable processing times is investigated in this research. In such an area, our focus is mostly motivated by the adoption of just-in-time (JIT) philosophy with the objective of minimizing total weighted tardiness and earliness as well as job compressions/expansion cost simultaneously. Also the optimal set amounts of job compressions/expansion plus the job sequence are determined on each machine. It is assumed that the jobs processing times can vary within a given interval, i.e., it is permitted to compress or expand in return for compression/expansion cost. A mixed integer linear programming (MILP) model for the considered problem is firstly proposed and thereafter the optimal jobs set amounts of compression and expansion processing times in a known sequence are determined via parallel net benefit compression–net benefit expansion called PNBC–NBE heuristic. An intelligent water drop (IWD) algorithm, as a new swarm-based nature-inspired optimization one, is also adopted to solve this multi-criteria problem. A heuristic method besides three meta-heuristic algorithms is then employed to solve small- and medium- to large-size sample-generated instances. Computational results reveal that the proposed IWDNN outperforms the other techniques and is a trustable one which can solve such complicated problems with satisfactory consequences.