The Aspen-Boulder Coal Company runs a loading facility consisting of a large coal tipple. When the coal trains arrive, they are loaded from the tipple. The standard coal train takes 3 hours to load, and the tipple's capacity is 1.5 standard trainloads of coal. Each day, the railroad sends three standard trains to the loading facility, and they arrive at any time between 5 A.M. and 8 P.M. local time. Each of the 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 $5,000 per engine per hour. In addition, a high-capacity train arrives once a week every Thursday between 11 A.M. and 1 P.M. 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 mine to its capacity in six hours by a single loading crew. This crew (and its associated equipment) cost $9,000 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 the following considerations: 

 

How often should the second crew be called out? 

What are the expected monthly demurrage costs? 

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

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

Can this tipple support a fourth standard train every day? 

 

倒煤台的操作方案(美国竞赛1993年B题) 

 

Aspen-Boulder煤矿公司经营一个包括一个单个的大型倒煤台在内的装煤设施。当装煤列车到达时，从倒煤台往上装煤。一列标准列车要用3小时装满，而倒煤台的容量是一列半标准列车。每天，铁道部门向这个装煤设施发送三列标准列车。这些列车可在当地时间上午5点到下午8点的任何时间内到达。每列列车有三辆机车。如果一列车到达后因等待装煤而停滞在那里(即处于等待服务状态)的话、铁道部门要征收一种称为滞期费的特别费用、每小时每辆机车5000美元。此外，每周星期四上午11点到下午l点之间有一列大容量列车到达。这种特殊的列车有五辆机车并能装两列标准列车的煤。一个装煤工作班要用6个小时直接从煤矿运煤来把空的倒煤台装满。这个工作班(包括它用的设备)的费用是每小时9000美元。可以调用第二个工作班运行一个附加的倒煤台操作系统来提高装煤速度，而费用为每小时12000美元，出于安全的原因，当往倒煤台装煤时，不能往列车上装煤。每当由于往倒煤台装煤而中断往列车上装煤时，就要征收滞期费。 

 

煤矿公司的经理部门要请教你们如何决定该倒煤台的装煤操作的午预期开支，你们的分析应包括考虑以下的问题：

① 应调用几次第二个工作班?

② 预期的月滞期费是多少?

③ 如果标准列车能按调度在确切时间到达，什么样的日调度安排能使装煤费用最少？

④ 调用第三个费用每小时12000美元的倒煤台操作系统工作班，能否降低年操作费用?

⑤ 该倒煤台每天能否再装第四辆标准列车的煤? 

 

本题是由位于科罗拉多州Golden的科罗拉多矿业学院的Genc Woolsey根据他在怀俄明州一家煤矿公司做顾问中的问题建议的。位于纽约州的西点军校的ChriArney和Jack Robortson据此形成了本问题。