Lookup or SUMIF ??

You can use SUMPRODUCT

F1: =SUMPRODUCT(--($A$1:$A$10=$D$1),--($B$1:$B$10=$E$1))

Where A holds dates and D1 holds criteria, and B holds shift & E1 holds criteria.

(If using XL2007 you can use COUNTIFS but this is not backwards compatible)

An alternative would be to create a concatenation key at source, eg:

C1: =$A1&":"&$B1
copied down to C10

You can then dispense with array use traditional COUNTIF utilising the new concatenation column - this is arguably preferable method to Sumproduct ... more so with big models...

F1: =COUNTIF($C$1:$C$10,$D$1&":"&$E$1)

EDIT

To SUM if we assume we insert a column such that A holds date, B holds Shift & C holds values to sum .. criteria values are moved to E1 (date) & F1 (shift) then:

SUMPRODUCT approach:

=SUMPRODUCT(--($A$1:$A$10=$E$1),--($B$1:$B$10=$F$1),$C$1:$C$10)

Using concatenation where D holds concatenation of A & B, SUMIF approach:

=SUMIF($D$1:$D$10,$E$1&":"&$F$1,$C$1:$C$10)