Applying Circular Coloring to Open Shop Scheduling


Department of Industrial Engineering,Sharif University of Technology


IN this paper, a new approach to formulate a class of scheduling problems is introduced, which
can be applied to many other discrete problems with complicated structures. The concept
of graph circular coloring is applied to develop a model for the special case of an open shop
scheduling problem. In this problem, there are some independent jobs to be processed in a
shop with dedicated renewable resources. Each job consists of several tasks with no precedence
restriction. Each task is processed without preemption. The processing time of the tasks is given.
Processing each task requires using some multiple speci ed types of resource, while no more than
one task can use each resource, simultaneously. Some tasks can be shared by more than one job
and the process may be repeated more than once. The objective is to develop a schedule which
yields the minimal makespan length of all jobs, as well as the number of cycles. The model is rst
developed for cases when the processing time of each task is one unit and, then, it is generalized
by relaxing this restriction. In both cases, a circular coloring formulation is shown in comparison
with traditional formulation (single process execution) results in an improved makespan and also
the required information regarding the optimum number of cycles to repeat the process.