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Controlling Air Pollution

The Nori & Leets Co., one of the major producers of steel in its part of the world, 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 Table 3. The Board of Directors has instructed management to have the engineering staff determine how to achieve these reductions in the most economical way.

Table 3 Clean air standards for Nori & Leets Co.

Pollutant Required reduction in annual emission rate (million pounds)

Particulates 60

Sulfur oxides 150

Hydrocarbons 125

Table 4 Reduction in emission rate from maximum feasible use of abatement method for Nori & Leets Co.

Taller smokestacks Filters Better fuels

Pollutant   Blast furnaces Open-hearth furnaces Blast Open-hearth    Blast   Open-hearth

Particulates 12 9 25 20 17 13

Sulfur oxides 35 42 18 31 56 49

Hydrocarbons 37 53 28 24 29 20

The steel works has 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 types of abatement methods are (1) increasing the height of the smokestacks,1 (2) using filter devices (including gas traps) in the smokestacks, and (3) including cleaner high-grade materials among the fuels for the furnaces. All these methods have technological limits on how much emission they can eliminate, as shown (in millions of pounds per year) in Table 4.

However, the methods can be used at any fraction of their abatement capacities shown in this table. Because they operate independently, the emission reductions achieved by each method are 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 (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 upon 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.

Table 5. Total annual cost from maximum feasible use of abatement method for Nori & Leets Co.

Abatement method Blast furnaces Open-hearth furnaces

Taller smokestacks 8 10

Filters 7 6

Better fuels 11 9

An analysis was conducted to estimate the total annual cost that would be incurred by each abatement method. In addition to increased operating and maintenance expenses, consideration was given also to the initial costs (converted to an equivalent annual basis) of the method as well as any resulting loss in efficiency of the production process. This analysis led to the total cost estimates (in millions of dollars) given in Table 5 for using the methods at their full abatement capacities. It also was determined that the cost of a method being used at a lower level is essentially proportional to its fractional capacity. Thus, for any given fraction used, the total annual cost would be that fraction of the corresponding quantity in Table 5.

The stage now was set to develop the general framework of the company’s plan for pollution abatement. This plan would consist of specifying which types of abatement methods would be used and at what fractions of their abatement capacities for (1) the blast furnaces and (2) the open-hearth furnaces. Because of the combinatorial nature of the problem of finding a plan that satisfies the requirements with the smallest possible cost, an operations research team was formed to solve the problem.

Formulate a linear programming model to solve Nori & Leets air pollution problem. Define your variables clearly and write out the constraints and the objective with a brief explanation.

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