AbstractSuppose a given set of jobs has to be processed on a multi‐purpose facility which has various settings or states. There is a choice of states in which to process a job and the cost of processing depends on the state. In addition, there is also a sequence‐dependent changeover cost between states. The problem is then to schedule the jobs, and pick an optimum setting for each job, so as to minimize the overall operating costs.A dynamic programming model is developed for obtaining an optimal solution to the problem. The model is then extended using the method of successive approximations with a view to handling large‐dimensioned problems. This extension yields good (but not necessarily optimal) solutions at a significant computational saving over the direct dynamic programming app