In 1980, a natural gas shortage occurred in the summer due to scorching weather. Ben Elliot of Enerco, the principal producer and transporter of natural gas in the Gulf South Region, informed Agri-Chem Corporation’s general manager Harry Sinclair about the problem. Enerco had a plan to distribute gas to its customers in the event of a shortage, based on Federal Power Commission norms. The Federal Power Commission ordered Enerco to prioritize gas distribution to its consumers. Residential and commercial heating take precedence. Commercial and industrial businesses that demand natural gas resources are given second priority.
Industrial companies that use natural gas as boiler fuel are the third priority. The company employs linear programming because it is a commonly used mathematical modeling method that aids managers in resource allocation planning and decision-making. With the existing natural gas limits, Agri Chem is to maximize profit. Under the allocation provision, Agri- Chem’s natural gas usage was primarily classified as a second and third priority (DeMartino et al., 2022). The Agri-Chem corporation’s difficulty has been in selecting the compounds that would be directly impacted by the restriction, as Enerco was entitled to do so amid supply shortages. The decision of Agri-Chem is examined in the following paragraphs.
Analysis
When faced with a fuel shortage, it was important for the firm to monitor pipeline pressures and reductions to keep levels at a minimum. Ben Elliot recommended that their clients commence the reduction process to lower the impact on their industrial processes. The limitation would affect Agri-complexes, Chem’s which included a Texas Division. Bill Elliot did not go into great detail about which goods would be cut, but he did say that it would be primarily based on a customer’s consumption habit (Urade et al., 2019). As a result, Agri-Chem could choose which complex could sustain the curtailments with the most negligible profit loss.
During the recovery period, Agri-Chem undertook a week-long assessment of its goods to develop a mitigation strategy for natural gas allocation in the event of a restriction. Agri-Chem corporation is therefore vulnerable to threats of rolling brownouts which can strain its natural gas supply system capacity (Shruti & Kutralam, 2019). Enerco must keep track of pipeline pressures to maintain minimal levels. Enerco had not specified the products that were to be restricted. As a result, Agri-Chem has the freedom to make selective cuts to reduce profit margins. For the curtailments, a natural gas allocation contingency plan is required.
Table 1: Contribution to Profit and Overhead.
Table 2: Operational Data.
The two companies’ contracts stipulated a limit of 90,000 cubic feet by 103 per day for their complexes, but restrictions and regulations are based on actual usage. The daily use of natural gas in Currant is 85,680cubic feet by 103 per day. Enerco expects gas curtailments of 20% to 40%, and Agri-Chem is trying to figure out which of its complexes would be the least experienced by a gas restriction. Based on the information in the table, the values can be determined as follows:
Let the first letter of products represent the units produced. Therefore:
- Am = Ammonia produced.
- AP = Ammonium Phosphate produced.
- AN = Ammonium Nitrate produced.
- Ur = Urea produced.
- HA = Hydrofluoric acid produced.
- Cl = Chlorine produced.
- CS = Caustic soda produced.
- VC = Vinyl chloride monomer produced.
Solution
Inventories are economic resources used to meet current and future firm production requirements. When the demand for an inventory item is unpredictable, keeping a specific amount on hand is critical. Customers needed electricity to run air conditioning and refrigeration devices. Thus, electrical producing plants were running at total capacity. However, natural gas remained a preferred boiler fuel despite long-term intentions to switch from electricity to coal, oil, or nuclear power (DeMartino et al., 2022). A linear programming approach might be helpful when attempting to reduce or maximize an objective. Natural gas consumption is currently at 85,680,000 cu. ft. per day. To maximize the production output, therefore, we use the formula below:
At the maximum production level of the scale: 8Am + 10AP + 12AN + 12Ur + 7HA + 18Cl + 20CS + 14VC=85680 cubic. Ft. per day. This formula implies that there would be a 100% operational level with all units’ products equally, resulting in an availability of 85,680,000 cu. Ft. per day (Cavalho et al., 2018). In addition, the following information was obtained from the study to develop a production schedule to prove the mathematical relationship.
Figure 1: 100% production level output.
While determining the constraints in the function above;
Units of Ammonia produced (Am) = 
= 1200 tons
Ammonium Phosphate produced (AP) = 
= 540 tons
Ammonium Nitrate produced (AN) = 
= 490 tons
Urea produced (Ur) = 
= 160 tons
Hydrofluoric acid produced (HA) = 
= 560 tons
Chlorine produced (Cl) = 
= 1200 tons
Caustic soda produced (CS) = 
= 1280 tons
Vinyl chloride monomer produced (VC) = 
= 840 tons
Table 3: Production Schedule.
Since 85,680,000 cubic feet is the amount of natural gas currently used per day and the company projects curtailments range between 20 and 40 percent, then deducting a 20% production level from the current 85,680,000cubic feet will give 68,544,000 cubic feet per day. The new constraints therefore become:
- Am ≤ 1200.
- AP ≤ 540.
- AN ≤ 490.
- Ur ≤ 160.
- HA ≤ 560.
- Cl ≤ 1200.
- CS ≤ 1280.
- VC ≤ 840.
Based on the above constraints, when the production level is at 20% curtailments, the linear programming equation becomes:
Total unit produced: 8Am +10AP +12AN +12Ur +7HA +18Cl +4CS +14VC =17136 cubic feet. Hence, this equation and the constraint in it are represented below:
Figure 2: 20% natural gas production level.
From this level, therefore, the optimal mix solution becomes:
- Ammonia produced, Am = 1200 tons per day
- Ammonium Phosphate produced, AP = 540 tons per day
- Ammonium Nitrate produced, AN = 490 tons per day
- Urea produced, Ur = 160 tons per day
- Hydrofluoric acid produced, HA = 560 tons per day
- The chlorine produced, Cl = 1200 tons per day
- Caustic soda produced = 853.33 tons per day
- Vinyl chloride monomer produced, VC = 840 tons per day
- z = $54,280 per day. These figures reveal that caustic soda production reduced from 1280 tons per day to 853.33 tons.
Alternatively, when the production level is set at 40% curtailments, the function objective becomes: 8AM +10AP + 12AN + 12Ur + 7HA + 18Cl +8CS +14VC=34272 cubic feet. In addition, when using the same constraints, the 40% curtailments can be represented as follows: 8Am + 10AP + 12AN + 12Ur + 7HA + 18Cl +8CS +14VC<51408. This figure therefore contributes to the production units as shown in figure below:
Figure 3: 40% production level.
The optimal solution then becomes
Ammonia produced, Am = 1200 tons per day
Ammonium Phosphate produced, AP = 540 tons per day
Ammonium Nitrate produced, AN = 490 tons per day
Urea produced, Ur = 160 tons per day
Hydrofluoric acid produced, HA = 560 tons per day
The chlorine produced, Cl = 718.2222 tons per day
Caustic soda produced, CS = 568.89 tons per day
Vinyl chloride monomer produced, VC = 840 tons per day
z = $295,480 per day
This reveals that the production of caustic soda has further reduced from 853.33 tons per day to 568.89 tons per day, reflecting a 2/3 deviation in production at each level. As a result, ammonium phosphate, ammonium nitrate, urea ammonia, hydrofluoric acid, and vinyl chloride are the least impacted by a gas restriction.
Justification
Agri-Chem corporation’s best action plan in the event of a restriction is to stop producing caustic soda and minimize chlorine production, which will help maximize the firm’s profitability. Agri-Chem followed the modeling processes of describing the problem, constructing a model, acquiring input data, developing a solution, testing the solution, analyzing the results, and finally implementing the results (Awais et al., 2019). The study’s findings were crucial to linear programming. Generally, the Agro-Chem corporation will need to lower its production of Caustic Soda to 568.89 tons in a day and decrease chlorine production to 718.22 tons daily.
Summary and Conclusion
The 1982 summer was associated with an exceptional heat wave which resulted in a natural gas scarcity. Due to dwindling natural gas supplies, Enerco imposed curtailments to maintain minimal levels. The restrictions would impact the production of Agri-Chem. The firm had to figure out which of its complexes would be the least affected by the gas restrictions. Agri-Chem established that caustic soda and chlorine would provide the least in terms of profitability using a Linear program model and data from a week’s examination of production.
Agri-Chem management should maximize efficiency while dealing with natural gas shortages. Agri-Chem management uses linear programming to make strategic decisions that maximize earnings while integrating gas pipeline reductions. Linear programming effectively solves optimization problems by changing and simplifying assumptions to reduce production costs and increase revenues (Tulsian & Pandey, 2017). From the average utilization of 85,680 ft3 x 103 per day, Agri-Chem corporation experienced cuts ranging from 20% to 40%. Caustic soda is included in the optimal 20% curtailment, while Chlorine and Caustic Soda are included in the 40% curtailment, according to Agri-Chem. As a result, linear programming is an excellent method for finding optimization.
References
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