Sensitivity Analysis involving reducing air pollution
Controlling Air Polution
Nori & Leets Co. is one of the major producers of steel in its part of the world. It is located in the
city of Steeltown and is the only large employer there. Steeltown has grown and prospered along
with the company which now employs nearly 50,000 residents. Therefore, the attitude of the
townspeople always has been "What's good for Nori & Leets is good for the town." However,
this attitude is now changing; uncontrolled air pollution from the company's furnaces is ruining
the appearance of the city and endangering the health of its residents.
A recent stockholders' revolt resulted in the election of a new enlightened board of directors for
the company. These directors are determined to follow socially responsible policies, and they
have been discussing with Steeltown city officials and citizens' groups what to do about the air
pollution problem. Together they have worked out stringent air quality standards for the
The three main types of pollutants in this airshed are particulate matter, sulfur oxides, and
hydrocarbons. The new standards require that the company reduce its annual emission of these
pollutants by the amounts shown in the following table.
Required Reduction in Annual
Emission Rate (in million pounds)
The board of directors has instructed management to have the engineering staff determine how to
achieve these reductions in the most economical way. The steelworks have two primary sources
of pollution, namely, the blast furnaces for making pig iron and the open-hearth furnaces for
changing iron into steel. In both cases, the engineers have decided that the most effective
abatement methods are (1) increasing the height of the smokestacks, (2) using filtler devices
(including gas traps) in the smokestacks, and (3) including cleaner, high-grade materials among
the fuels for the furnaces. Each of these methods has a technological limit on how heavily it can
be used (e.g., a maximum feasible increase in the height of the smokestacks), but there also is
considerable flexibility for using the method at a fraction of its technological limit.
The next table shows how much emissions (in millions of pounds per year) can be eliminated
from each type of furnace by fully using any abatement method to its technological limit.
Reduction in Emission Rate from the Maximum Feasible Use of an Abatement Method
For purposes of analysis, it is assumed that each method also can be less fully used to achieve
any fraction of the abatement capacities shown in this table. Furthermore, the fractions can be
different for blast furnaces and open-hearth furnaces. For either type of furnace, the emission
reduction achieved by each method is not substantially affected by whether or not the other
methods also are used.
After these data were developed, it became clear that no single method by itself could achieve all
the required reductions. On the other hand, combining all three methods at full capacity on both
types of furnaces (which would be prohibitively expensive if the company's products are to
remain competitively priced) is much more than adequate. Therefore, the engineers concluded
that they would have to use some combination of the methods, perhaps with fractional capacities,
based on their relative costs. Furthermore, because of the differences between the blast and the
open-hearth furnaces, the two types probably should not use the same combination.
An analysis was conducted to estimate the total annual cost that would be incurred by each
abatement method. A method's annual cost includes increased operating and maintenance
expenses, as well as reduced revenue due to any loss in the efficiency of the production process
caused by using the method. The other major cost is the start-up cost (the initial capital outlay)
required to install the method. To make this one-time cost commensurable with the ongoing
annual costs, the time value of money was used to calculate the annual expenditure that would be
equivalent in value to this start-up cost.
This analysis led to the total annual cost estimates given in the following table for using the
methods at their full abatement capacities.
Total Annual Cost from the Maximum Feasible Use of an
$ 8 million
$ 10 million
$ 7 million
$ 6 million
$ 11 million
$ 9 million
It also was determine that the cost of a method being used at a lower level is roughly
proportional to the fraction of the abatement capacity given in the preceding table that is
achieved. Thus, for any given fraction achieved, the total annual cost would be roughly that
fraction of the corresponding quantity in the cost table.
The stage now is set to develop the general framework of the company's plan for pollution
abatement. This plan needs to specify which types of abatement methods will be used and at
what fractions of their abatement capacities for (l) the blast furnaces and (2) the open-hearth
Part a: You have been asked to head an operations research team to analyze this problem.
Management wants you to begin by determining which plan would minimize the total annual
cost of achieving the required reductions in annual emission rates for the three pollutants.
Develop a LP model and solve by stating what methods should be used to attack the pollution
Sensitivity Analysis Requirement:
Management wants to conduct some what-if analysis. Since the company does not have prior
experience with the pollution abatement methods under consideration, the cost estimates
provided for each technology could easily be off by as much as 10% in either direction.
Part b: Analyze the effect of an inaccuracy in estimating each cost parameter for the abatement
methods. If the true value is 10% less or 10% more than the estimated value, would this change
the optimal solution. Provide a table illustrating whether the optimal value will change as a
result of a 10% increase or decrease. Using this table, make a recommendation about where to
focus further work in estimating the cost parameter more closely.
Part c: Suppose the requirement for particles emission is increased to 65 million pounds.
What effect will this have on the company with regards to cost?
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