The　movable　unit　equipped　with　a　set　of　lockers　has　been　recently　developed　as　a　new　mode　to　improve　the　efficiency　of　the　last　mile　delivery.　Locating　a　set　of　movable　parcel　locker　units　appropriately　is　a　fundamental　factor　to　promote　the　merits　of　movable　parcel　lockers.　However,　the　difficulty　in　determining　where　to　locate　movable　parcel　locker　units　arises　from　the　stochastic　characteristics　of　demands.　Therefore,　we　propose　a　robust　optimization　approach　to　determine　the　number　of　movable　parcel　locker　units　and　their　locations　simultaneously　with　the　aim　to　minimize　the　operating　cost　under　stochastic　demands　and　mobility　restrictions.　To　reduce　the　complexity　of　the　optimization　model,　the　non-linear　constraints　have　been　transformed　into　the　linear　counterparts,　resulting　in　an　integer　linear　programming　(ILP)　model　that　can　be　solved　by　commercially　available　mathematical　programming　solvers.　The　results　from　the　numerical　examples　indicate　the　proposed　approach　can　obtain　high　robustness　with　a　small　extra　cost　within　reasonable　time.　In　addition,　it　is　found　that　if　each　unit　is　equipped　with　more　lockers,　fewer　movable　parcel　locker　units　are　required　to　accommodate　the　demands　with　less　operating　cost,　as　the　demand　points　can　be　clustered　into　a　few　intensive　self-pickup　sites.