  Coffman and Sethi proposed a heuristic algorithm, called LD, for
multi-processor scheduling, to minimize makespan over flowtime-optimal
schedules. LD algorithm is a natural extension of a very well-known list
scheduling algorithm, Longest Processing Time (LPT) list scheduling, to our
bicriteria scheduling problem. Moreover, in 1976, Coffman and Sethi conjectured
that LD algorithm has precisely the following worst-case performance bound:
$\frac{5}{4} - \frac{3}{4(4m-1)}$, where m is the number of machines. In this
paper, utilizing some recent work by the authors and Huang, from 2013, which
exposed some very strong combinatorial properties of various presumed minimal
counterexamples to the conjecture, we provide a proof of this conjecture. The
problem and the LD algorithm have connections to other fundamental problems
(such as the assembly line-balancing problem) and to other algorithms.
