Solved Problems on Process Analysis
Operations Management 70371
Practice Problems on Process Analysis: Solutions
1. On a typical weekday in January, 4,200 customers visit the Pittsburgh Wal-Mart. It is estimated that, on average, there are 350 customers in the store. Assuming that the store is open 14 hours a day, how much time does the average customer spend in the store? Solution:
- Since the average number of customers in the store is 350, I=350.
- 4,200 customers go through the system in a 14 hr. day. Thus, the throughput rate
(R) is 4200 customers/day or 4200/14 = 300 customers/hr.
- Applying Little’s Law (I=R*T) the time an average customer spends in the store is: T=I/R = 350/300 = 1.17 hours = 70 minutes
2. In 2006, Shouldice Hospital admitted 14,965 patients. In 2007, a 20% increase in admissions is expected. Currently the hospital has 390 beds. Assume the hospital operates 365 days a year (and, please assume one patient per bed!).
a) If the average patient stays in the hospital 8 days, how many beds were empty, on average, in 2006?
Solution:
- Average stay, T = 8 days
- 14,965 patients went through the system in a year. This implies R=14,965/365 =
41 patients/day.
- Thus the number of patients in the hospital on average is I=R*T= 41*8 = 328, and the number of average empty beds is (390-328)=62.
b) On average, how many beds do you expect to be empty in 2007?
Solution:
- The number of beds needed will also increase by 20 % to a total of 393.6, implying that not enough beds are available.
3. The total number and gender mix of employees in a certain company remains constant. Due to turnover, on average the company hires 150 men and 200 women each year. It is estimated that on average a woman stays 50% longer than a man.
What proportion of the employees are women?
Solution:
- Since the total number and gender mix of employees remains constant, the throughput rate of this system equals the input rate (rate of hiring).
-
Let m denote men and w women. We have R(m) = 150 men/year and R(w) = 200
Practice Problems on Process Analysis: Solutions
1. On a typical weekday in January, 4,200 customers visit the Pittsburgh Wal-Mart. It is estimated that, on average, there are 350 customers in the store. Assuming that the store is open 14 hours a day, how much time does the average customer spend in the store? Solution:
- Since the average number of customers in the store is 350, I=350.
- 4,200 customers go through the system in a 14 hr. day. Thus, the throughput rate
(R) is 4200 customers/day or 4200/14 = 300 customers/hr.
- Applying Little’s Law (I=R*T) the time an average customer spends in the store is: T=I/R = 350/300 = 1.17 hours = 70 minutes
2. In 2006, Shouldice Hospital admitted 14,965 patients. In 2007, a 20% increase in admissions is expected. Currently the hospital has 390 beds. Assume the hospital operates 365 days a year (and, please assume one patient per bed!).
a) If the average patient stays in the hospital 8 days, how many beds were empty, on average, in 2006?
Solution:
- Average stay, T = 8 days
- 14,965 patients went through the system in a year. This implies R=14,965/365 =
41 patients/day.
- Thus the number of patients in the hospital on average is I=R*T= 41*8 = 328, and the number of average empty beds is (390-328)=62.
b) On average, how many beds do you expect to be empty in 2007?
Solution:
- The number of beds needed will also increase by 20 % to a total of 393.6, implying that not enough beds are available.
3. The total number and gender mix of employees in a certain company remains constant. Due to turnover, on average the company hires 150 men and 200 women each year. It is estimated that on average a woman stays 50% longer than a man.
What proportion of the employees are women?
Solution:
- Since the total number and gender mix of employees remains constant, the throughput rate of this system equals the input rate (rate of hiring).
-
Let m denote men and w women. We have R(m) = 150 men/year and R(w) = 200