In　this　work,　we　incorporate　human　factors　and　real-life　operations　into　newly　proposed　multitasking　scheduling　problems　with　periodic　shift　activities.　It　is　motivated　by　personnel　resource　scheduling　with　periodic　work　shifts　under　the　requirement　of　providing　continuous　service　to　customers.　We　model　the　problem　as　two　identical　parallel　machine　scheduling　with　complementary　non-available　time　periods,　and　consider　two　models　with　the　objectives　of　the　makespan,　i.e.　the　maximum　completion　time　and　respectively　the　total　completion　time.　We　then　prove　that　the　Greedy　algorithm　and　SPT　rule　are　of　asymptotic　and　parametric　approximation　ratios　for　the　two　models,　respectively.