Water Resources Management
Questions and Answers
1. A set of six alternative water resources development programs is available. The programs
produce both flood protection and water supply benefits. The benefits (Bi) and costs (Ci)
towards the two objectives of increasing national income (N) and increasing regional income
( R) are given below:
Land Made
Alternative Water Supply Gross Benefits and Costs
Flood-Free
(acres) (mgd) (Discounted, US$ million)
CN BN CR BR
1 2 0 3.0 4.0 .5 1.0
2 .5 1 4.0 6.5 1.0 .5
3 1 1 3.5 4.5 1.0 1.5
4 1 .5 1.5 1.5 1.5 2.5
5 0 2 2.5 3.0 .5 1.0
6 1.5 .5 2.0 3.5 1.0 1.0
a. Draw the net benefit transformation curve
b. Identify dominated alternatives, if any
2. On a river there are 2 factories. The upstream one is a paper mill that discharges a lot of
waste into the river. Downstream is a Coca-Cola plant, which requires very pure water (with
no pollutant).
For each factory there is a cost function for decreasing the pollution. The mill discharges 1,000
cubic meters of water per hour, each cubic meter having 100 units of pollutant. Treatment cost
at the mill for removing X units of pollutant from a cubic meter of water is CP (X1) = X12. The
1
1,000 cubic meters per hour discharge from the mill is diluted by an additional 9,000 cubic
meters per hour of flow in the river. The coke factory takes in 1,000 cubic meter per hour of
the 10,000 cubic meters per hour flow. The cost for pollution removal of X2 units at the coke
factory is CC (X2) = ex2
Suppose the law requires that the coke plant be entitled to clean water. The paper mill may
either
1. Clean the water before it discharges into the river
2. Reimburse the coke company for treatment costs incurred at the withdrawal point
Provide (e.g. schematics, tables, formulae) in a clear but thorough manner the following:
a. The boundaries of the system under consideration
b. Parameters which completely characterize the state of the system
1
, c. The relationship between the input to and output from the system
d. The inputs over which you have no control
e. The criteria for measuring system performance; also the relationships between control
policies, and the criteria for measuring system performance.
Finally, summarize by
f. Providing a mathematical representation of the paper factory’s control problem
g. Suppose there were no law requiring the paper mill to provide clean water. In this case the
coke plant might wish to pay the paper mill to clean its effluent, or simply do its own cleaning.
Would the solution to the problem in (f) be any different than the solution in this case? What
other issues might be involved?
3. Compute present value of the two different time streams of costs and benefits, which arise
from two different control strategies. Use discount rates of 2 and 10 percent.
Control Strategy Cost (-) or Benefit (+) Years of
Occurrence
A + $10,000 t = 1,2…10
+ $ 20,000 t = 11,12…20
- $30,000 t = 10
B + $10,000 t=0
+ $ 5,000 t = 1,2 …5
+ $15,000 t = 5,6…20
2
Questions and Answers
1. A set of six alternative water resources development programs is available. The programs
produce both flood protection and water supply benefits. The benefits (Bi) and costs (Ci)
towards the two objectives of increasing national income (N) and increasing regional income
( R) are given below:
Land Made
Alternative Water Supply Gross Benefits and Costs
Flood-Free
(acres) (mgd) (Discounted, US$ million)
CN BN CR BR
1 2 0 3.0 4.0 .5 1.0
2 .5 1 4.0 6.5 1.0 .5
3 1 1 3.5 4.5 1.0 1.5
4 1 .5 1.5 1.5 1.5 2.5
5 0 2 2.5 3.0 .5 1.0
6 1.5 .5 2.0 3.5 1.0 1.0
a. Draw the net benefit transformation curve
b. Identify dominated alternatives, if any
2. On a river there are 2 factories. The upstream one is a paper mill that discharges a lot of
waste into the river. Downstream is a Coca-Cola plant, which requires very pure water (with
no pollutant).
For each factory there is a cost function for decreasing the pollution. The mill discharges 1,000
cubic meters of water per hour, each cubic meter having 100 units of pollutant. Treatment cost
at the mill for removing X units of pollutant from a cubic meter of water is CP (X1) = X12. The
1
1,000 cubic meters per hour discharge from the mill is diluted by an additional 9,000 cubic
meters per hour of flow in the river. The coke factory takes in 1,000 cubic meter per hour of
the 10,000 cubic meters per hour flow. The cost for pollution removal of X2 units at the coke
factory is CC (X2) = ex2
Suppose the law requires that the coke plant be entitled to clean water. The paper mill may
either
1. Clean the water before it discharges into the river
2. Reimburse the coke company for treatment costs incurred at the withdrawal point
Provide (e.g. schematics, tables, formulae) in a clear but thorough manner the following:
a. The boundaries of the system under consideration
b. Parameters which completely characterize the state of the system
1
, c. The relationship between the input to and output from the system
d. The inputs over which you have no control
e. The criteria for measuring system performance; also the relationships between control
policies, and the criteria for measuring system performance.
Finally, summarize by
f. Providing a mathematical representation of the paper factory’s control problem
g. Suppose there were no law requiring the paper mill to provide clean water. In this case the
coke plant might wish to pay the paper mill to clean its effluent, or simply do its own cleaning.
Would the solution to the problem in (f) be any different than the solution in this case? What
other issues might be involved?
3. Compute present value of the two different time streams of costs and benefits, which arise
from two different control strategies. Use discount rates of 2 and 10 percent.
Control Strategy Cost (-) or Benefit (+) Years of
Occurrence
A + $10,000 t = 1,2…10
+ $ 20,000 t = 11,12…20
- $30,000 t = 10
B + $10,000 t=0
+ $ 5,000 t = 1,2 …5
+ $15,000 t = 5,6…20
2
