运营管理2考试习题

一、Determining the capacity level （确定能力水平）expanding the capacity P287-288

1、Cost of waiting is known等待成本已知

①：算一个总的成本MC（including the equipment， human resource）

②：再算受影响的顾客 affected number of Customers

③：算一个收益MB（用受影响的顾客*所获得的时间*等待成本）

④：比较MC和MB（MC<MB，it’s worthwhile expanding）

例题：1)For a service station, they want to increase an additional equipment to increase efficiency. An additional equipment requires an investment of $100000,assume useful life to be 5 years. An operator must be hired to run the equipment and paid $15 per hour. Assume the additional equipment is operated from 8:00am to 10:00am and also from 5:00pm to 7:00pm in the whole year, and it works 5 days a week. Assume every month has 3.5 weeks. Because of it, the average waiting time per customer will drop from 45min to 15min or a gain of 30min,and will affect 20.5 customers per hour. If we assume that the value of waiting for the customer is $4.5 per hour. So is it worthwhile expanding the capacity to one more equipment? Why?

答案：Calculate the total cost of the whole year:

($15*4hours *5days *3.5weeks*12mouth )+($100000/5years)=$32600

the total number of customers affect :

20.5customer*4hours*5days*3.5weeks*12=17220customers

The increased value for customer (or saved value for customer):

17220customers*30min/60min*$4.5=$38745

$38745>$32600 so it’s worthwhile expanding one equipment.

2、Cost of waiting is not known等待成本未知 P290

a= marginal cost of capacity expansion 总成本

b= cost of waiting per time unit and per customer 等候成本

w = the marginal reduction of average waiting time per customer赚取的时间

N = total number of customers whose average waiting time will be reduced over the time

horizon considered所受影响的顾客

a w*N

（上面那道题改成等待成本未知）

二、Customer is turned away（打发顾客）to calculate the optimal capacity P290 P(D C) *C0 (其中Co表示每过剩一个单位的能力成本，Cs表示每短缺一个单CS C0

*位的能力成本)注意：①根据P(D C) C0这个公式算出P（D>C*）② 根据P（D<C*）CS C0

=1- P（D>C*）算出得到一个数③ 根据z x ，因为是服从正态分布，因此知道均值和