Partially-Concurrent Open Shop Scheduling

The partially-concurrent open shop scheduling problem is presented. The standard open shop scheduling problem is generalized by allowing some operations to be processed concurrently. This generalization is directly motivated from a real-life timetabling project of assigning technicians to airplanes in an airplane garage. A schedule for the partially-concurrent problem is represented by a digraph. We show that the scheduling problem is equivalent to a problem of orienting a given undirected graph, called a conflict graph. The schedule digraph is then modeled by a matrix, generalizing the rank matrix representation. The problem is shown to be NP-Hard. The rank matrix representation is also used in an algorithm that heuristically constructs an open shop schedule.