As　a　special　Travelling　Salesman　Problem　(TSP),　the　Single-Picker　Routing　Problem　(SPRP)　in　warehouses　is　of　important　theoretical　and　practical　significance.　In　manual　order　picking,　the　items　are　usually　picked　up　by　a　picker　with　a　cart.　To　speed　up　the　picking　process,　the　picker　is　allowed　to　stop　the　cart　to　pick　up　the　items　individually　and　return　to　the　location　of　the　cart.　This　paper　proposes　a　mixed　integer　linear　programming　formulation　for　an　order　picking　problem　with　the　decoupling　of　the　picker　and　the　cart　in　a　multi-block　warehouse,　where　the　picker　capacity　is　at　most　four.　And　based　on　this　model,　order　batching　problem　is　also　analysed.　Through　numerical　experiments,　the　cost　of　above　decoupling　problems　is　computed　under　different　settings　of　the　speed　ratio　and　the　capacity　of　the　picker　while　he/she　is　travelling　alone.　The　results　indicate　how　the　decoupling　of　picker　and　cart　leads　to　cost　reduction.　Our　model　shows　good　performance　for　orders　of　small　and　medium　scale　and　hence　has　great　potential　to　improve　the　order　picking　operation　which　is　executed　by　decoupling　containers　and　robots/vehicles　in　modern　digital　warehouse　systems.　©　2024　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.