Agri Chem Case Analysis
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Agri Chem Case Analysis
Introduction
Agri Chem faces a challenge of reduced natural gas supply, following a notification from Enerco, that gas supplies were being rapidly depleted, thus leading to rationing of natural gas. Based on the priorities that Enerco gives from the Federal Power Commission, it is notable that Agri Chem will be significantly affected the rationing. In providing details on rationing, Enerco did not provide proportions for rationing. Agri Chem must determine its usage pattern to determine how best to maximize profits under the circumstances. The problem is to determine which of Agri Chem’s complexes would be least affected by a gas curtailment.
Analysis
The rationing of natural gas is expected to have a significant impact on Agri-Chem, given the high level of usage. Agri Chem mostly utilizes natural gas for the second and third priority, which comprise the commercial use as a raw material source and industrial use as a broiler fuel. This was likely to lead to ‘rolling brownouts’ due to natural gas curtailments. The fact that Enerco does not provide guidelines on the manner in which natural gas will be allocated based on products gives Agri Chem an opportunity to determine its own proportions in a bid to ensure that profitability is maximized under the conditions. While Agri Chem had an allocation of 90,000 ´ 10^{3} cubic feet per day based on its contract with Enerco, this would be reduced by 20% to 40% following the curtailment. This would greatly affect Agri Chem, which utilizes natural gas as broiler fuel except for ammonia production which required natural gas as a raw material.
The situation at hand presents a complex scenario in which the company’s productivity is likely to be curtailed by the rationing of natural gas, given that Agri Chem considerably depends on natural gas for production purposes. This calls for a solution to optimize gas usage under the current circumstances, which essentially calls for a formula for gas usage to ensure that the company’s profits are maximized under the circumstances. Agri Chem has an advantage in that Enerco does not provide proportions for gas allocation and hence the company has the liverty to determine its capacities as deemed appropriate. Determining the product that would be least affected by the curtailment of natural gas helps the company to establish how well it can be utilized to provide optimal results for the company. Linear programming provides a simple solution for this complex situation, such that Agri Chem can determine how best to approach the problem presented by the gas shortage.
Solution
The main objective is to determine, based on Agri Chem’s complexities, the product that will be least affected by the gas curtailment. The solution involves creation of a linear programming equation that bases its calculation on the contribution, current capacity, production rate and natural gas usage, provided in the table of financial and operation data on page 6. This is optimized using linear programming, putting the possible constraints (20% and 40%) into consideration, to determine the product that would be least affected by the natural gas curtailment. Linear programming is considered effective in obtaining solutions for optimal use of resources and profit maximization because it makes use of simple formulas to determine solutions under different constraints (Haidar, 2015). It is therefore effective in making decisions on complex issues affecting organizations, such as the gas allocation dilemma faced by Agri Chem. In this case, two constraints are present. The process begins by determining the new constraints, representing the expected impact when gas supply is reduced by 20% or 40%. Using excel, calculations are made to determine the new quantities. Using these constraints, it is possible to determine the number of tons that can be produced per day to maximize profits as indicated on the calculations on page 7. The gas constraints are developed with reference to the possible changes, from 85,680,000 cu. ft. per day, which Agri Chem utilizes, once the curtailment is done. This is shown on page 7. The results indicate that Caustic Soda would be the least affected by the gas curtailment. This is because the company can operate optimally with Caustic Soda being produced at low levels; 423.2 tons/day when curtailment is 20% and zero tons/day when curtailment is at 40%. Profitability can then be calculated based on the quantities determined.
Justification
The current situation at Agri-Chem calls for an effective measure to determine the utilization of the natural gas supplies under the constraints.
- Linear programming is an effective optimization technique, suitable for complex problem solving, such as in the case of Agri Chem.
- Through the use of linear programming, Agri Chem can maximize its profits by assessing the gas proportions needed for the company and how this can be allocated to ensure optimal use of the available natural gas.
- This solution provides guidance for Agri Chem on the utilization of natural gas, such that it can be effectively allocated for optimal results and loss reduction.
- Linear programming gives better outcomes due to its simplicity and definite formula – single and straightforward, thus promoting accuracy.
- The calculation of optimal levels for profitability helps in promoting decision making e.g. in the case of Agri Chem where the company determines the complexities that are least affected by natural gas rationing.
- The solution provides a basis for determining the result of different scenarios – in this case the company can determine the profit optimization at 20% and 40% curtailment.
Conclusion
The problem presented in this case involves a situation in which Agri Chem’s production is affected by the curtailment of gas supply due to the effects of a heat wave. Enerco provides that Agri Chem’s supply may be affected by 20% to 40%. This calls on Agri Chem to come up with a formula that will optimize the situation, to ensure that it maintains sustainable profitability under the circumstances. A linear programming solution in which constraints are developed at the curtailment proportions provides that, caustic soda would be least affected by the gas curtailment, at the point of optimal profitability.
Question: Which of Agri-Chem’s complexes would be least affected by a gas curtailment?
Financial and Operational Data
Contribution Capacity Production Rate Natural Gas Usage
Product ($/Ton) (Tons/Day) (% of Capacity) (1,000 Cu.Ft./Ton)
Ammonia $80 1,500 80 8
Ammonium phosphate $120 600 90 10
Ammonium nitrate $140 700 70 12
Urea $140 200 80 12
Hydrofluoric acid $90 800 70 7
Chlorine $70 1,500 80 18
Caustic soda $60 1,600 80 20
Vinyl chloride monomer $90 1,400 60 14
Working
Let X_{1 }= ammonia ; X_{2 }= ammonium phosphate ; X_{3 }= ammonium nitrate ; X_{4 }= urea ; X_{5 }= hydrofluoric acid ; X_{6 }= chlorine ; X_{7 }= caustic soda ; X_{8 }= Vinyl chloride monomer
Agri Chem’s current natural gas usage = (1,200 × 8 + 540 × 10 + 490 × 12 + …) = 85,680,000 cu. ft. per day
At 20% curtailment, availability is 0.8 x 85,680 = 68,554,000 cu. ft. per day
Therefore, gas constraint = 8X_{1} + 10X_{2} + 12X_{3} + 12X_{4} + 7X_{5} + 18X_{6} + 20X_{7} + 14X_{8} ≤ 68,544
Using Excel, the following solution is obtained.
X_{1} | X_{2} | X_{3} | X_{4} | X_{5} | X_{6} | X_{7} | X_{8} | |
Tons/day | 1200 | 540 | 490 | 160 | 560 | 1200 | 433.2 | 840 |
At 40% curtailment, availability is 0.6 × 85,680 = 51,408,000 cu. ft. per day
Constraint: 8X_{1} + 10X_{2} + 12X_{3} + 12X_{4} + 7X_{5} + 18X_{6} + 20X_{7} + 14X_{7} ≤ 51,408
Excel calculation results in the following:
X_{1} | X_{2} | X_{3} | X_{4} | X_{5} | X_{6} | X_{7} | X_{8} | |
Tons/day | 1,200.00 | 540.00 | 490.00 | 160.00 | 560.00 | 718.22 | 0.00 | 840.00 |
Reference
Haidar, A. D. (2015). Construction Program Management – Decision Making and Optimization
Techniques. London: Springer
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