solution. Experience has shown, however, that linear programming on a computer
is by far the most economic approach to solving this type of problem. By this
method, most of the many possible solutions can be examined quickly and effectively. Before discussing the solution approach used in this study, let us quickly
review the investment environment for any typical refinery unit. This is illustrated
in a simplified form in Fig. 19.
The total cost curve, on linear graph paper, shows that as a volume throughput is
increased, the total cost of a unit will increase. However, the plot of unit volume
cost ($/BPCD) against throughput shows the reverse; that is, the cost per unit of
throughput will decrease as the volume of throughput increases. It is this type of
cost that is reflected in an LP model.
Figure 19 also shows a plot of the average cost slope and the incremental cost
slope at a given throughput level. This average cost slope includes all the costs
associated with a particular unit. The slope is linear and must pass through the
origin. The incremental cost slope reflects the change in cost per unit throughput
over a short range. This slope is always tangential to the total cost curve at any
throughput under consideration.
It can be seen that the average cost gives the model “greater than to be expected”
incentive for changing the size of the unit, while the incremental cost curve on the
other hand gives the expected incentive. The incremental cost ignores all fixed costs
at the solution level and consists mainly of the expected return on investment.
The technique used in this study was to begin the solution by establishing a very
nominal cost on all units. This allowed any unit to be chosen in the solution. Once
the LP had selected an optimal unit configuration with those nominal costs, a
recursive program for investment cost estimating was used to determine average
cost of the units at the solution throughputs. These average costs were based on a
minimum return of investment and an expected economic life calculated on a
discounted cash flow basis.
These new calculated costs were then substituted for the original arbitrary cost in
the model. This average costing tended to delete the very unrealistically small units
Incremental cost slope
Average cost slope
Total cost, $s
Volume throughput, (BPCD)
Cost per unit throughput, $/BPCD
U n it co st cu rve ($/B PCD)
T o ta l co st cu rve ($s)
Fig. 19 Cost parameters for
any typical refinery unit
780
D.S.J. Jones and P.R. Pujado ´
is by far the most economic approach to solving this type of problem. By this
method, most of the many possible solutions can be examined quickly and effectively. Before discussing the solution approach used in this study, let us quickly
review the investment environment for any typical refinery unit. This is illustrated
in a simplified form in Fig. 19.
The total cost curve, on linear graph paper, shows that as a volume throughput is
increased, the total cost of a unit will increase. However, the plot of unit volume
cost ($/BPCD) against throughput shows the reverse; that is, the cost per unit of
throughput will decrease as the volume of throughput increases. It is this type of
cost that is reflected in an LP model.
Figure 19 also shows a plot of the average cost slope and the incremental cost
slope at a given throughput level. This average cost slope includes all the costs
associated with a particular unit. The slope is linear and must pass through the
origin. The incremental cost slope reflects the change in cost per unit throughput
over a short range. This slope is always tangential to the total cost curve at any
throughput under consideration.
It can be seen that the average cost gives the model “greater than to be expected”
incentive for changing the size of the unit, while the incremental cost curve on the
other hand gives the expected incentive. The incremental cost ignores all fixed costs
at the solution level and consists mainly of the expected return on investment.
The technique used in this study was to begin the solution by establishing a very
nominal cost on all units. This allowed any unit to be chosen in the solution. Once
the LP had selected an optimal unit configuration with those nominal costs, a
recursive program for investment cost estimating was used to determine average
cost of the units at the solution throughputs. These average costs were based on a
minimum return of investment and an expected economic life calculated on a
discounted cash flow basis.
These new calculated costs were then substituted for the original arbitrary cost in
the model. This average costing tended to delete the very unrealistically small units
Incremental cost slope
Average cost slope
Total cost, $s
Volume throughput, (BPCD)
Cost per unit throughput, $/BPCD
U n it co st cu rve ($/B PCD)
T o ta l co st cu rve ($s)
Fig. 19 Cost parameters for
any typical refinery unit
780
D.S.J. Jones and P.R. Pujado ´