A simulation factory control model under a chance constraint

A control model for a three-level man–machine production system under random disturbances is considered. The system comprises the factory level, several sections and multiple production units. The factory is faced with manufacturing several different products with planned target amounts at the given due date. Each unit can manufacture all kinds of products by utilizing different types of renewable resources. In order to introduce control actions all production units have to be inspected at control points to observe the output of the products. The problem is to develop control models at each production level, in order to minimize the factory’s average total expenses under a chance constraint. The optimal variables are the starting time of the manufacturing process and the capacities of all types of resources to be hired throughout the planning horizon. Two models are developed at the factory level: a search coordinate descent model for optimized variables and the reallocation model to redistribute both the resources and the planned target among the sections. At the section level a hierarchical “tree” of optimal reallocation models to redistribute both the resources and the target amounts among the subordinated elements at the adjacent lower level will be considered. At the unit level control actions boil down to determining control points and production speeds. All the developed optimal control models are imbedded in a three-level simulation model which provides representative statistics in order to check the fitness of the developed factory model. A numerical example based on simulation is presented. Practical applications on a real man–machine plant are outlined.