In June 1980, Harry Sinclair, General Manager of the Texas Division of Agri-Chem Corporation, received notification from Ben Elliot of Enerco that natural gas supplies were being rapidly depleted. In the event of a shortage, Enerco, the main producer and distributor of natural gas in the Gulf South region, would allocate gas to its customers under the following provisions established by the Federal Power Commission:
First Priority: Residential and commercial heating and cooling
Second Priority: Commercial and industrial firms that use natural gas as a source of raw material
Third Priority: Industrial firms that use natural gas as a boiler fuel
Elliot related to Sinclair that most of Agri-Chem's uses were in the second and third priority classifications. Hence, Agri-Chem would probably be subjected to "rolling brownouts", temporary and periodic curtailments of natural gas supplies. Enerco planned to monitor its pipeline pressures and order reductions to maintain minimum levels. Elliot preferred that Enerco's customers initiate the reduction process to minimize the effect on their industrial processes. Enerco was authorized, however, to curtail supplies unilaterally if pipeline pressure fell below minimum levels.
The natural gas shortage was created by the unprecedented heat wave of the summer of 1980. Electrical generating plants were operating at capacity to supply electricity to operate air conditioning and refrigeration units. Although long-range plans called for these utility companies to convert to coal, oil, or nuclear fuel, natural gas remained the dominant boiler fuel.
Agri-Chem's problem was to determine which of its complexes would be least affected by a gas curtailment. Its Texas Division is located in the greater Houston area; plants are located in the suburbs of Deer Park and Battleground. Both of these areas would be included in the curtailment region in the event of a brownout. Except for Agri-Chem's ammonia operations, all gas purchased was used as boiler fuel. In its ammonia plant, gas was used as a source of raw materials. (The manufacture of ammonia uses natural gas in the steam reforming process.) In a detailed discussion with Elliot, Sinclair learned that Enerco would not specify the products to be curtailed. The curtailment procedure would be based primarily on a customer's usage pattern. Hence, Agri-Chem had the flexibility to absorb curtailments where they would have minimum impact on profits.
Based on this information, Sinclair called a staff meeting to discuss a contingency plan for allocation of natural gas among the firm's products if curtailments became a reality. The specific objective was to minimize the impact on profits contribution. After a week of study, the information in Tables 1 and 2 was presented to Sinclair.
Table 1. Contribution to Profit
Ammonium phosphate 120
Ammonium nitrate 140
Hydrofluoric acid 90
Caustic soda 60
Vinyl chloride monomer 90
Table 2. Operational Data
(tons/day) Production rate
(% of capacity) Natural gas consumption
(1000 cu. ft./ton)
Ammonia 1,500 80 8.0
Ammonium phosphate 600 90 10.0
Ammonium nitrate 700 70 12.0
Urea 200 80 12.0
Hydrofluoric acid 800 70 7.0
Chlorine 1,500 80 18.0
Caustic soda 1,600 80 20.0
Vinyl chloride monomer 1,400 60 14.0
Agri-Chem's contract with Enerco specified a maximum of 90,000 cu. ft. X 103 per day for its complexes. However, curtailments are projected to be based on current usage, not on contractual maximums. Enerco projects curtailments in the range of 20 to 40 percent.
1. Formulate an LP model to represent the production plan before the curtailments, including:
1). Define the decision variables.
2). Define the objective function.
3). Define the constraints for production quantities and natural gas usage.
2. Find the optimal solution by using Excel Solver for the above situation before the curtailments.
1). How much to produce for each products?
2). What is the optimal objective function value?
3). Based on the optimal solution, what is the natural gas usage (defined as the current usage)?
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