A restaurant has tracked the average frequency of tables needed for a month for lunch

and dinner service. The data is as follows:

Tables needed Lunch Avg. Frequency Dinner Avg. Frequency

$303\mathrm{.}60$

$314\mathrm{.}650\mathrm{.}31$

$326\mathrm{.}40\mathrm{.}64$

$336\mathrm{.}60\mathrm{.}66$

$343\mathrm{.}41\mathrm{.}7$

$352\mathrm{.}453\mathrm{.}5$

$361\mathrm{.}87\mathrm{.}2$

$371\mathrm{.}119\mathrm{.}25$

$381\mathrm{.}527\mathrm{.}6$

$391\mathrm{.}173\mathrm{.}9$

$400\mathrm{.}42$

A waiter can handle four tables and the restaurant needs one beverage person for each eight

tables plus one busboy per twelve tables. To improve customer service the restaurant always

rounds up a fractional waiter, beverage, or busboy load. The restaurant wants to simulate the

number of tables needed and calculate the staffing required for waiters, busboys, and beverage

servers.

MGMT $6108$: Quantitative Methods for Managers

a$.$ Set up a probability and cumulative probability distribution for the number of tables

needed for lunch and dinner services.

b$.$ Using Excel random number generator, simulate the table requirement for $2$ weeks for

lunch and dinner service. Show the table requirement.

c$.$ Determine the staffing required for waiters, busboys, and beverage servers for each day

for each service. Show the staffing requirement. Calculate the average staffing

requirement per day for waiters, busboys, and beverage servers.

d$.$ Run the simulation for $5$ replications with different random numbers. Record the

average staffing requirement for each replication. Discuss the variation of staff

requirement in each replication. If you were the operations manager of the restaurant,

how would you use the simulation results to plan employee scheduling