The.Algorithm.Design.Manual.Springer-Verlag.1998

Job Scheduling
An even more general formulation seeks critical paths in networks where certain jobs are restricted to
certain people. Such networks are known as disjunctive networks. Finding critical paths on such
networks is more complicated than CPM/PERT, but implementations are described below.
In any sufficiently large and sufficiently real scheduling application, there will be combinations of
constraints that are difficult or impossible to model using these techniques. There are two reasonable
ways to deal with such problems. First, we can ignore enough constraints that the problem reduces to one
of the types that we have described here, solve it, and then see how bad it is using the other constraints.
Perhaps the schedule can be easily modified by hand to satisfy constraints like keeping Joe and Bob apart
so they can't kill each other. Another approach is to formulate your scheduling problem via linear-integer
programming (see Section ) in all its complexity. This method can be better only if you really know
enough about your desired schedule to formulate the right linear program, and if you have the time to
wait for the program to give you the solution. I would start out with something simpler and see what
happens first.
Another fundamental scheduling problem takes a set of jobs without precedence constraints and assign
them to identical machines so as to minimize the total elapsed time. Consider a copy shop with k Xerox
machines and a stack of jobs to finish by the end of the day. Such tasks are called job-shop scheduling.
They can be modeled as bin-packing problems (see Section ), where each job is assigned a number
equal to the number of hours it will take and each machine is represented by a bin with space equal to the
number of hours in a day.
More sophisticated variations of job-shop scheduling provide each task with allowable start and required
finishing times. Effective heuristics are known, based on sorting the tasks by size and finishing time. We
refer the reader to the references for more information. Note that these scheduling problems become hard
only when the tasks cannot be broken up onto multiple machines or interrupted (preempted) and then
rescheduled. If your application has these degrees of freedom, you should exploit them.
Implementations: Pascal implementations of Balas's algorithm for disjunctive network scheduling and
Hu's algorithm for assigning jobs to processors with precedence constraints appear in [SDK83]. See
Section .
Algorithm 520 [WBCS77] of the Collected Algorithms of the ACM is a Fortran code for multiple-
resource network scheduling. It is available from Netlib (see Section ).
Notes: The literature on scheduling algorithms is a vast one. For a more detailed survey of the field, we
refer the reader to [Cof76, LLK83].
Good expositions on CPM/PERT include [Eve79a, Law76, PGD82, SDK83]. Good expositions on job-
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