A generalized control model for man-machine production systems with disturbances

Abstract

A control model for a two-level man-machine production system is considered. The system comprises a section and several production units. Within the planning horizon the section is faced with manufacturing several different products with planned target amounts. Each unit can manufacture all kinds of products. In the course of manufacturing, each unit utilizes different types of non-consumable resources which may be reallocated among the units. Each production unit can manufacture a product at several possible speeds which correspond to one and the same resource capacities. Those speeds depend only on the degree of intensity of manufacturing and are subject to random disturbances. To carry out the process of manufacturing, the products have to be rescheduled among the units. This means that for each unit and for each product assigned to that unit the corresponding planned amount and the planning horizon have to be determined. Controlling the system is carried out at two levels: the section level and the unit level. At the unit level all production units are controlled separately. For each unit and for each product manufactured by that unit decision-making centers on determining: (i) control points to observe the product's output; (ii) the speeds to manufacture the product. If at a routine control point it is anticipated that a unit is unable to meet its deadline on time, emergency is called. The section level is then faced with the problem of both resource and target amount reallocation among the units. New resource capacities and target amounts for each product and each production unit are decision variables to be determined. The objective is to maximize the probability of the slowest unit to accomplish the planned amounts of its products by the due date. The problem is too difficult to obtain a precise or even an approximate solution. Heuristic algorithms are outlined on both levels. The model's performance is verified via extensive simulation.