Due Friday, Mar

$($Waiting Line Models$)$ A single public health worker is inoculating children against measles at

a local clinic. An average of $6$ children per hour is expected to arrive according to a Poisson

distribution. He serves the children at a rate of $8$ per hour. Assume that the service$-$time

distribution is approximately exponential. Use the Excel "Lec $11$ MMk Model" to answer the

following questions.

$($a$)$ For the 'inoculation system', find:

i$)$ the utilization of the health worker

ii$)$ the average time spent by a child in the system

iii$)$ the average number of children in the system

iv$)$ the average number of children in line

v$)$ the average number of children in the system if another health worker is added

to the system $($assume only one waiting line in the system$)$ who has the same

service rate as the existing one.

$($b$)$ At what rate must children be served in order to reduce the average time spent in the

system to $15$min $?$

$($ABC analysis$)$ Determine an A$-$B$-$C classification for these items. Data available in $"$HW$2$

Data.xIsx". $($use a theoretical distribution: A $70\%,$ B $20\%,$ C $10\%)$

$($Newsvendor Model$)$ The Katie's Card Shop sells calendars with different Colonial pictures

shown for each month. The once$-$a$-$year order for each year's calendar arrives in September.

From past experience the September to March demand for the calendars can be

approximated by a normal distribution with mean $500$ and standard deviation $120.$ The

calendars cost $$1\mathrm{.}50$ each, and Katie sells them for $$3$ each.

$($a$)$ If Katie throws out all unsold calendars at the end of March $($i$.$e$.,$ salvage value is zero$),$

how many calendars should be ordered?

$($b$)$ If Katie reduces the calendar price to $$1$ at the end of March and can sell all surplus

calendars at this price, how many calendars should be ordered?

$($EOQ & Safety Stock Model$)$ A Regional Hospital $($RH$)$ consumes $500$ boxes of bandages per

week at a constant rate. The price of bandages is $$70$ per box. The cost of processing an

order is $$60,$ and the cost of holding one box for a year is $$10\mathrm{.}5.$ The lead$-$time is $3$ days.

$($a$)$ How many boxes of bandages should RH order every time $($i$.$e$.,$ EOQ$)?$

$($b$)$ Currently, RH orders $900$ boxes of bandages every time. If they order based on the results

calculated in $($a$)$ above, how much could RH save in the total annual cost?

$($c$)$ Suppose that the demand on bandages becomes uncertain which is normally distributed

with mean $500$ boxes of bandages per week and a standard deviation of $100$ boxes per

week. The purchasing department uses a re$-$order point system to manage its inventory

of bandages and maintains a service level of $95\%.$ What is the reorder point for the

bandages?