The Detroit Edison Company owns and operates a coal-fired power plant in Monroe, Michigan. Coal is generally brought by train to the plant from mines in nearby states and is unloaded by a single unloader system. Originally, coal was brought into the power plant entirely by rail. Difficulties developed in meeting the plant's coal needs as the generating capacity was increased. The more recent plan combined rail and lake-vessel delivery of coal to satisfy the plant's requirements. Costly delays were occurring.

Several factors contributed to the difficulties - the major contributor being the design of the single-car unloader and its rate of breakdown. To alleviate the problems, Detroit Edison considered the addition of a second multimillion-dollar unloader system. Although a simulation model of the entire rail-coal movement system was available, an analytic model was built to focus on the unloader. The analytic model was a modified version of a standard single- and multiple-server finite-source queueing model. Other solutions to the problem were also studied:

• Reducing the frequency of unloader breakdowns,
• Reducing the repair time, and
• Changing the cycle between the mine and the power plant.

The factors considered were:

• The impact of a second unloader system on the coal throughput,
• L, the average number of trains in queue, and
• W, the average time a train spent in the unloader system.

Assumptions about the model included:

• Coal availability does not affect the train cycle rate.
• All trains are the same size.
• A train can wait at the facility while an unloader is being prepared.
• When two unloaders are broken, two crews work independently on them.
• When one unloader is broken, only one crew repairs it.
• A train that is in a facility when one unloader breaks down is rerouted to the other unloader facility. (The average repair time of the unloader is substantially greater than the time necessary to reroute the train.)

Data were collected from records on breakdowns, trip-completion times, the use of a single unloader and two unloaders. The analytic mathematical model provided answers within an hour, whereas the simulation model would have taken at least a day.

The results of the study showed management that they must differentiate between ways of increasing unloader availability, a concept not previously recognized. The analytic model, originally developed only to evaluate the addition of an unloader, provided ongoing information about changing the system configuration to meet system constraints (such as coal throughput and wait time).