Solving parallel machine problems with delivery times and tardiness objectives

This paper studies the NP-hard problem of scheduling jobs on identical parallel machines with machine-dependent delivery times to minimize the total weighted tardiness. A mixed integer linear programming formulation is presented that does not require machine-indexed variables due to a transformation of the problem. A variable neighborhood search (VNS) algorithm is proposed incorporating a local search that utilizes fast evaluation techniques (FET) to significantly improve computational efficiency of the search in four different neighborhoods. In experiments, the VNS is compared with other solution approaches on a large set of randomly generated test instances. Additionally, results for the computational benefits of our FETs are reported.