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LP technology
Block Convey Flow
Diverge
Interchange
Merge Tank
Calculation
If the block is in an accumulating situation (outflow rate is blocked or partially blocked downstream) and doesn't have any more capacity for accumulation, a state sensitive boundary applies: Xin<=Xout
Select. A permanent relational constraint applies between the inflow effective rate and the selected outflow effective rate: Xin=Xout selected
Proportional. A set of permanent relational constraints applies to insure the pro- portions: Xout_i = factor_i*Xin (i: 0=>n-1)
Batch/Unbatch. Permanent relational constraints: Xout_i = Xin (i: 0=>n-1)
Neutral, Priority, Distributional and Supply Sensing. Permanent relational con- straint Xin = Xout_1+...... Xout_n
(Other calculations are beyond the scope of this document.)
As long as the tank is full, Xin<=Xout. As long as the tank is empty, Xout<=Xin (State sensitive relational constraint)
Same as the Diverge with Xout and Xin reversed See Interchange
The LP calculation
The Executive block maximizes an objective function composed of the set of effective rates for the LP area. If there is no block with bias order involved in the LP area, the Executive block maximizes the sum of all the effective rates in the LP area – in this case, only one LP calcula- tion is necessary.
If the blocks in the LP area have bias, the Executive must determine multiple intermediate objective functions and the Solver must perform multiple intermediate calculations. The num- ber of recalculations is equal to the number of blocks with bias plus 1.
When the LP area involves blocks with bias order, the calculations are made in cascading order. For each bias order, an intermediate calculation is made with an objective function depending on the type of block that is being evaluated:
• Biasblock.ThefunctiontomaximizeisthesumoftheeffectiveratesattachedtotheBias blocks with an identical bias order. When the calculation is made, the function is used as a new rule for the succeeding intermediate calculations. The calculation is: sum effective rates within the bias order>= result of the maximized function.
• Merge/DivergeinPrioritymode.Thefunctiontobemaximizedcontainstheeffectiverates from the variable inflow and/or outflow branches of the block. The lower the priority of the branch, the higher the coefficient associated with the effective rate. The calculation is: sum p*Xp (for p: 1=>n with 1 top priority and n lowest priority). When the calculation is fin- ished, the objective function is used as a new rule for the next intermediate calculations (sum p*Xp >= result of the maximized function).
• Merge/Diverge in Batch/Unbatch, Distributional, Neutral, Proportional, Select, or Sensing mode. This calculation is beyond the scope of this document.
When all the intermediate LP calculations have been made, the last LP calculation maximizes the sum of all the effective rates for the LP area.
Discrete Rate

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