Decision unit

The basic building block in the definition of a complex system, as well as the key element in our learning architecture, is what we will designate as an infimal decision unit or subsystem (Mesarovic et al., 1970 Findeisen et ai, 1980), (Fig. 10). These decision units will in general correspond to a particular piece of equipment or section of the plant. The overall system is represented by a single supremal decision unit (Mesarovic et al., 1970 Findeisen et al., 1980), DUq, and contains a total of K interconnected infimal decision units (Fig. 11), DU., k = l,...,K. 

For each of the infimal decision units, °oe has to consider several groups of input and output variables (Fig. 10). Among the inputs are... 

Fig. 11. Complex system as a sequence of infimal decision units.

As final solution formats, interval vector decision policies, X p, replace their pointwise counterparts, x p. Thus, a decision policy, Xpp, in the context of this section is an interval vector whose components are intervals of decision variables associated with one or more of the infimal decision units. No connection variables or disturbance factors are involved in their definition ... 

Our search procedures represent a departure from the above type of paradigm. Rather than simply accepting and implementing a decision policy found by DUg, that optimizes an overall measure of performance, the infimal subsystems and corresponding plant personnel play an active role in the construction and validation of solutions. One tries to build a consensus decision policy, Xpp, validated by all subsystems, DU , k = I,..., K, as well as by the whole plant, DUg, and only when that consensus has been reached does one move toward implementation. Within this context, the upper-level decision unit, DUg, assumes a eoordination role. 

To declare a decision policy, Xp,p, as either unacceptable, acceptable or leading to a significant improvement, each decision unit compares its current levels of performance with the ones that are expected within X p. The current levels of performance for unit k are provided by the (y lXcurrent) d estimates obtained from a sample of data records, just as in the case of (y,(. Xj3p) and crfy lXop). A comparison of these reference performance values for Xcu em " ilh the ones achieved by Xpp is made by each decision unit. As a result of this comparison, a final evaluation of Xp,p by decision unit k leads to one of the three possible outcomes ... 

In the bottom-up approach the initiative to start the learning process is taken by one of the infimal decision units. Since solutions found at this unit may include connection variables, the request for given values of these variables is propagated backward, to unit A + 1, through temporary loss functions. After successive backpropagation steps, the participation of several other fhe operators associated with them, a final decision... 

On the other hand, the top-down approach starts the learning process at the supremal decision unit, DUq, and only on a second stage does it move down to the infimal decision units for approval and validation. 

The process of X p validation and refinement starts with a final detailed analysis of its realization, through the computation of (yj. XDp) and o (y Xup), k = 0,l,...,K, estimates. If for some reason one or more infimal decision units judge the implementation of X p to be unacceptable, an additional attempt is made to refine the decision policy and find a revised version of it, X p, that is accepted and validated by all infimal decision units, through additional applications of basic to the decision units in conflict with the initial X p version (see Saraiva, 1993 Saraiva and Stephanopoulos, 1992d, for details). 

Once agreement and consensus have been reached by all infimal decision units, for X p to be declared an active decision policy, it is necessary to bring it to the attention of DUq. The effects of a possible implementation of Xdp on the system as a whole are examined, to check that it also translates into improved performance from a global perspective. If this final validation test is passed, X p represents an active decision policy, and one can proceed to its implementation. 

In the top-down approach the supremal decision unit, DUq, starts the learning process by itself, and identifies a decision policy, X p. Then, in a... 

Let s assume that the inputs to the supremal decision unit are a subset of all the decision variables attached to infimal decision units, consisting of those variables that are believed to be particularly influential with respect to the operation of the overall system. Then, an application of basic to DUj, results directly in the identification of a decision policy, X p. This decision policy is then passed down to the lower level in the hierarchy, where it is submitted to a process of validation and refinement by all infimal decision units that is identical to the one that takes place in the bottom-up approach. 

Both operating costs and quality losses were combined together, leading to the following overall performance measure, yg, for the supremal decision unit ... 

The learning process was initiated at the top-digester infimal decision unit, leading to a solution, Xjj, that involves local decision variables and a range of white liquor sulfidity (fraction of active reactants in the white... 

Barr Court Decision, United States of America, Plaintiff, v. Barr Laboratories, Inc., et al. Defendants, Civil Action No. 92-1744,1992. 

In the 1936 decision United States v. Butler m the US Supreme Court (SC) confirmed the federal power to tax for the purpose of providing funds for payment of the nation s debts and making provision for the general welfare (297 US 1, 56, 64 ff). Before this revolutionary decision, the constitutionality of a federal UI programme was in question. This may be one reason for the institutional design of the US UI system (namely a federal-state partnership) and the federal unemployment tax system.41... 

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