Stable Earliest Starting Schedules for Cyclic Job Shops: A Linear System Approach

We consider a cyclic job shop where an identical mixture of parts of different types, called a minimal part set (MPS), is produced repetitively in the same processing order. The precedence relationships among events (start of operation) are represented by a directed graph that has a recurrent structure. Each operation starts as soon as all its preceding operations are complete (called earliest starting). There is a class of desirable schedules that has the minimum cycle time and an identical schedule pattern for every MPS. By using linear system theory on minimax algebra, we characterize the set of all possible such schedules. We develop an efficient algorithm to find one among such schedules that minimizes a performance measure related to work-in-progress inventory. We also discuss an application to a flexible manufacturing system.