Maria opened her authentic Mexican restaurant Mi Cazuela (a cazuela is a clay cooking bowl with a small handle on each side) in Pasadena, California, in the 1980s. It quickly became popular for the tasty food and use of fresh organic produce and all-natural meats. As her oldest child, you have been asked to run the restaurant. If you are able to gain her confidence, she will eventually hand over the restaurant to you.

You have definite ideas about increasing the profitability at Mi Cazuela. Lately, you have observed a troubling trend in the restaurant. An increasing number of customers are expressing dissatisfaction with the long wait, and you have also observed that some people leave without being served.

Your initial analysis of the situation at Mi Cazuela indicates that one way to improve customer service is to reduce the waiting time in the restaurant. You also realize that by optimizing the process for the peak time in the restaurant, you will be able to increase the profit.

Customers arrive in groups that vary in size from one to four (uniformly distributed). Currently, there are four tables for four and three tables for two patrons in the dining area. One table for four can be replaced with two tables for two, or vice versa. Groups of one or two customers wait in one queue while groups of three or four customers wait in another queue. Each of these waiting lines can accommodate up to two groups only. One- or two-customer groups are directed to tables for two. Three- or four-customer groups are directed to tables for four.

The restaurant remains open seven days a week from 5 P.M. till 11 P.M. The total number of customer groups visiting the restaurant each day varies uniformly between 30 and 50 or U(40,10). The customer arrival pattern is as follows:

Processes at the Restaurant

When a table of the right size becomes available and a waiter is free, he or she seats the customer, writes down the order, and delivers the order to the kitchen. Cooks prepare the food in the kitchen and bring it out. Any available waiter delivers the food to the customer. Customers enjoy the dinner. A waiter cleans the table and collects payment from the customers. The customers leave the restaurant. The various activity times are as follows:

Analyze and answer the following questions:

1. On average, how many customers leave the restaurant (per day) without eating?

2. What is the range of time a customer group spends at the restaurant?

3. How much time does a customer group wait in line?

From To Percent 5 P.M. 6 PM 7 P.M. 9 P.M. 10 P.M. 6 P.M. 7 P.M. 9 PM 10 P.M. 11 PM 10 20 55 10 S Activity # Activity Time Distributions 1 2 3 4 5 6 7 8 Activity Waiter seats the customer group. Waiter writes down the order. Waiter delivers the order to the kitchen. Cook prepares food. Cook brings out the food. Waiter delivers food to customer group. Customers eat. Waiter cleans table and collects payment + tips. N(2.0.5) min N(3, 0.7) min N(2, 0.5) min N(5, 1) min N(2, 0.5) min N(2, 0.5) min N(10, 2) min N(3, 0.8) min From To Percent 5 P.M. 6 PM 7 P.M. 9 P.M. 10 P.M. 6 P.M. 7 P.M. 9 PM 10 P.M. 11 PM 10 20 55 10 S Activity # Activity Time Distributions 1 2 3 4 5 6 7 8 Activity Waiter seats the customer group. Waiter writes down the order. Waiter delivers the order to the kitchen. Cook prepares food. Cook brings out the food. Waiter delivers food to customer group. Customers eat. Waiter cleans table and collects payment + tips. N(2.0.5) min N(3, 0.7) min N(2, 0.5) min N(5, 1) min N(2, 0.5) min N(2, 0.5) min N(10, 2) min N(3, 0.8) min