Unrelated parallel machine scheduling with eligibility constraints and delivery times to minimize total weighted tardiness

This paper addresses an unrelated parallel machine scheduling problem with job-machine-dependent delivery times and eligibility constraints motivated by a distributed manufacturing environment. The objective is total weighted tardiness minimization. We present a mixed integer linear programming (MILP) formulation and conduct an analysis of the scheduling problem to derive precedence properties that can be integrated in local search procedures to increase computational efficiency. We implement a variable neighborhood search (VNS) algorithm for the problem at hand and examine the effect of integrating the properties on the performance. The tests show that the theoretical findings can reduce computational effort significantly. Furthermore, we propose another heuristic approach based on the Apparent Tardiness Cost rule and a memetic biased random-key genetic algorithm. In experiments, we compare the MILP and (meta-)heuristics on a large set of randomly generated problem instances. The VNS procedure outperforms the other algorithms.