A Network Flow Model for Job-Shop Scheduling Problem with Time-Windows

In this paper, we discuss generalized Job-shop Scheduling Problem with Time-windows, in which machines are distinguished, each job has to be started and finished within a given time window and the goal is to minimize the cost of processing. By indexing all the time dots of starts and ends of time windows, and describing them as nodes, the Job-shop Scheduling Problem with Time-windows is transformed into a network flow problem. Furthermore, an 0-1 integer programming mathematical model is built and a simulated annealing algorithm is given for solution.