This paper investigates a parallel machine scheduling problem featuring a single common server responsible for both loading and unloading operations. Each job consists of a unit-time loading operation, non-preemptive processing on one of \(m\) identical machines, and a unit-time unloading operation executed by the same server. The objective is to minimize the makespan. Unlike classical loading-only common-server models, our setting requires the server to handle an unloading operation immediately after a job's processing phase concludes. We prove that the corresponding decision problem is strongly NP-complete when the number of machines is given as part of the input. Furthermore, we analyse the worst-case performance of the List Scheduling (LS) and Longest Processing Time (LPT) heuristics. For three machines, we establish that Algorithm LS achieves an approximation ratio of at most \(5/2\). For an arbitrary fixed \(m \ge 3\), we show that the general LS bound approaches \(4-3/m\) as the number of jobs grows, whereas for Algorithm LPT, we prove the finite-instance ratio $3-\frac{2}{m}+\frac{(m-1)(m-2)}{mn}.$ Thus, for each fixed \(m\), the LPT bound approaches \(3-2/m\) as the number of jobs grows.

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