Hierarchical control of semi-automated production systems

An integrated control model of a hierarchical production system is presented where the output can be measured only at preset control points as it is impossible or costly to measure it continuously. Three levels are considered—company, section, production unit—each level faces stochastic optimization problems. Each unit produces a given target amount by a given due date (common to all units) and has several possible speeds, which are subject to disturbances. On the unit level, at each control point, decision-making centres on determining both the next control point and the speed to proceed with up to that point. The section level is faced with problems of either reallocating resources among the section's units or reassigning the remaining target amounts among the units so that the faster one will help the slower one. The company level is faced with similar problems, i.e. reallocating resources or reassigning target amounts among the sections. Two different cases are considered: (1) cost parameters are not taken into account, i.e. there are two conflicting objectives, namely to maximize the probability of completing the production on the due date and to minimize the number of control points, but the first objective is dominant; (2) the objective is to maximize the expected net profit. Various optimization problems at each level are presented. Examples from steel, construction and mining industries are given.