Job-shop resource scheduling via simulating random operations

We are concerned with a problem of scheduling a flexible manufacturing cell with random time operations. A job-shop production section comprises a set of n jobs (orders) and a set of m machines (processors). Each order consists of a chain of operations, each of which needs to be executed during an uninterrupted period on a given processor. Each operation is carried out under random disturbances. For each order, its due date and the probability of meeting the deadline on time are pregiven. Orders are of different importance and a priority index has to be set for each order by the management, i.e. by practitioners who are responsible for the job-shop. Certain operations need additional resources to be delivered beforehand (equipment, experimental stations, etc.) to process these operations. The problem is to obtain a deterministic schedule for feeding-in those resources which guarantees, with a chance constraint, that each order can meet its due date on time. Developing such a schedule will prevent the premature feeding-in of costly resources. A heuristic algorithm is developed that comprises two stages. At the first stage, upper bounds of time moments of feeding-in resources are determined on the basis of providing for each order an additional time interval to obtain for that order a new due data which is shifted to the left on the time axis. In this way, we obtain an analogue of the chance constraint. At the second stage, an optimal schedule of feeding-in resources is developed. This is carried out via simulation. A numerical example is presented.