# Waiting Line Models, Decision Analysis and Forecasting

1) WAITING LINE MODELS -AMC Movie Theatre has only one box office clerk. For the movie theatre's normal offerings, customers arrive at the average rate of 3 per minute. On the average, each customer who comes to see a movie can be sold a ticket at the rate of 6 per minute. Assume arrivals follow the Poisson distribution and service times follow exponential distribution.

A) What is the probability that no customers are in the system?

B) What is the average number of customers waiting in line?

C) What is the average time a customer spends in the waiting line?

D) Do the operating characteristics indicate that the one-clerk system provides an acceptable level of service? Explain your thoughts.

2) DECISION ANALYSIS -Riverlake Fashion Centre must decide how many lots of assorted ski wear to order for its three stores. Information on prices, sales, and inventory costs has led to the following payoff table (in thousands):

Demand

Order Size Low Medium High

1 Lot 12 15 15

2 Lot 9 25 35

3 Lot 6 35 60

A) What decision should be made by one who is an optimist?

B) What decision should be made by one who is conservative?

C) What decision should be made by using minimax regret?

D) What approach would be deemed as preferrable- optimistic, conservative, or minimax regret? Eplain your position.

3) FORECASTING -The number of soda cans sold in a vending machine each week over a 10-week period were as follows: 338, 219, 278, 265, 314, 323, 299, 259, 287, 302

A) Develop forecasts using 3 and 4 week moving averages.

B) Compute the Mean Squared Error (MSE) for the 3 and 4 week moving average forecasts.

C) Of the two, what appears to be the best number of weeks of past data to use in the moving average computations?

D) Discuss briefly the benefits of using the moving average method for forecasting purposes.

keywords: queue analysis

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