Answer :

Introduction

The following pages discuss the business problem pertaining to New South Wales Division of BK Chemical Corporation. 

The problem has occurred due to shortage of natural gas which in turn is due to unprecedented heat wave of the summer. Hence, the main producer and distributer of natural gas in the region, MaxEnergy has issued a notification that natural gas supplies were getting depleted rapidly and ‘rolling brownouts’ will be introduced as a temporary curtailment measure as necessary. Further, in the event of shortage, the available gas will be allocated under the following provisions established by the Federal Commission:

1. First Priority: Residential and commercial heating and cooling
2. Second Priority: Commercial and industrial firms that use natural gas as a source of raw material
3. Third Priority: Industrial firms that use natural gas as a boiler fuel.

David, the General Manager of the New South Wales Division of BK Chemical Corporation, needs to come up with a contingency plan so as to tackle this expected shortage of natural gas supply (BK Chemical Corporation Case Study, 2020).

Business Problem 

Curtailment Plan

David, the General Manager of the New South Wales Division of BK Chemical Corporation, has learnt that all of BK Chemical's uses were in the third priority classification, except ammonia operations which is the second priority classification. Hence, BK Chemical would probably be subjected to “rolling brownouts”, the temporary and periodic curtailments of natural gas supplies.

MaxEnergy has notified that the natural gas supply may be reduced in the range of 20 per cent to 40 per cent of existing contracted supply. BK Chemicals has a contract of a maximum of 90,000 x 10³ cu.ft. per day for its production.

However, MaxEnergy would not specify the products to be curtailed. The curtailment procedure would be based primarily on a customer's usage pattern. Hence, BK Chemical had the flexibility to absorb curtailments where they would have minimum impact on profits (BK Chemical Corporation Case Study, 2020).

Operational Data

David has acquired following data related to profit and operations regarding various products:

Main Objective of the Contingency Plan

In consultation with the company’s CEO, it has been determined that the main target of nullifying the impact of natural gas supply reduction should be to minimise the impact on profit. In other words, profit maximisation is contingency plan’s main target under given situations of natural gas supply reduction.

Business Problem for BK Chemicals

The business problem for BK Chemicals is to arrive at such production level of various products that the impact of natural gas supply shortage is minimized with respect to the overall profit.

In other words, profit maximization under the given constraints, that is, reduction in natural gas supply needs to be attained (Cooper, 2014).

Formulation of a Linear Program

The above identified business problem for BK Chemicals can be solved with the help of Linear Programming as it is an optimization technique that can be effectively used to maximize or minimize a target value by finding values of the variables that impact the target value. The constraints need to be linear and also the objective function needs to be linear (Sierksma & Zwols, 2015).

These conditions are satisfied in the above scenario and hence, we can use the linear programming technique to find the contingency plan for BK Chemicals in order to tackle the anticipated natural gas supply reduction.

The linear objective function will aim to maximize the contribution or profit from different product lines. This will be done by changing the values of the variable named ‘Production Rate (% capacity)’. In turn, this will be lead to automatic change in production, natural gas consumption and profit contribution.

The constraints include the limit to supply of natural gas consumption (Dantzig & Thapa, 1997). 

Base Case

The variables can be defined as:

The linear objective function can be defined as follows for the base case (Dantzig, 1982):

Maximise Profit (p) = 80*1500a + 120*600b + 140*700c + 140*200d + 90*800e + 70*1500f + 60*1600g + 90*1400h

Subject to:

a, b, c, d, e, f, g, h >= 0

a, b, c, d, e, f, g, h <= 100

8*1500a + 10*600b + 12*700c + 12*200d + 7*800e + 18*1500f + 20*1600g + 14*1400h <= 90000

The above function defines variables a-h that indicate production capacity percentage for each of the products. The objective linear function defines the sum total of the profit contribution from production of each product line.

The constraints define the production rate percentage that must lie between 0% to 100% for any of the products. Further, the last constraint defines the sum total of the natural gas consumption corresponding to the production of each product line.

The Solver function in MS-Excel was used to solver the above linear program as follows (MacDonald, 1995):

This represents the current scenario, whereby the total profit is $538,600 and natural gas consumption is 85,680 cubic units which is less than the available 90,000 cubic units. When Solver function was applied to maximize the overall profit by tweaking the production rate (in yellow), the result is as follows:

By running all products at 100% capacity (except Caustic soda), the profit has increased from $538,600 to $648,000 whereby all of available 90,000 cubic units of natural gas are being utilized.

20% Reduction Case

The variables can be defined as:

The linear objective function can be defined as follows for the 20% reduction case:

Maximise Profit (p) = 80*1500a + 120*600b + 140*700c + 140*200d + 90*800e + 70*1500f + 60*1600g + 90*1400h

Subject to:

a, b, c, d, e, f, g, h >= 0

a, b, c, d, e, f, g, h <= 100

8*1500a + 10*600b + 12*700c + 12*200d + 7*800e + 18*1500f + 20*1600g + 14*1400h <= 72000

The above function defines variables a-h that indicate production capacity percentage for each of the products. The objective linear function defines the sum total of the profit contribution from production of each product line.

The constraints define the production rate percentage that must lie between 0% to 100% for any of the products. Further, the last constraint defines the sum total of the natural gas consumption corresponding to the production of each product line. The availability of natural gas has reduced by 20% to reach 72,000 cubic units from earlier 90,000 cubic units.

The Solver function in MS-Excel was used to solver the above linear program as follows:

By running all products at 100% capacity (except Caustic soda and chlorine), the profit is still higher at $586,000 as compared to current scenario where profit is only $538,600.

40% Reduction Case

The variables can be defined as:

The linear objective function can be defined as follows for the 40% reduction case:

Maximise Profit (p) = 80*1500a + 120*600b + 140*700c + 140*200d + 90*800e + 70*1500f + 60*1600g + 90*1400h

Subject to:

a, b, c, d, e, f, g, h >= 0

a, b, c, d, e, f, g, h <= 100

8*1500a + 10*600b + 12*700c + 12*200d + 7*800e + 18*1500f + 20*1600g + 14*1400h <= 54000

The above function defines variables a-h that indicate production capacity percentage for each of the products. The objective linear function defines the sum total of the profit contribution from production of each product line.

The constraints define the production rate percentage that must lie between 0% to 100% for any of the products. Further, the last constraint defines the sum total of the natural gas consumption corresponding to the production of each product line. The availability of natural gas has reduced by 40% to reach 54,000 cubic units from earlier 90,000 cubic units.

The Solver function in MS-Excel was used to solver the above linear program as follows:

By running all products at 100% capacity (except Caustic soda and chlorine), the profit is a little lower at $516,000 as compared to current scenario where profit is $538,600.

Assumptions

Some of the assumptions are clear from the case study itself, such as:

1. The curtailment procedure would be based primarily on a customer's usage pattern. Hence, BK Chemical had the flexibility to absorb curtailments where they would have minimum impact on profits.
2. The numbers collected from David are reliable and accurate. In other words, the objective function and constraints are known with certainty and there will be no change in the same.
3. The target objective for contingency plan is profit maximization.
4. The provided contribution profit accounts for various other costs that are involved in the production process. There is no other hidden cost.

Some of the additional assumptions that can be drawn are (Lewis, 2008):

1. BK Chemicals is able to use the flexibility of absorbing natural gas curtailment such that impact on profit is minimised. This is to say that the company is able to adjust the production levels of various products without any feasibility or logistic issues. The units are perfectly divisible.
2. BK Chemicals is able to operate at 100% capacity of the production as and when needed without involving any additional costs.
3. BK Chemicals is able to procure other raw materials and labour as and when required.
4. The production done in accordance with contingency plan is appropriate to meet the market demand. That is to say that there is demand for the products in quantities that BK Chemical decides to produce such that its profit is maximized.

Discussion and Recommendations

The above discussion can be summarized as follows with respect to profit maximisation and product lines:

From the above table, it is clear that BK Chemicals is not attaining the profit maximization objective even under current scenario. With the given numbers and 90,000 cubic units of natural gas, the company can increase its profit from $538,600 to $648,000. This indicates operational inefficiency and lack of analysis prior to announcement of the natural gas curtailment plans.

Further, if we compare the current scenario with 20% reduction case where profit will be maximised, then we can see that profit actually goes up from $538,600 to $586,000. This indicates that due to the act of creating contingency plan, the 20% reduction in natural gas supply may actually benefit the company by increasing overall profit through adjustment of various product lines.

However, if we compare the current scenario with 40% reduction case where profit will be maximised, then we can see that profit reduces from $538,600 to $516,000. This is the only scenario where the company will face an impact on profit.

From the above table, we can see that as soon as natural gas supply is reduced by 20%, caustic soda production goes to zero. This is due to combination or one of the factors that this product line has the lowest profit contribution of $60/ton and it uses the highest quantity of natural gas at 20,000 cubic units/ton. Hence, this is the least profitable product line under given constraints.

The next in line is Chlorine product line whose production rate reduces to 66.7% under 20% natural gas reduction scenario and further reduces to zero under 40% natural gas reduction scenario. This is due to combination or one of the factors that this product line has the second lowest profit contribution of $70/ton and it uses the second highest quantity of natural gas at 18,000 cubic units/ton. Hence, this is a very low profit product line under given constraints.

Hence, it is recommended that in order to attain the profit maximisation objective, the company should first maximise the base case scenario such that profit increases to $648,000. This can be easily achieved by tweaking the production rates of various products. As and when the natural gas supply is curtailed by 20% and 40%, BK Chemical can use the above provided production rates keeping in mind the profit maximisation objective. The company should also consider alternative products instead of caustic soda and chlorine such that profit can be increased further.