An Example of Loosely Coupled Stages in Dynamic Programming

This paper considers the problem of determining which jobs, of a specified set, should be done in a given week, and whether or not nonnormal working time arrangements should be used. Such arrangements are more expensive in the sense that plant has to be kept going under undesirable conditions, but, on the other hand, delaying work until the next week will influence the mix of work in that week and hence the economics of operation in that week. There is an interaction between weekly work schedules, which is resolved by means of dynamic programming. The extent of coupling between weeks depends on the extent of overspill from one week to the next. The dynamic programming approach shows how the existence of a small level coupling may be used to reduce the computational load. In very loosely coupled systems the problem reduces to a simple two-stage problem. In uncoupled systems the problem reduces to a single-stage problem.