Ross White's machine shop uses $2,500$ brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased

from a supplier $100$ miles away for $$15$ each, and the lead time is $2$ days. The holding cost per bracket per year is $$1\mathrm{.}50($or $10\%$ of the unit cost$)$ and the ordering

cost per order is $$18\mathrm{.}75.$ There are $250$ working days per year.

Required:

a$)$ What is the EOQ?

b$)$ Given the EOQ, what is the average inventory? What is the annual inventory holding costs?

c$)$ In minimizing cost, how many orders would be made each year? What would be the annual ordering cost?

d$)$ Given the EOQ, what is the total annual inventory cost, including purchase cost?

e$)$ What is the time between orders?

f$)$ What is the reorder point, ROP?

$3.$ Refer to Problem $2.$ Suppose Ross wants to reexamine his decision of buying the bracket and is considering making the brackets in$-$house. He has determined that setup costs would be $$25$ in machinist time and lost production time, and $50$ brackets could be produced in a day once the machine has been set up$.$ Ross estimates that the cost $($including labor time and materials$)$ of producing one bracket would be $$14\mathrm{.}80.$ The holding cost would be $10\%$ of this cost.

Required:

a$)$ What is the daily demand rate?

b$)$ What is the optimal production quantity? Round up to nearest whole number.

c$)$ Given the optimal production run size in part b$,$ what is the total annual inventory cost $($including purchase cost, holding, and setup costs$)?$

$4.$ After analyzing the costs of various options for obtaining brackets, Ross $($refer to $2$ & $3$ above$)$ recognizes that although he knows that lead time is $2$ days and demand per day averages $10$ units, the demand during the lead time often varies. Ross has kept very good records and has determined lead time demand is normally distributed with a standard deviation of $1\mathrm{.}52$ units. Assume this company always orders $250$ units each time an order is placed.

Required:

a$)$ What Z value would be appropriate for a $97\mathrm{.}5\%$ service level? Use the normal distribution table.

b$)$ What safety stock should Ross maintain if he wants a $97\mathrm{.}5\%$ service level. Round up to nearest whole number.

c$)$ What is the adjusted ROP for the brackets?

d$)$ What is the annual inventory holding cost including safety stock if the annual holding cost per unit is $$2\mathrm{.}50?$

Hints: When standard deviation of lead time demand is known, safety stock$=$ Z $*$ standard deviation of the lead time demand. However, if you are given lead time, the daily demand and standard deviation of the daily demand, the safety stock $=$ Z $*$ standard deviation of the daily demand $*$ SQRT$($lead time$).$

ROP $=$ lead time $*$ daily demand $+$ safety stock!