# Project #28132 - Operations: Queuing Models: Waiting Line Management

**EACH PART OF QUESTION MUST BE ANSWERED**

Assignment # 2A

Intent: This situation is intended to help managers evaluate different alternative designs when multiple servers are available.  The alternative design options could include, (1) using the servers as a single team, (2) pulling customers from a single line, (3) pulling customers from multiple lines.  Part I of this problem runs the numbers for the different designs.  More importantly, part II evaluates the alternatives for managerial insights.  However, numbers are necessary to draw useful managerial insights.

A fast-food franchise is considering opening a drive-in window food service operation.  Customer arrival has a mean arrival rate of 48 cars per hour.  Arriving customers place orders at an intercom station at the back of the parking lot and then drive up to the service window to pay for and receive their order.  It takes two minutes for a server to complete the service.  At the current demand rate, a single server would not be a feasible alternative.  Two employees are made available for the service.  For simplicity, assume Poisson distribution for arrival and exponential distribution for service.  The following three service alternatives are being considered:

(1) A single-station operation where two employees work as a team to serve each customer.  The average service time for this alternative is 1 minutes.

1. A two-station operation with two service windows and two employees.  Newly arriving customers join a single queue (single-line) which feeds both service windows.  The employee stationed at each window fills the order and takes the money for customers arriving at that window.  The average service time at each window for this alternative is 2 minutes.

(3) There are two service windows and two employees.  There is a separate queue for each of the service windows (multi-line).  Newly arriving customers randomly choose one of two queues (assume that arrival is equally split between the two lines).  The employee stationed at each window fills the order and takes the money for customers arriving at that window.  The average service time at each window for this alternative is 2 minutes.

(I) Compute the following operating characteristics for each alternative:

(a)  Average number of cars waiting for service.

(b)  Average number of cars in the system.

(c)  Average time a car waits for service (in minutes).

(d)  Average time in the system (in minutes).

(II) Compare your results in the three cases. Under what conditions would you prefer which system? Then, why do some services (e.g. groceries) offer case (3)?

Assignment # 2B

Intent: This situation is intended to help managers see the tradeoffs between labor cost and cost of customer waiting.  Managers often try to use resources at a very high utilization.  But high utilization, at the expense of long customer wait, is not always helpful. This problem indicates how an optimal workforce staffing can be derived to minimize overall cost.  This problem also illustrates how different designs may be necessary for the same service for different customer segments.

Part I

A walk-in-clinic provides medical services to a college campus where most customers are students.  The Director of the clinic is considering use of queuing formulas to determine the best level of staffing.  On the basis of past record, the director finds that the clinic receives, at the average, 18 customers per hour, and service records estimate that each provider (doctor or nurse) takes 10 minutes to treat a patient.  The hourly cost of a provider is \$80 per hour.  The cost of keeping a customer waiting in line is estimated to be \$100 per hour (this includes patient’s time, cost of inconvenience, bad word of mouth, loss of future business, etc).  In order to use queuing models, assume that arrivals follow to a Poisson distribution and service times are exponentially distributed.  Patients are treated by the first available provider on a first-come-first-serve basis from a single line. [Note: This is an M/M/C systems, use appropriate formula/table].  Determine the optimal number of providers (level of staffing) that minimizes the total cost of labor and customer waiting.  What is the corresponding minimum total (hourly) cost?

Part II

Now, assume that instead of students, the customers are top level business executives.  The revised cost of keeping a customer waiting in line is estimated to be \$1000 per hour (this includes executive’s time, cost of inconvenience, bad word of mouth, loss of future business, etc).  The arrival rate, service rate and other policies are the same as above.  Determine the optimal number of providers that minimizes the total cost of labor and customer waiting.  What is the corresponding minimum total (hourly) cost?

Compare your results in parts I and II above.

 Subject Business Due By (Pacific Time) 04/20/2014 12:00 pm
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