Scheduling with Deadlines and Loss Functions on k Parallel Machines

An optimal schedule is developed for H jobs on K identical machines in single stage production. The optimal schedule minimizes \sum b[max (0, A_i - d_i)] where A_i is the actual completion time for job i and d_i is the deadline for job i. A common deadline, t₀, is assumed for all jobs, i.e., d_i - t₀, i - 1, ..., H.