Hesitant　multiplicative　preference　relation　(HMPR)　is　a　straightforward　and　efficient　tool　for　representing　hesitant　fuzzy　information　in　decision　making.　The　aim　of　this　paper　is　to　develop　a　method　to　obtain　priority　vectors　from　HMPRs　in　the　context　of　multistage　decision-making　(MSDM).　To　start　the　investigation,　a　simple　linear　programming　model　motivated　by　the　idea　of　orness　is　purposed　to　calculate　the　relative　weights　of　different　stages.　Based　on　these　obtained　weights,　we　develop　a　least　square　deviation　method　as　well　as　a　convergent　iterative　algorithm　for　prioritizing　and　ranking　the　MSDM-HMPR　problems.　The　prominent　property　of　this　method　is　then　studied.　Finally,　a　practical　example　concerning　the　selection　of　logistics　service　providers　is　given　to　illustrate　the　feasibility　and　applicability　of　the　proposed　approach.