A UNIFIED HIERARCHICAL CONTROL ALGORITHM FOR CONSTRAINED NONLINEAR MULTI-DELAY INTERCONNECTED SYSTEMS: APPLICATION TO PRODUCTION PLANNING

摘要

In this paper, a hierarchical control algorithm is presented which unifies several previous algorithms in an effective way so as to handle the problem of constrained, non-linear, multi-delay interconnected systems in its most general form. A class of application models that fall within this category are integrated production planning models, which involve distributed time delays and constraints on both the state and decision variables. These problems are very difficult to solve by centralized optimal control methods even when their dimensionality is very small. Therefore, various hierarchical control optimization algorithms have been developed in the literature by invoking the costate prediction principle which can only partially deal with the problem. For completeness, the paper provides a brief overview of the previous work on the nonlinear hierarchical control problem, as well as a summary of the related production planning literature that deals with the problem of modifying the current production capacity level through R & D expenditures or automation acquisition and modernization. The paper develops an enhanced integrated model, which includes automation acquisition for improving the productivity of labor with inventory and marketing considerations. The unified algorithm of the paper is applied to this model, and a sensitivity study is carried out that reveals the dynamic interactions of the intrisic components of the model. The managerial implications are also discussed. It thus become clear that the present unified model and optimization technique can be of invaluable help to decision makers for evaluating and testing alternative corporate strategic plans.