MGTS $352$ Homework $5-$ Inventory Management

Total points: $10$

A museum of natural history opened a gift shop $2$ years ago. Managing inventories has become a problem. Low inventory turnover is squeezing profit margins and causing cash flow problems.

One of the top$-$selling SKUs in the container group at the museum's gift shop is a bird feeder. Sales are $18$ units per week, and the supplier charges $$60$ per unit. The cost of placing an order with the supplier is $$45.$ Annual holding cost is $25$ percent of a feeder's value, and the museum operates $52$ weeks per year. Management chose a $390-$unit lot size so that new orders could be placed less frequently.

a$.[2$ points$]$ What is the annual cycle$-$inventory cost of the current policy of using a $390-$unit lot size? Would a lot size of $468$ be better? $($i$.$e$.,$ costs related to cycle stock only$)$

b$.[3$ points$]$ Calculate the EOQ and its total annual cycle$-$inventory cost. How frequently will orders be placed if the EOQ is used?

$($round the EOQ to the nearest integer;

Time Between Orders $($TBO$)$ can be expressed in various ways for the same time period, e$.$g$.,$ weeks, $$ days, etc. you can choose your preferred way.$)$

c$.[$Reorder Point for Variable Demand and Constant Lead Time$]$

$[2$ points$]$ Suppose that the average demand is $18$ units per week with a standard deviation of $5$ units. The lead time is constant at $2$ weeks. Determine the safety stock and reorder point if management wants a $90$ percent cycle$-$service level.

$($Hint: choose a z score corresponding to a CSL that is the closest to $90\%$;

when safety stock is not an integer, think about whether the result should be rounded up or rounded down. To be practical, both safety stock and reorder point need to be integers.$)$

d$.[$Periodic Review System$]$

$[3$ points$]$ Recall that demand for the bird feeder is normally distributed with a mean of $18$ units per week and a standard deviation in weekly demand of $5$ units. The lead time is $2$ weeks, and the business operates $52$ weeks per year.

In a Q system where reorder point is used, the lot size for each order is $75$ units. What is the equivalent $P$ system if management still wants a $90$ percent cycle$-$service level? In other words, what are the Time Between Reviews $P$ and Target Inventory Level $T?$

$($Hint: in a P system, when Time Between Reviews $P$ is not an integer, the result needs to be rounded to the nearest integer, to be practical.

After calculating this part, you can compare part $($c$)$ and part $($d$)$ to see the differences between $Q$ system and $P$ system.$)$