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DATA ENVELOPMENT ANALYSIS 205

costs would be required to change the hiring plan based on a training cost of E875 per temporary
nurse?
4 Suppose that the hospital hired ten full-time nurses at the beginning of January in order to satisfy part of the
requirements over the next six months. If the hospital can hire full-time nurses for E16.50 per hour, including
fringe benefits, what effect would it have on total labour and training costs over the six-month period as
compared to hiring only temporary nurses? Assume that full-time and temporary nurses both work
approximately 160 hours per month. Provide a recommendation regarding the decision to hire additional
full-time nurses.

CASE PROBLEM 5 Cinergy Coal Allocation*

inergy Corporation manufactures and distributes electricity for customers located in Indiana, Kentucky
C and Ohio. The company spends $725 to $750 million each year for the fuel needed to operate its coal-
fired and gas-fired power plants; 92 per cent to 95 per cent of the fuel used is coal. Cinergy uses ten coal-
burning generating plants: five located inland and five located on the Ohio River. Some plants have more than
one generating unit. As the seventh-largest coal-burning utility in the United States, Cinergy uses 28–29 million
tons of coal per year at a cost of approximately $2 million every day.
The company purchases coal using fixed-tonnage or variable-tonnage contracts from mines in Indiana (49
per cent), West Virginia (20 per cent), Ohio (12 per cent), Kentucky (11 per cent), Illinois (5 per cent) and
Pennsylvania (3 per cent). 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 Cinergy’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 generating unit is expected
to produce and to provide a measure of each generating unit’s efficiency, referred to as the heat rate. The heat
rate is the total BTUs required to produce one kilowatt-hour (kWh) of electrical power.

Coal Allocation Model
Cinergy uses a linear programming model, called the coal allocation model, to allocate coal to its generating
facilities. The objective of the coal allocation model is to determine 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 electricity each unit must produce.
The cost to process coal, called the add-on cost, depends upon the characteristics of the coal (moisture
content, ash content, BTU content, sulfur content and grindability) and the efficiency of the generating unit. The
add-on cost plus the transportation cost are added to the purchase cost of the coal to determine the total cost
to purchase and use the coal.

Current Problem

Cinergy signed three fixed-tonnage contracts and four variable-tonnage contracts. The company would like to
determine the least-cost way to allocate the coal available through these contracts to five generating units. The
relevant data for the three fixed-tonnage contracts are as follows:
*
The authors are indebted to Thomas Mason and David Bossee of Cinergy Corp. for their contribution to this case problem.

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