Scheduling and control for a failure prone system of open shop with job overlaps

In most classical multi-operation scheduling and control models, an assumption that different operations of a given job cannot be processed simultaneously is usually accepted. But in real-life applications, many different circumstances exist (i.e., with job overlaps). When overlapping of jobs is permitted, the paper reduces the complex problem of scheduling production of N types of products, each with n jobs, in an open shop with m unreliable machines, into simpler problems. The paper extends the application of a flow model on infinite horizon, of a single failure prone machine to build a system model of from orders arriving to completion of productions on infinite horizon, of a single failure prone machine to build a system model from orders arriving to completion of productions of finite horizon. After presenting an asymptotic optimal scheduling policy, based on discussing the model of the system, the optimal control production policy, etc., the paper presents the production planning of the system and its new heuristic iterative algorithm to determine the selection of setup times and the production order of products, etc.