ETF2480 Business Modelling

ETF2480 Business Modelling

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ETF2480 Business Modelling

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ETF2480 Business Modelling

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Course Code: ETF2480
University: Monash University

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Country: Australia

Question:

In order to present your results in a concise and readable format, you may wish to organise the values in tables. In all question parts you should also include some written explanation and interpretation.
(a) You are a member of the Management Science Team, and have been asked to start the discussion of pollution abatement decisions by reporting to the next meeting as follows: Briefly explain to the team the problem you wish to solve, and, in general terms, the method you plan to use to solve it.
(b) Consider the statement just below Table 2: “It was determined that the cost of a method being used at a lower level… is roughly proportional to the fraction of the full abatement capacity of the method that is achieved.” Show that you understand this statement by performing the following calculation, showing your working:
Suppose we were to spend $6 million per annum on costs associated with taller smokestacks for blast furnaces, and $5 million per annum on costs associated with filters for blast furnaces. What is the total estimated emission abatement from blast furnaces for each of the pollutants? (Answer to the nearest million kg in each case.)
(c) Set up a spreadsheet model for this problem, including all decision variables, parameters, any intermediate variables, constraints, and the final cost.
(d) Alex Williams has a role at the steel mill as liaison officer with the Department of Environment, and claims that increasing the height of smokestacks has more effect on where the pollution lands than on how much is produced. Alex therefore argues that the maximum possible amount should be spent on the filter method for each type of furnace, and three quarters of the maximum possible amount should be spent on taller smokestacks.

Answer:

The steel company of Broken Valley has been now been facing a harsh criticism and opposition on its location site from the residents on its neighborhood due to air pollution that has greatly increased from the recent time from the normal activities that are being carried out by the company, and this has adversely affected the health of all living things around the company and also resulted to corrosion on the properties own by the resident community, the emission of the excess air pollutant components is done through blast furnace and open hearth furnace,   the company is now in the process of ensuring that the air pollutant components that include particulate matter, sulphur oxides, and hydrocarbons amounts are reduced. Therefore through the analysis of engineers it is proposed that proper abatement methods are to be considered at moderate cost, which includes using of filters devices in the smoke stacks and using taller smoke stacks.

b)

Abatement techniques

Filters

Taller smoker

Cost

$ 7 millions

$ 8 millions

 

In millions kg

In millions kg

Particulates

25

12

Sulphur oxide

18

35

Hydrocarbons

28

37

Comparison to the cost of $ 5 million and $ 6 millions

Abatement techniques

Filters

Taller smoker

Cost

$ 5 millions

$ 6 millions

 

In millions kg

In millions kg

Particulates

17.86

9

Sulphur oxide

12.86

26.25

Hydrocarbons

20

27.75

Total amount of pollutant per respective abatement techniques

Abatement techniques

Filters

 

In millions kg

Particulates

45

Sulphur oxide

49

Hydrocarbons

52

 

Abatement techniques

Taller smoker

Particulates

21

Sulphur oxide

77

Hydrocarbons

90

Total amount of the pollutant per respective pollutants
45×1 + 21×2 = < 60 49x1 + 77x2 = < 120 52x1 + 90x2 = < 75 Maximum 13x1 + 18x2                      Particulate 45 21   60 Sulphur oxides 49 77   120 Hydrocarbons 52 90   75 Check the excel file d) Total amount of pollutant per respective abatement techniques Abatement techniques Filters   In millions kg Particulates 45 Sulphur oxide 49 Hydrocarbons 52   Abatement techniques Taller smoker Particulates 15.75 Sulphur oxide 57.75 Hydrocarbons 67.5 Total amount of the pollutant per respective pollutants 45x1 + 15.75x2 = < 60 49x1 + 57.75x2 = < 120 52x1 + 67.5x2 = < 75 Maximum 13x1 + ¾ *18x2  13x1 + 13.5x2  Based on the excel model it is clearly shown that the suggestion of Alex William worked to reduce the amount or total emission of the three type of pollutant, as shown the total amount of pollutants emitted reduced to 59.54, 68.34 and 73.06 respectively from the maximum 60, 70 and 75 millions of kilogram, due to reduction of the three pollutants a direct total cost too was observed to have dropped from $18.36 million to 17.97 million, a clear indication that more moderate cost could be involved if maximum possible amount should be spent on the filter method for each type of furnace, and three quarters of the maximum possible amount should be spent on taller smokestacks. e) Total amount of pollutant per respective abatement techniques Abatement techniques Filters   In millions kg Particulates 45 Sulphur oxide 49 Hydrocarbons 52   Abatement techniques Taller smoker Particulates 18.08 Sulphur oxide 66.31 Hydrocarbons 77.5 Total amount of the pollutant per respective pollutants 45x1 + 18.08x2 = < 60 49x1 + 66.31x2 = < 120 52x1 + 77.5x2 = < 75 Taller smoke stacks = 10*3/4 = $7.5 $10 + $8 = $15.5 Maximum cost 13x1 + 15.5x2  The model used to solve the new correction from Alex's suggestion by considering changing only the expenditure on smokestack height in the Hearth furnaces, as shown the total amount of pollutants emitted reduced to 59.74, 69.07 and 73.92 respectively from the maximum 60, 70 and 75 millions of kilogram, due to reduction of the three pollutants a direct total cost too was observed to have dropped from $18.36 million to $18.15 million Part 2 a) The techniques abetment achieved for the filters were able to reduce 1.2931 millions of kg while for taller smoke stacks was able to reduce 0.0862 millions of kg. And the total cost incurred for this was $18.36 millions b) In case the particulates and hydrocarbon maximum amount are increase by one unit , that is 61 and 76 respectively, the different in the total cost between the first scenario when it is at 60 and 70 with when it is at 61 and 76 will be equivalent to 0.26065, which is referred to as shadow prices. ci) from the sensitive report it is clear that the cost of the filter abatement technique will be changed, this generally will affect both the amount of the emission that will take place on the blast filters, this will therefore have a projected change on the total cost of the that will used in in the whole process of using the two air abetment techniques cii) reduction of 10% Total amount of pollutant per respective abatement techniques Abatement techniques Filters   In millions kg Particulates 42.58 Sulphur oxide 46.36 Hydrocarbons 49.2   Abatement techniques Taller smoker Particulates 21 Sulphur oxide 77 Hydrocarbons 90 Total amount of the pollutant per respective pollutants 42.58x1 + 21x2 = < 60 46.36x1 + 77x2 = < 120 49.2x1 + 90x2 = < 75 Maximum 12.3x1 + 18x2                      Particulate 42.58 21   60 Sulphur oxides 46.36 77   120 Hydrocarbons 49.2 90   75 Increase 10% Total amount of pollutant per respective abatement techniques Abatement techniques Filters   In millions kg Particulates 47.42 Sulphur oxide 51.64 Hydrocarbons 54.8   Abatement techniques Taller smoker Particulates 21 Sulphur oxide 77 Hydrocarbons 90 Total amount of the pollutant per respective pollutants 47.42x1 + 21x2 = < 60 51.64x1 + 77x2 = < 120 54.8x1 + 90x2 = < 75 Maximum 13.7x1 + 18x2                      Particulate 47.42 21   60 Sulphur oxides 51.64 77   120 Hydrocarbons 54.8 90   75 d) the policy initiated by government reduced the initial required cost from $18.36207 million to 17.87931 million, therefore the scheme is a good policy that will help the company use a moderate cost in controlling the amount of air pollutants. 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