# 24.docx - Case Problem 5 DUKE ENERGY COAL ALLOCATION Duke...

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Case Problem 5 DUKE ENERGY COAL ALLOCATION* Duke Energy manufactures and distributes electricity to customers in the United States and Latin America. Duke recently purchased Cinergy Corporation, which has generating facilities and energy customers in Indiana, Kentucky, and Ohio. For these customers Cin- ergy has been spending \$725 to \$750 million each year for the fuel needed to operate its coal-fired and gas- fired power plants; 92% to 95% of the fuel used is coal. In this region, Duke Energy uses 10 coal- burning generating plants: five located inland and five located on the Ohio River. Some plants have more than one generating unit. Duke Energy uses 28–29 million tons of coal per year at a cost of approximately \$2 million every day in this region. The company purchases coal using fixed-tonnage or variable-tonnage contracts from mines in Indiana (49%), West Virginia (20%), Ohio (12%), Kentucky (11%), Illinois (5%), and Pennsylvania (3%). The company must purchase all of the coal contracted for on fixed-tonnage contracts, but on variable-tonnage contracts it can purchase varying amounts up to the limit specified in the contract. The coal is shipped from the mines to Duke Energy’s generating facilities in Ohio, Kentucky, and Indiana. The cost of coal varies from \$19 to \$35 per ton and transportation/delivery charges range from \$1.50 to \$5.00 per ton. A model is used to determine the megawatt-hours (mWh) of electricity that each gen- erating unit is expected to produce and to provide a measure of each generating unit’s effi- ciency, referred to as the heat rate. The heat rate is the total BTUs required to produce 1 kilowatt-hour (kWh) of electrical power. Coal Allocation Model Duke Energy uses a linear programming model, called the coal allocation model, to allo- cate coal to its generating facilities. The objective of the coal allocation model is to deter- mine the lowest-cost method for purchasing and distributing coal to the generating units. The supply/availability of the coal is determined by the contracts with the various mines, and the demand for coal at the generating units is determined indirectly by the megawatt- hours of