1990 Problem B: Coal Tipple Operations

The Aspen-Boulder Coal Company runs a loading facility consisting of a single large coal tipple.  When coal trains arrive, they are loaded form the tipple.   The standard train takes 3 hours to load and the tipple’s capacity is 1 – ½ standard trainloads of coal.  Each day, the railroad sends three standard trains to the loading facility and they arrive any time between 5AM and 8PM local time.  Each of these trains has three engines.  If a train arrives and sits idle while waiting to be loaded, the railroad charges a special fee called a demurrage.  The fee is $5000 per engine per hour.  In addition, a high-capacity train arrives once a week every Thursday between 11AM and 1PM.  This special train has five engines and holds twice as much coal as a standard train.  An empty tipple can be loaded directly from the mine3 to its capacity in 6 hours by a single loading crew.  This crew (and its associated equipment) costs $9000 per hour.  A second crew can be called out to increase the loading rate by conducting an additional tipple-loading operation at the cost of $12,000 per hour.  Because of safety requirements, during tipple loading, no trains can be loaded.  Whenever train loading is interrupted to load the tipple, demurrage charges are in effect.

The management of the Coal Company has asked you to determine the expected annual costs of this tipple’s loading operations.  Your analysis should include following considerations;

a)      How often should the second crew be called out?

b)      What are the expected monthly demurrage costs?

c)      If the standard trains could be scheduled to arrive at precise times, what daily schedule would minimize loading costs?

d)      Would a third tipple-loading crew at $12,000 per hour reduce annual operations costs?

e)      Can this tipple support a fourth standard train every day?