Applying Circular Coloring to Open Shop Scheduling

In this paper, a new approach to formulate a class of scheduling problems is introduced, whichcan be applied to many other discrete problems with complicated structures. the conceptof graph circular coloring is applied to develop a model for the special case of an open shopscheduling problem. in this problem, there are some independent jobs to be processed in ashop with dedicated renewable resources. each job consists of several tasks with no precedencerestriction. each task is processed without preemption. the processing time of the tasks is given.processing each task requires using some multiple specified types of resource, while no more thanone task can use each resource, simultaneously. some tasks can be shared by more than one joband the process may be repeated more than once. the objective is to develop a schedule whichyields the minimal makespan length of all jobs, as well as the number of cycles. the model is firstdeveloped for cases when the processing time of each task is one unit and, then, it is generalizedby relaxing this restriction. in both cases, a circular coloring formulation is shown in comparisonwith traditional formulation (single process execution) results in an improved makespan and alsothe required information regarding the optimum number of cycles to repeat the process.