PRACTICE PROBLEM I
WAITING LINE THEORY
Chapter 14

C&S bank can operate up to 4 drive-in teller windows. Currently each window
costs $10/hr. to operate. Each teller window can serve a customer on the average in 72 seconds. Bank customers arrive at the drive-in service system at an average rate of 35/hr. It is estimated that it costs the bank$40/hr. per customer tied up in the
system. This cost is due to customers switching banks if they must spend too much time in the
service system. An on-line computer system can be added to each teller window at an
additional cost of $15/hr per teller window and this will reduce the average service time at each window from 72 seconds to 36 seconds. A. How many teller windows would you recommend that the bank operate and should they use or not use the on-line computer system? What would be the cost per hour to operate this service system using your recommendation? B. If the bank is CURRENTLY using two teller windows without the computer system what is: (1) the maximum number of customers being served at any point in time? (2) the average number of customers actually being served? C Given your recommendation (in A) what is the average time a customer spends actually being served? D. Given your recommendation (in A) determine the: 1. Average number of customers waiting in line to be served 2. Average number of customers in the Service System 3. Average time (seconds) that a customer spends waiting in line to be served 4. Average time (seconds) that customers spend in the Service System E. Given the Current situation what is the average time(seconds) a customer spends in the Service System? F. Given your recommendation how many minutes less do customers spend at the teller window actually being served? G. Given Your Recommendation: 1) What is the Probability that 3 customers are waiting in Line 2) What is the Probability that No More Than 2 customers are in the Service System 3) What Percent of the time are there less than 4 customers Waiting in Line? ANSWERS: A. Use k = 1 teller window and also use the on-line computer TC =$46.54/hr.
B. 1) k=2; 2) 0.70
C. 36 sec.
D. 1) .1885/hr E. 82.08 sec
2) .5385/hr F. 0.6 minutes
3) 19.39 seconds G.
4) 55.39 seconds

PRACTICE PROBLEM II
WAITING LINE THEORY
Chapter 14

The UPS company at the Greenville NC unloads trucks Currently at just ONE unloading dock. Assume that the shipping department is considering adding a second
dock area, installing a conveyor system or both. Given the following productivity and cost information determine UPS' minimum cost alternative. (UPS operates the
shipping department 52 weeks per year and 40 hours per week)

Truck rental and operator cost is $200/hr. Current Dock cost per dock is$30/hr.
Trucks arrive at the service system at an average rate of 3 trucks per hour.
Without the conveyor system each dock can service(unload) 4 trucks per hour.
With the conveyor system each dock can service a truck on average in 10 minutes.

A. In order to minimize the total hourly cost of the truck unloading operation, UPS must
decide how many docks to use and whether they should or should not use a conveyor with
each dock? THE CURRENT ARRANGEMENT IS TO USE JUST ONE DOCK AND
NO CONVEYOR. YOU ARE A MANAGEMENT CONSULTANT AND HAVE
BEEN ASKED TO SHOW THE COST PER HOUR OF EACH REASONABLE
POSSIBILITY AND THEN MAKE A POLICY RECOMMENDATION.

B. If UPS is CURRENTLY using ONE unloading dock without the conveyor
what is: 1) the maximum number of Trucks being served (unloaded) at any point in time?
2) the average number of trucks actually being served (unloaded)?
3) What is the probability that At Least 2 Trucks are waiting in Line
4) What percent of the time are there more than 3 Truck waiting in Line
5) What is the probability that No More than 3 Trucks are in the Service System

C. How many MINUTES less will trucks spend WAITING IN LINE BEFORE BEING

D. Given your recommendation (in A) determine the:
1. Average number of Trucks waiting in line to be served (unloaded)
2. Average number of trucks in the Service System
3. Average time (seconds) that trucks spends waiting in line to be served (unloaded)
4. Average time (minutes) that trucks spend in the Service System

E. How many minutes less on average are trucks in the Service System with your recommendation
than in the current situation.

F. Given the Current Situation: 1) What is the probability that at Least 2 Trucks are waiting in Line 2) What is the Probability that Only ONE Truck is waiting in Line? 3) What Percent of the time are there Less than 4 Truck in the Service System?

ANS: A: K = 2, use conveyor, TC = 216.66/hr. B: 1) one; 2) .75 3) .4219 4) .2373 5) .6836
C: 44.33 minutes D: 1).0333 2) .5333 3) 39.96 sec 4) 10.666 min. 5) 5 min. E: 49.334 min F) ?