Minimizing total tardiness and earliness on unrelated parallel machines with controllable processing times

Job scheduling has always been a challenging task in modern manufacturing and the most real life scheduling problems which involves multi-criteria and multi-machine environments. In this research our direction is largely motivated by the adoption of the Just-In-Time (JIT) philosophy in parallel machines system, where processing times of jobs are controllable. The goal of this paper is to minimize total weighted tardiness and earliness besides jobs compressing and expanding costs, depending on the amount of compression/expansion as well as maximum completion time called makespan simultaneously. Jobs due dates are distinct and no inserted idle time is allowed after starting machine processing. Also each machine is capable of processing only some predetermined jobs and operations with probably different speeds. A Mixed Integer Programming (MIP) model is proposed to formulate such a problem and is solved optimally in small size instances. A Parallel Net Benefit Compression-Net Benefit Expansion (PNBC–NBE) heuristic is then presented to acquire the optimal jobs set amount of compression and expansion processing times in a given sequence. To solve medium-to-large size cases, a proposed heuristic, two meta-heuristics and a hybrid technique are also employed. Experimental results demonstrate that our hybrid procedure is a proficient method and could efficiently solve such complicated problems.