Try this...

Enter this formula in cell F3 of the Summary sheet and copy down:

=LOOKUP(2,1/((ISNUMBER(FIND(LEFT(INDEX(Input!A$2:A$28,MATCH(B3,Input!B$2:B$28,0)),FIND("-",INDEX(Input!A$2:A$28,MATCH(B3,Input!B$2:B$28,0)))),Input!A$2:A$28)))/(Input!E$2:E$28<>"")),Input!F$2:F$28)

You can shorten that a bit by using named ranges.

Name: Item
Refers to: =Input!$A$2:$A$28

Name: Doc
Refers to: =Input!$B$2:$B$28

Name: Dates
Refers to: =Input!$E$2:$E$28

Name: Status
Refers to: =Input!$F$2:$F$28

Then the formula becomes:

=LOOKUP(2,1/((ISNUMBER(FIND(LEFT(INDEX(Item,MATCH(B3,Doc,0)),FIND("-",INDEX(Item,MATCH(B3,Doc,0)))),Item)))/(Dates<>"")),Status)