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<br /> <br />"h <br /> <br />tv <br />00 <br /> <br />t; find: min [~~t > 0, t = 1,2" . ., T] ................(23~<: <br /> <br />Once these maximums and minimums have'been selected, the .,; <br />f r:. <br />next item is to compare them with each other and select the <br />largest absolute valued one. After having made the choice, the <br />index on the specified decision or slack variable is now denoted <br />by a "p", and these variables now become dp or <Pp depending on <br />the decision among alternatives. <br /> <br />Because the particular decision variable or slack variable <br />to be modified has been selected, the remaining decisions and <br />slacks will remain constant and can therefore be temporarily <br />ignored. ~he next computation necessary is to determine which <br />of the boundaries of the problem are approached first. If the <br />non-negativity constraints on the variables are in effect, one <br />consideration is how far a decision or slack variable can be <br />moved without forcing a state variable to become negative. In <br />order to accomplish this, the constrained derivatives of each <br />state variable with respect to the particular decision or <br />slack variable are computed using Cramer I s rule on the matrix <br />of system derivatives. From these values, the maximum move may <br />be computed. Writing the appropriate relationships in discrete <br />form, <br /> <br />Determining the Step Size -- <br /> <br /> v s.o) ( ~:~r <br /> (s. - = <br /> :L :L <br />or for the slack variables: <br /> v s.o) (::~r <br /> (s. - = <br /> :L :L <br /> <br />, <br />. <br />,1 <br /> <br />I <br />,'-j <br /> <br />~ <br /> <br />~ <br />~ <br /> <br />(dpV _ dpO) <br /> <br />, . . , . . . . . , . . . . . . . . (24) <br /> <br />v <br /><Pp ..'..................,........ (25) <br /> <br />Three cases exist in which a state variable can be driven to <br />zero, namelV a decrease in dp' an increase in d , and an <br />increase (or loosening) in <Pp' Since a search i~ necessary <br />among the state variables to see which specific state goes to <br />zero first, Eqs. 24 and 25 can be incorporated: <br /> <br />Case l. <br /> <br />Fe:"~;;;; <br /> <br />d v= <br />P <br /> <br />max <br /> <br />,,L <br /> <br />os. <br />:L <br />8d <br />p <br /> <br />> 0] ................. (261 <br /> <br /> <br />l5 <br />