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(Solved) Sensitivity Analysis involving reducing air pollution


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

 

Steeltown airshed.

 

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.

 

Pollutant

 


 

Required Reduction in Annual

 

Emission Rate (in million pounds)

 

60

 

150

 

125

 


 

Particles

 

Sulfur Oxides

 

Hydrocarbons

 


 

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

 


 

Pollutant

 


 

Particles

 

Sulfur Oxide

 

Hydrocarbons

 


 

Taller

 

Smokestacks

 

OpenBlast

 

Hearth

 

Furnac

 

es Furnace

 

s

 

12

 

9

 

35

 

42

 

37

 

53

 


 

Filters

 


 

Blast

 

Furnace

 

s

 

25

 

18

 

28

 


 

OpenHearth

 

Furnace

 

s

 

20

 

31

 

24

 


 

Better Fuels

 


 

Blast

 

Furnace

 

s

 

17

 

56

 

29

 


 

OpenHearth

 

Furnace

 

s

 

13

 

49

 

20

 


 

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

 

Abatement Method

 

Taller smokestack

 


 

Blast

 

Furnaces

 

$ 8 million

 


 

Open-Hearth

 

Furnaces

 

$ 10 million

 


 

Filters

 


 

$ 7 million

 


 

$ 6 million

 


 

Better fuels

 


 

$ 11 million

 


 

$ 9 million

 


 

Abatement Method

 


 

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

 

furnaces.

 

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

 


 

problem

 

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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DATE ANSWERED

Oct 15, 2019

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