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This paper addresses the scheduling problem on two identical parallelmachines with a single server in charge of loading and unloading operations ofjobs. Each job has to be loaded by the server before being processed on one ofthe two machines and unloaded by the same server after its processing. No delayis allowed between loading and processing, and between processing andunloading. The objective function involves the minimization of the makespan.This problem referred to as P2, S1|sj , tj |Cmax generalizes the classicalparallel machine scheduling problem with a single server which performs onlythe loading (i.e., setup) operation of each job. For this NP-hard problem, nosolution algorithm was proposed in the literature. Therefore, we present twomixedinteger linear programming (MILP) formulations, one with completion-timevariables along with two valid inequalities and one with time-indexedvariables. In addition, we propose some polynomial-time solvable cases and atight theoretical lower bound. In addition, we show that the minimization ofthe makespan is equivalent to the minimization of the total idle times on themachines. To solve large-sized instances of the problem, an efficient GeneralVariable Neighborhood Search (GVNS) metaheuristic with two mechanisms forfinding an initial solution is designed. The GVNS is evaluated by comparing itsperformance with the results provided by the MILPs and another metaheuristic.The results show that the average percentage deviation from the theoreticallower-bound of GVNS is within 0.642%. Some managerial insights are presentedand our results are compared with the related literature.

Scheduling on parallel machines with a common server in charge of loading and unloading operations