The Total Weighted Completion Time \(\big(\sum w_j C_j\big)\)

WSPT Algorithm

Note

The problem \(1\| \sum C_j\) is a special case of \(1\| \sum w_j C_j\) with weights \(w_j = 1\). Thus, SPT is the same as WSPT when \(w_j = 1\), allowing us to focus on \(1\| \sum w_j C_j\).

Independence jobs (show_mytime)

Info

The symbol for the problem is \(1 \: | \: \: | \: \sum w_j C_j\)

Sequence jobs

Info

The symbol for the problem is \(1 \: | \: prec \: | \: \sum w_j C_j\)

Release jobs

Info

The symbol for the problem is \(1 \: | \: r_j \: | \: \sum w_j C_j\)