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Description of Business Problem

1.Define the Business Problem.

2.Formulate a Linear Program for 20 and 40% curtailment of Natural gas usage.

3.Discuss the Sensitivity Analysis.

4.Provide a discussion of BarCo’s Options and your recommendations for action.

In the dynamic business environment of today, allocation of resources must regularly be adjusted, particularly when important events take place. Certain companies have an organised stage-gating procedure for resource allocation. Linear Programming is a technique used to determine the ideal allocation of resources like manpower, machines, materials, etc. by a company. It is applied for determining the perfect product mix of the company to maximise its gains (Paris, 2016). The present study is based on the evaluation of business problem of BarCo Corporation by making use of linear programming model in order to assist them in managing business operations in an effective manner. The study will include descriptive analysis of their business problem and formulation of linear programming of the same. On the basis of the equation, sensitivity analysis for the case will be discussed in order to provide options and recommendations for action for BarCo.

Description of business problem

Managerial authority of Texas division of the Bar Co Corporation had acknowledged a notification from Max Energy regarding rapid depletion of supply of natural gas. Further, due to the shortage of Max Energy is supposed to make allocation of gas to its as per the provisions of priority prescribed by the Federal Commission:

First priority

Residential and commercial heating and cooling.

Second priority

Commercial and industrial firms which make use of natural gas as a raw material.

Third priority

Industrial firm which make use of natural gas as a boiler fuel

The BarCo is covered under classifications of second and third priority. Therefore, there is a high likelihood that the organisation would be subjected to temporary brownouts and frequent reductions of natural gas supplies. Max Energy is planning to evaluate their pipeline pressures in order to make reductions for maintaining minimum level. Max Energy wants that its clients initiate the curtailment process to mitigate the impact of their industrial activities. However, Max Energy was also authorised for curtailment of supply in an unilateral manner if pipeline pressure fell below minimum levels. The shortage of natural gas was because of the record heat wave of 2010. Electrical generating plants had been functioning at their full capacity for supplying electricity to operate refrigeration and AC units.


So BarCo’s problem is primarily to decide which of its complexes would be least affected by the fact of gas curtailment because it’s both of the working areas would be inclusive in process of the curtailment region in the event of a brownout. Its main objective is to minimise the impact on the profit/overhead contribution. Besides the ammonia operations, all natural gas acquired was used as fuel. In the ammonia operations, natural gas was employed as a raw material. The CEO of Max Energy is not opening up about the products that should be curtailed. Instead the process of curtailment would be primarily based on the usage pattern of the consumer. Henceforth, the company is required to analyse the impact of 20 and 40% curtailment of the natural gas usage on the profits / overheads. Consequently, by using the comparative approach company should select that alternative which has least effects on the workings of the company and through which they can earn higher profits.

Formulation of Linear Programming Problem

In this case study, demonstration of an interesting utilisation of linear programming is shown:

Let:

 X1 ammonia

X2 ammonium phosphate

X3 ammonium nitrate

X4 urea

X5 hydro?uoric acid

X6 chlorine

X7 caustic soda

X8 vinyl chloride monomer

Objective function regarding this case study:

Profit maximization: 80X1 + 120X2 + 140X3 + 140X4 + 90X5 + 70X6 + 60X7 + 90X8

Subject to the constraints

Subject to the subsequent check:

X1 ≤ 1,200      X5 ≤ 560

X2 ≤ 540         X6 ≤ 1,200

X3 ≤ 490         X7 ≤ 1,280

X4 ≤ 160         X8 ≤ 840

Curtailment of 20%

Present utilisation of natural gas: 85,680 cu. ft. *103/day

20 percent curtailment: 68,554 cu. ft. * 103 /day

Hence, the ninth constraint is: 8X1+ 10X2 +12X3 +12X4+ 7X5 +18X6 v20X7+ 14X8 ≤ 68,544

Curtailment of 40%

For a 40 percent natural gas curtailment, the ninth constraint is:

8X1 + 10X2+ 12X3 +12X4 +7X5+ 18X6 + 20X7+ 14X8 ≤ 51,408

Obtaining the optimal solution to an LP model is crucial. However, it is not the only information required. There is a huge amount of sensitivity information or in simple terms information regarding what happens on changing the data values (Borgonovo and Plischke, 2016). A sensitivity analysis is a method applied to identify how varied values of an independent variable affect a specific variable under a proposed set of assumptions. In simple terms, it is the study of how the vagueness in the output of a system could be allocated to distinct sources of uncertainty in its input (Nasseri and Ebrahimnejad, 2013). By considering the present case scenario, BarCo has two options at its discretion. As required by Max Energy, the company would have to curtail its natural gas usage in the range of 20 to 40 percent. Sensitivity analysis of above two options is as follows:


Curtailment of 20%

Curtailment of 20% shows that availability is 0.8 × 85,680 = 68,554,000 cu. ft. per day. By considering this factor, the constraint of gas will be

8X1 + 10X2 + 12X3 + 12X4 + 7X5 + 18X6 + 20X7 + 14X7 ≤ 68,544

And consequently profit for business will be:

Ammonia

Amm. Phosphate

Amm. Nitrate

Urea

Hydro Acid

Chlorine

Caustic Soda

Vinyl Chloride

Tons/Day

1,200.0

540.0

490.0

160.0

560.0

1,200.0

423.2

840.0

Profit

$80

$120

$140

$140

$90

$70

$60

$90

$487,192.00

Due to the curtailment of natural gas, production of the caustic soda will be reduced from 1,280 tonnes/day to only 423.2 tonnes/day.

Curtailment of 40%

Curtailment of 20% shows that availability is 0.6 × 85,680 = 51,408,000 cu. ft. per day. By considering this factor, the constraint of gas will be

8X1 + 10X2 + 12X3 + 12X4 + 7X5 + 18X6 + 20X7 + 14X7 ≤ 51,408

 

Ammonia

Amm Phosphate

Amm Nitrate

Urea

Hydro Acid

Chlorine

Caustic Soda

Vinyl Chloride

Tons/Day

1,200.00

540.00

490.00

160.00

560.00

718.22

0.00

840.00

Profit

$80

$120

$140

$140

$90

$70

$60

$90

$428,075.56

Due to the curtailment of nature gas, production of the caustic soda is eliminated completely and the production of the chlorine will be reduced from 1,200 to 718.2 tonnes/day.

By considering sensitivity analysis, it can be said curtailment of 20% is comparatively better as it will assist business in earning higher profits with the available resources (Vanderbei, 2015).

BarCo has two options at its discretion. As required by Max Energy, the company would have to curtail its natural gas usage in the range of 20 to 40 percent. As identified from the sensitivity analysis above, by 20% reduction in natural gas usage the company is able to reduce the production of the caustic soda will be reduced from 1,280 tonnes/day to only 423.2 tonnes/day. The profit, in this case, will be $487,192. On the other hand, if the natural gas usage is curtailed by 40% then BarCo will be eliminating the production of caustic soda entirely and will reduce production of chlorine from 1,200 to 718.2 tonnes/day. However, the profits would come down to $428,075. It is recommended that Barco opts for the 20% curtailment as opting for the other alternative would reduce profit considerably which the company does not intend to do. Hence, a 20% cut in natural gas consumption is feasible. Apart from this, several other recommendations are proposed to the company so that it can earn better value from resource allocation in the present scenario (Bellman and Dreyfus, 2015).

Sensitivity Analysis


Firstly, the executives should be mindful of the domination of averages. A singular unit might have lines of geographic or business pockets with starkly varied returns. It is unusual to experience a 15% fall in one area while other is seeing double-digit growth. Indeed, the difference is usually more substantial across granular market sections within the one SBU than across larger SBUs (Dantzig, 2016). Barco has already segmented its business, but now it needs to define the extent of granularity which could be something of an art because the executives cannot argue over trade-offs across innumerable micro-markets. The senior management needs to drill down to the tiniest meaningful segment, where a movement of resources is likely to have a considerable impact on the overall Group. In addition to this, every segment must have a different external market even if natural gas is not fully divisible (Schoenwitz et al., 2017).

Secondly, the growing demand for natural gas and the shortage in its supplies highlights the significance of adopting renewable sources of energy. As BarCo uses natural gas as a raw material in some of its processes mainly ammonia operations hence, the gas could not be completely eliminated from here. Though there is always an option of looking for alternatives, still the need for natural gas, in this case, cannot be entirely overruled (Fahimnia, Sarkis, and Davarzani, 2015). However, rest of the uses of the company also fall into the category of using natural gas as a boiler fuel. In this case, the organisation can contemplate using renewable sources of energy for better long-term outcomes and impact. This way BarCo will not have to depend on natural gas for all its operations as it will be compensating it will be renewable energy sources. Besides this, the firm will be in a position to better prioritise and allocate natural gas among its other important operations (Schoenwitz et al., 2013).


Thirdly, BarCo must concentrate on value creation. At times, investments exercise a direct impact on the business and the NPV of all future cash flows related to them could be quantified (Kolman and Beck, 2014). Evaluating which segment requires and deserves more natural gas and attention demands the correct metrics. Hence, the organisation should develop and use the right metrics for evaluating this. An example of the most common metrics is ROI or return on investment i.e. to say which activity would pay off the investment made in it by allocating the portion of natural gas (Wisner et al., 2014).

Fourthly, any exercise of natural gas allocation should be based on hard data so that decisions are underpinned by logic and facts. Biases should not crop up while taking the decision of resource allocation (Du and Pardalos, 2013). This can be done by persuading the prioritisation of opportunities on the basis of their ROI or value creation; commitment toward a minimum yearly reallocation; and re-anchoring which eliminates the optimistic projections of management about quick improvements. This could be carried out by developing a framework underpinned by external forecasts and presuming that there would be no increase in natural gas supplies; executives can then discuss if it is still worth allocating natural gas to (Acar et al., 2017).

Conclusion

It can be concluded that optimal resource allocation is a mouthful, however with a simple meaning i.e. shifting resources, talent, money and attention of the management to areas which will deliver the maximum value to the company. The speed of global change is rising, rendering it more challenging to tell how Max Energy will address its natural gas crunch. Hence, BarCo should try becoming more self-reliant in terms of using renewable sources of energy wherever possible thereby leaving natural gas for the most important operations. In addition to this, it has been identified through linear programming and sensitivity analysis that BarCo must opt for a 20% curtailment in its usage of natural gas because this will reduce the production of caustic soda and will not reduce the profits by a huge margin. Eventually, even with the sincerest intentions, allocation of resources (natural gas in this case) can fall prey to internal power dynamics and organisational inertia. It is recommended that the senior executives exercise proper discretion and rule out biases while taking decision pertaining to allocation of resources.

References

Acar, M.F., Zaim, S., Isik, M. and Calisir, F., 2017. Relationships among ERP, supply chain orientation and operational performance: An analysis of structural equation modelling. Benchmarking: An International Journal, 24(5).

Bellman, R.E. and Dreyfus, S.E., 2015. Applied dynamic programming. Princeton University press.

Borgonovo, E. and Plischke, E., 2016. Sensitivity analysis: a review of recent advances. European Journal of Operational Research, 248(3), pp.869-887.

Dantzig, G., 2016. Linear programming and extensions. Princeton University press.

Du, D.Z. and Pardalos, P.M. eds., 2013. Handbook of combinatorial optimisation: supplement (Vol. 1). Springer Science & Business Media.

Fahimnia, B., Sarkis, J. and Davarzani, H., 2015. Green supply chain management: A review and bibliometric analysis. International Journal of Production Economics, 162, pp.101-114.

Kolman, B. and Beck, R.E., 2014. Elementary linear programming with applications. Elsevier.

Nasseri, S.H. and Ebrahimnejad, A., 2013. Sensitivity analysis on linear programming problems with trapezoidal fuzzy variables. In Optimizing, Innovating, and Capitalising on Information Systems for Operations (pp. 64-82). IGI Global.

Paris, Q., 2016. An economic interpretation of linear programming. Springer.

Schwitz, M., Gosling, J., Naim, M. and Potter, A., 2013. HOW TO BUILD WHAT BUYERS WANT–UNVEILING CUSTOMER PREFERENCES FOR PREFABRICATED HOMES.

Schoenwitz, M., Potter, A., Gosling, J. and Naim, M., 2017. Product, process and customer preference alignment in prefabricated house building. International Journal of Production Economics, 183, pp.79-90.

Solow, D., 2014. Linear Programming: An introduction to finite improvement algorithms. Courier Corporation.

Vanderbei, R.J., 2015. Linear programming. Springer.

Wisner, J.D., Tan, K.C. and Leong, G.K., 2014. Principles of supply chain management: A balanced approach. Cengage Learning.

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