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