Question

The city of Lakewood has one magistrate who performs civil marriage ceremonies. She works eight hours on regular business days. On average, couples arrive every 15 minutes to be married. The ceremony, including information processing, usually takes about 10 minutes. The city estimates that the time that people spend waiting to be married costs them $10 per hour in goodwill and prospective campaign donations. There are two ways that they are considering to reduce this waiting cost:

a. Install a computer system to do the information processing. This will speed up each ceremony by 40 %. The city already owns the hardware; it will cost $100 per day to operate the system.

b. Hire another magistrate, at the cost of $75 per day.

Which option will save more money? Back up your recommendations with an explicit cost analysis. What assumptions have you made in order to do your analysis?

Answer 1

We compare the two options with the existing system

Current arrival rate = 1 / 15 minutes * 60 minutes per hour = 4 couples per hour

Serice rate = 1 / 10 minutes * 60 minutes per hour = 6 per hour

Option 1: service time will improve by 40% . Current service time is 10 minutes. After 40% improvement, service time = 10 - 10*40% = 6 minutes.

Therefore service rate will be = 1 / 6 minutes * 60 minutes per hour = 10 per hour

a) A comparative cost analysis of both options versus the current system is given below.

We can see that option results in substantial cost reduction. Therefore option 2 is recommended

b) In this case, there will be two separate systems, with arrival rate equal to half of earlier i.e. 2 per hour.

Average number of couplpes waiting in each line = λ2/μ/(μ-λ) = 2²/6(6-2) = 0.1667 . So total waiting cost per day for the two lines = 2*0.1667*10*8 = $ 26.67

Clearly this is not a better solution as compared to any of the earlier options.