US3891836A - Apparatus for optimizing multiunit processing systems - Google Patents

Apparatus for optimizing multiunit processing systems Download PDF

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US3891836A
US3891836A US45462074A US3891836A US 3891836 A US3891836 A US 3891836A US 45462074 A US45462074 A US 45462074A US 3891836 A US3891836 A US 3891836A
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feed stream
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Wooyoung Lee
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ExxonMobil Oil Corp
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0205Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
    • G05B13/021Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a variable is automatically adjusted to optimise the performance
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B01PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01JCHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
    • B01J19/00Chemical, physical or physico-chemical processes in general; Their relevant apparatus
    • B01J19/0006Controlling or regulating processes
    • B01J19/0033Optimalisation processes, i.e. processes with adaptive control systems

Abstract

A processing system comprising a plurality of individual units is optimized by first estimating the yields of the individual units at a standard set of operating conditions and then establishing optimum flow rates using a linear programming model or similar mathematical tehniques. Individual units are then controlled and locally optimized consistent with a sensitivity analysis which is performed by treating a proposed change in operating conditions of an individual unit as a disturbance in the unit yield column of the linear programming model. The overall system may then be optimized for the changes in operating conditions by determining and establishing new flow rates. The steps of changing operating conditions and establishing new flow rates may be repeated until the sensitivity analysis reveals that any further change in operating conditions will not further improve the profit of the overall system.

Description

United States Patent Lee June 24, 1975 APPARATUS FOR OPIIMIZING I MULTIUNIT PROCESSING SYSTEMS m ry Examinerloseph F. Ruggiero [75] Inventor: Wooyoung Lee, Cherry Hill, NJ. Anomey' Agem or Flrm c' Huggeu [73] Assignee: all? Oil Corporation, New York. [57] ABSTRACT A processing system comprising a plurality of individl Filed: ual units is optimized by first estimating the yields of A L No; 454,620 the individual units at a standard set of operating con- I pp ditions and then establishing optimum flow rates using Related Application Data a linear programming model or similar mathematical I63] Continuation-in-part of Ser. No. 246,445, April 21, tehniques. Individual units are then controlled and lol972,abandoned. cally optimized consistent with a sensitivity analysis which is performed by treating a proposed change in [52] U-S- Cl. 3 5l-l2; 235/150 /1 operating conditions of an individual unit as a distur- [51] Int. Cl. G06f 15/46; 606g 7/58 bance in the unit yield column of the linear r0 ram- P 8 [58] Field of Seard 235/1501. ming model. The overall system may then be opti- 235/l5l.l2; 444/1 mized for the changes in operating conditions by determining and establishing new flow rates. The steps of [56] References Cited changing operating conditions and establishing new UNlTED STATES PATENTS flow rates may be repeated until the sensitivity analy- 3 075 700 M963 Bishop H 235/150}l sis reveals that any further change in operating condi- 3:079:079 2/1963 p i et a] H 235/1501 tions will not further improve the profit of the overall 320L572 8/1965 Yetter 235/!5] y 3,594,559 7/1971 Pemberton 235M501 X 3,62l,2l7 11/1971 Carr 235/1501 x 18 C|a|m5- 19 D'awmg Figures OVERALL SYSTEM COMPUTER i817 2 T y-1a, r- 7" 7 -1 l l M I 1 I'm a f i LOCAL 2 l I LOAL LOCAL 12, come j I come COMP. UNIT l UNlT UNIT- 1 5 6 lS l 12;, "1| l I j l I 1212 I LOCAL I COMP. D3 l i umt '29 141 i I 3 l i I25 I213 l UNIT l UN" 2 10 I 7 i bg M ii 12 1 I UNIT 1 1 I I2 4 l2 I 4 t\ 5 I L f" J PATENTEI] JUN 2 4 I975 AM 5 mm W m 4 llllll... N M Wm U I, L I MWM W3 E 3 LC 44 Q a a 0 M f I 4 2 PATENTEDJUN24 I975 3.891, 836

SHEET 2 ESTIMATE UNIT COSTS AND YIELDS AT STANDARD OPERATING CONDITIONS Fig Z TRANSMIT COSTS AND YIELDS TO SYSTEM PLANNING /24 SOLVE LP FOR T TRANSMITTED YIELDS TRANSMIT LOCAL /26 OBJECTIVE FUNCTION AND LP SOLUTION TO LOCAL UNITS DETERMINE IF A CHANGE IN YIELD OF UNIT WILL CORRECT SATISFY LOCAL LP OBJECTIVE FUNCTION SOLUTION IF CHANGE SATISFIES LOCAL OBJECTIVE 30 FUNCTION, TRANSMIT TO SYSTEM PLANNING PATENTEDJUN24 I975 3.891.836

SHEET 3 ESTIMATE UNIT COSTS AND YIELDS AT STANDARD SYSTEM PLANNING i /24 SOLVE LP FOR J TRANSMITTED YIELDS TRANSMIT LOCAL 26 OBJECTIVE FUNCTION AND LP SOLUTION TO LOCAL UNITS T Ml FA HANGE I N YI IE LD g T T WILL TRANSMIT CORRECTED SATISFY LOCAL LP SOLUTION TO OBJECTIVE FUNCTION SYSTEM PLANNING IF CHANGE SATISFIES LOCAL OBJECTIVE FUNCTION, CORRECT my 30a LP SOLUTION SOLVE LP AT OVERALL SYSTEM COMPUTER USING ESTIMATED YIELDS CHANGE IN YIELDS WILL SATISFY LO OBJECTIVE FUNCTION DETERMINE IF IF CHANGE SATISFIES LOCAL OBJECTIVE FUNCTIONJRANSMIT CHANGE TO LOCAL UNIT DETERMINE IF LOCAL UNIT CAN MAKE CHANGE IF LOCAL UNIT CAN TO SYSTEM COMPUTER MAKE CHANGE, TRANSMIT CORRECT PATENTEDJuN24 I975 3. 891. 8 36 SHEET 5 OVERALL 54 SYSTEM COMPUTER I 'lg- 4 A 56 56 x! CA /48 i I GASOLINE CRuOE 1 --l FUEL CRUDE 2'---"""" PROCESSNG HEATING OIL CRUDE 3/i/v JET FUEL 3 L 52 CRuOE 4 L 50 LOCAL COMP.

LUBE I PROCESSING l I LUBE OIL Fig 5 A 24 CONSTRAINTMI) 2 x CONSTRAINTMZ) PATENTEI] JUN 2 4 1915 SHEEI SHEET PATENTEDJIJN 24 I975 NEW 300 SIMPLEX MQLTIPLI ERS NEW COSTS NEW BASIS MATRIX liq- I982 202 17 /2002 LT@Q1V SHEET PATENTED JUN 24 I975 lsp SHEET 2|4 CHECK IF c; 20

PATENTEDJUN 24 ms SW TCH NG SHEET PATENTED JUN 2 4 I975 W on w m m m 2 4 a w w w w a m a ll lllllllllllll ll c 8 PATENTEDJUN 24 ms sum 14 13 8 91; 8 36 o o o o c STORE l 11 1 soo STORE Ap 502 COMPUTE SENSITIVITY COEFFICIENTS 5' o 504 5= 1 6 A S1 Em COMPUTE NEW X's o sos J 4 1+ -m COMPUTE NEW INVERSE BASIS MATRIX 5, 50s I o I Q Q g m 0 I1 S -m COMPUTE NEW SIMPLEX MULTIPLIERS 51o 'm 2K S C COMPUTE NEW COST COEFFICIENTS 1 APPARATUS FOR OPTIMIZING MULTIUNIT PROCESSING SYSTEMS RELATED APPLICATION This is a continuation-in-part of copending application Ser. No. 246,445, filed Apr. 21, 1972, now abandoned which is incorporated herein by reference.

BACKGROUND OF THE INVENTION This invention relates to a method for optimizing large, complex processing systems comprising a plurality of individual units.

A number of techniques are available for optimization of such large processing systems. Linear programming is one of the most widely used techniques, and modern refinery complexes are optimized by linear programming almost without exception. However, a linear programming model is at best an approximation of a real physical system. For example, it is commonly assumed that the yield information incorporated into the LP (linear programming model) is relatively fixed and the coefficients of the constraint equations which represent these yields are also fixed. In reality, however, these yield coefficients are dependent upon the operating conditions of the units and any change in the operating conditions for a single unit will of necessity affect the operation of other units.

In many instances, the operating conditions may be closely controlled. Local unit managers have appropriate tools (i.e., mathematical models, optimizers, and process control computers) for the local optimization and control of their individual units. As a result, large amounts of detailed information about the processes are continuously generated which are valuable for accurate adjustment of operating conditions. Each process unit can thus be locally optimized and controlled continuously.

However, any change in operating conditions of a unit which locally optimizes the unit will not necessarily optimize the overall system. In fact, a change in operating conditions which optimizes the local unit may have an adverse effect on the overall system. As a result, changes in operating conditions of the individual units have been discouraged or avoided for fear of the adverse effect on the overall system.

Changes in the operating conditions of individual units have been avoided for another reason. Any attempt to change the operating conditions at an individual unit would necessarily render the LP and its solution obsolete since the yield coefficients in the LP for a particular unit would change. Such a change would therefore require the LP to be solved again and prior art computer techniques for solving LPs are extremely cumbersome and complex. In the case of a digital computer, a great deal of computer time is required to solve an LP, particularly where the LP described a complex processing system.

Because of the foregoing difficulties associated with making the changes in operating conditions in the prior art, individual local objective functions consistent with the overall objective function of the system have been assigned and every effort has been made to maintain those operating conditions at the individual units which will satisfy the local objective functions rather than change to better operating conditions. In other words, no effort is made to deliberately change the operating conditions at the units to optimize the overall system.

Sensitivity analyses such as that disclosed by C. S. Bightler and D. J. Wilde, Hydrocarbon Processing, 44, No. 2, 111 (1965) have been proposed to determine the effect of changes in LP constraints on the operation of a system. However, no specific method has been proposed to take advantage of the sensitivity analysis for changes in the yield coefficients of an LP which optimizes the overall system, i.e., making changes in the operating conditions which will optimize the overall system as indicated by the sensitivity analysis.

SUMMARY OF THE INVENTION It is an object of this invention to provide an improved method of and apparatus for controlling the operation of a processing system including a plurality of individual processing units supplied by a plurality of feed streams of materials being transformed by the units into a plurality of product streams flowing from the units where the marginal product yield and the marginal product cost for each unit are dependent upon the operating conditions.

It is a more specific object of this invention to provide an improved method of and apparatus for controlling the operation of the processing system in a manner so as to encourage and implement changes in operating conditions for the individual units even though those changes do require a change in the linear program model of the processing system.

In accordance with these objects, a preferred embodiment of the invention comprises feed stream computer means for generating initial feed stream signals representing the initial feed stream flow rates for a given yield and cost at each of the units under a given set of operating conditions so as to maximize the profitability of the overall system. Feed stream control means are coupled to the feed stream computer means for controlling the feed stream flow rates in response to the initial feed stream signals. Unit yield and cost computer means generate new yield and cost signals representing new yield and cost for one of the units corresponding to an increase in the profitability of the overall system. Unit control means are coupled to the unit yield and cost computer means for controlling the op erating conditions at the one unit in response to the new yield and cost signals. Another feed stream computer means is coupled to the unit yield and cost computer means for repeatedly and continuously generating new feed stream signals representing new feed stream flow rates in response to the new yield and cost signals. The other feed stream computer means is coupled to the feed stream control means for controlling the feed stream flow rates in response to the new feed stream signals.

It is also a specific object of this invention to provide an improved method of and apparatus for operating and utilizing a linear program model.

In accordance with this specific object, the feed stream computer means includes means for computing the feed stream flow rates x from the linear program model having an overall system objective function of maximizing the profitability.

subject to x +....p x =Q x 2 Ofor alli wherep .Q=

Q is the marginal profit coefficient of the jth unit, x is the flow rate of the ith stream, p j is the yield column of the jth unit and a function of operating conditions, Q is the demand constraint column. a is the yield coefficient of the ith feed stream producing the jth product stream unit, and b,- is the demand coefficient of the ith product stream.

It is another specific object of this invention to assure that all changes in operating conditions at the units improve the overall profitability of the system.

In accordance with this specific object, the unit yield and cost computer means includes means for computing a local objective function where Ac, is the change in the marginal profit coefficient for the mth unit, A is the change in the mth yield column for the mth unit and g" are the simplex multipliers [c. c,,] at the previous operating conditions where Q" is the inverse of the basis matrix in [p,,

- pill- Itis a further specific object of this invention to provide an improved method of and apparatus for correcting the linear program model after permitting a change in operating conditions at one of the operating units.

In accordacne with this specific object, the other feed stream computer means includes means for computing the feed stream flow rates where BRIEF DESCRIPTION OF THE DRAWINGS FIG. 4 is a simplified refinery system operated in accordance with the method of this invention;

FIG. 5 is a graphical solution of a local optimization problem;

FIG. 6 is a block diagram of a processing system operated in accordance with the method depicted in FIG.

FIGS. 7 (a-d) are schematic circuit diagrams of a local computer and process control shown in block form in FIG. 6 where FIG. 7a shows circuitry for computing unit yield and cost coefficients, FIG. 7b shows circuitry for computing the local constraints and the local objective function, and FIGS. 7(c and d) shows circuitry for correcting the linear program model",

FIGS. 8 (a-c) are schematic circuit diagrams of the system computer and control shown in block form in FIG. 6 where FIG. 8a shows circuitry for computing the solution to the linear program model, FIG. 8b shows circuitry for determining the bases in the linear program model and FIG. 8c shows circuitry for controlling the feed stream flow rates to the units;

FIG. 9 is a flow diagram for a programmed digital computer which performs the same correction of the linear program performed by the circuitry of FIGS. 7(0- FIG. 10 is a block diagram of a typical refinery system which is controlled in accordance with this invention;

FIG. 11 is a block diagram of a fluid catalytic cracking unit of the system shown in FIG. 6; and

FIG. 12 is a block diagram depicting the relation and interconnections between the circuit diagrams of FIGS. 7(a-d) and FIGS. 8(ac).

TABLE OF CONTENTS FOR THE DETAILED DESCRIPTION I. Complex Processing System Employing Invention II. Method of Operating Complex Processing System III. General Description of a Simple Processing System IV. Detailed Description of the Simple Processing System Including Analog Computer Control A. Computing Yield and Cost Coefficients at the Local Computer B. Computing an LP Solution at the System Computer C. Computing the Bases of the LP Solution at the System Computer D. Setting the Flow Rate Controls E. Computing and Storing the Inverse Basis Matrix F. Computing the Simplex Multipliers G. Checking Local Optimization H. Checking Local Constraints I. Checking the Local Objective Function j. Correcting the LP Solution 1. Computing Sensitivity Coefficients 2. Computing New X's 3. Computing New Basis Matrix 4. Computing New Simplex Multipliers 5. Computing New Cost Coefficients V. Control of the Simple Processing System with a Digital Computer A. Correction of the LP B. Computing the Local Objective Function VI. Numerical Examples VII. Method of Operating a Complex Refinery System. VIII. Modified Method of Operating a Complex System.

Claims (18)

1. Apparatus for controlling the operation of a processing system including a plurality of individual processing units supplied by a plurality of feed streams of materials being transformed by the units into a plurality of product streams flowing from the units, the product yield and the product cost or profit for each unit being dependent upon the operating conditions of the unit, said apparatus comprising: feed stream computer means for generating initial feed stream signals representing the initial feed stream flow rates for a given yield and cost at each of the units under a given set of operating conditions so as to maximize the profitability of the overall system; feed stream control means coupled to said feed stream computer means for controlling the feed stream flow rates in response to said initial feed stream signals; unit yield and cost computer means for repeatedly and continuously generating new yield and cost signals representing new yields and costs at one of the units corresponding to an increase in the profitability of the overall system; unit control means coupled to said unit yield and cost computer means for controlling the operating conditions at said one of said units in response to said new yield and cost signals; and another feed stream computer means coupled to said unit yield and cost computer means for repeatedly and continuously generating new feed stream signals representing new feed stream flow rates in response to said new yield and cost signals; said other feed stream computer means being coupled to said feed stream control means for controlling the feed stream flow rates in response to said new feed stream signals.
2. The apparatus of claim 1 wherein said feed stream computer means and said other feed stream computer means comprise an overall system computer and said yield and cost computer means comprises a local computer located at said one unit and remote from said system computer, said system including means for transmitting said new yield and cost signals from said local computer to said system computer.
3. The apparatus of claim 1 wherein said feed stream computer means comprises an overall system computer and said yield and cost computer means and said new feed stream computer means comprises a local computer located at said one unit and remote from said system computer, said apparatus including means for transmitting said new feed stream signals from said local computer to said system computer.
4. The apparatus of claim 1 wherein said feed stream computer means, said new feed stream computer means and said yield and cost computer means comprises an overall system computer, said apparatus comprising means for transmitting said new yield and cost signals from said system computer to said unit control means.
5. The apparatus of claim 1 wherein said feed stream computer means includes means for computing the initial feed stream flow rates in accordance with the linear program model having an overall system objective function of maximizing the profitability Z c1x1 + . . . . cnxn subject to p1x1 + . . . . pnxn Q xi > or = 0 for all i where pj
6. The apparatus of claim 5 wherein said unit yield and cost computer means includes means for automatically computing a local objective function for said one unit, said local objective function defining changes in product yield and product cost or profit for increasing the profitability of the overall system.
7. The apparatus of claim 6 wherein said means for automatically computing the local objective function computes the local objective function fm ( Delta cm - pi * Delta pm) > 0 where Delta cm is the change in the marginal profit coefficient for the mth unit, Delta pm is the change in the mth yield column for the mth unit and pi * are the simplex multipliers (c1 ...cn) Beta * at the previous operating conditions where Beta * is the inverse of the basis matrix in (p1...pn).
8. The apparatus of claim 7 wherein said other feed stream computer means includes means for computing said new feed stream flow rates
9. An apparatus for controlling the operation of a processing system including a plurality of individual processing units supplied by a plurality of feed streams of materials being transformed by the units into a plurality of product streams flowing from the units, a plurality of local control means associated respectively with the units, each of the local control means including condition control means responsive to condition control signals generated by the local control means for controlling the operating of each unit, and central control means including flow rate control means associated with each of the feed streams and responsive to flow rate control signals generated by the central control means, the product yield and the product cost or profit of each unit being dependent upon the operating conditions of each unit, said apparatus comprising: means for automatically computing the initial feed stream flow rates for a given product yield and a given product cost at each of the units so as to maximize the profitability of the overall system, said central control means generating initial flow rate control signals in response to the computed initial feed stream flow rates and applying the initial flow rate control signals to the flow rate control means to establish the initial feed stream flow rates; means for substantially continuously and automatically computing a new product yield and new product cost or profit for at least one of the units corresponding to an increase in the profitability of the overall system, said local control means associated with said one unit substantially continuously generating new condition control signals corresponding to the new computed product yield and the new product cost or profit and applying the new condition control signals to the condition control means associated with said one unit to establish new operating conditions; and means for substantially continuously and automatically computing new feed stream flow rates for all of the feed streams in response to the new product yield and the new product cost or profit for said one unit so as to maximize the profitability of the overall system, said central control means substantially continuously generating new flow control signals representing new feed stream flow rates and applying the new flow rate signals to the flow rate control means of the feed streams to establish the new feed stream flow rates.
10. The apparatus of claim 9 wherein said means for automatically computing the new product yield And the new product cost or profit are located at the local control means associated with the unit; said apparatus further comprising means for generating signals representing the new product yield and the new product cost or profit at the local control means; and means for transmitting the signals representing the new product yield and the new product cost or profit to said central control means.
11. The apparatus of claim 9 further comprising: means for substantially continuously and automatically computing local objective functions for each of the units at the local control means, said local objective functions defining changes in product yield and product cost or profit for increasing the profitability of the overall system; said means for substantially continuously and automatically computing the new product yield and the new product cost or profit being located at the local control means and being responsive to and consistent with the local objective function of said one unit.
12. The apparatus of claim 11 wherein said means for automatically computing feed stream flow rates operates so as to satisfy and be consistent with a linear program model having an overall objective function of maximizing the profitability Z c1x1 + .... cnxn subject to p1x1 + .... pnxn Q xi > or = 0 for all i where pj
13. The apparatus of claim 9 further comprising: means for substantially continuously and automatically computing local objective functions for each of the units at the central control means, said local objective functions defining changes in product yield and product cost or profit for increasing the profitability of the overall system; and said means for substantially continuously and automatically computing the new product yield and the new product cost or profit being located at the central control means and being responsive to and consistent with the signals representing the local objective function of said one unit
14. Apparatus for controlling a processing system including a plurality of individual processing units supplied by a plurality of feed streams of materials being transformed by the units into a pluraliTy of product streams flowing from the units, said system being characterized by a linear program model having an overall objective function of maximizing the profitability Z c1x1 + .... cnxn subject to p1x1 + .... pnxn Q where cj is the marginal profit coefficient of the coefficient jth unit, pj is a column vector of yield coefficients for the jth unit and the function of operating conditions of said jth unit, Q is a column vector of demand constraints on the product streams and xi is the flow rate of the ith feed stream, said system comprising: unit control means for controlling the operating conditions of said individual units; first computing means coupled to said unit control means for computing yield coefficients and profit or cost coefficients for each jth unit at a given set of operating conditions; second computing means for computing the flow rate xi for each said ith stream so as to maximize the profitability Z for the computed yield coefficients and profit or cost coefficients for each said jth unit at said given set of operating conditions; feed stream control means coupled to said second computing means for controlling the flow rate of materials in said feed streams; and third computing means coupled to said first computing means for computing a new flow rate xi1 for each said ith feed streams so as to maximize the profitability Z for a change in operating conditions at the mth one of said units, said change in operating conditions being represented by a substituted vector column pm1 for said mth unit and a substituted cost coefficient cm1, said third computing means comprising: first storage means for storing signals representing each flow rate xi* at a given set of operating conditions; second storage means for storing signals representing the change in yield coefficients Delta pm and a change in cost coefficients Delta cm at said mth unit; third storage means for storing signals representing the inverse basis matrix Beta * of the basis matrix Beta * of the vector columns pj* at the given set of operating conditions; means coupled to said second storage means and said third storage means for generating signals representing s Beta * Delta pm; and means coupled to said first storage means and said means for generating said s signals for generating signals representing
15. The apparatus of claim 14 further comprising fourth computing means coupled to said first computing means for determining the change in operating conditions for said mth unit so as to satisfy the local objective function fm cm -pi * pm thereby maximizing the overall profitability of the system.
16. Apparatus for controlling a processing system including a plurality of individual processing units supplied by a plurality of feed streams of materials being transformed by the units into a plurality of product streams flowing from the units, said system being characterized by a linear program model having an overall objective function of maximizinG profitability Z c1x1 + .... cnxn subject to p1x1 + .... pnxn Q where cj is the marginal profit coefficient of the jth unit, pj is a convector of yield coefficients for the jth unit and a function of operating conditions of said jth unit, Q is column vector of demand constraints on the product streams and xi is the flow rate of the ith feed stream, said apparatus comprising: means for controlling the operating conditions at the local unit so as to correspond to column vectors pj for a given set of operating conditions at each unit; means for controlling the feed stream flow rates xi to the local units so as to satisfy the overall objective function Z; and means for computing the new feed stream flow rates xi1 to replace old feed stream flow rates x*i after a change in operating conditions at the mth unit resulting in the substitution of a new yield column vector pm1 for an old yield column vector pm1 and a new cost coefficient cm1 for an old cost coefficient c*m comprising: first storage means for storing signals representing each flow rate x*i at a given set of operating conditions; second storage means for storing signals representing the change in yield coefficients Delta pm and a change in cost coefficients Delta cm at said mth unit; third storage means for storing signals representing the inverse basis matrix Beta * of the basis matrix Beta * of the vector columns p*j at said set of operating conditions; means coupled to said second storage means and said third storage means for generating signals representing x Beta * Delta pm; and means coupled to said first storage means and said means for generating said si signal for generating signals representing
17. The apparatus of claim 13 wherein said means for automatically computing feed stream flow rates operates so as to satisfy and be consistent with a linear program model having an overall objective function of maximizing the profitability Z c1x1 + .... cxn subject to p1x1 + .... pnxn Q xi > or = 0 for all i where pj
18. The apparatus of claim 1 wherein said unit yield and cost computer means includes means for automatically computing a local objective function for said one unit, said local objective function defining changes in product yield and product cost or profit for increasing the profitability of the overall system.
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