$4.$ KVS Pharmacy $($show your work$)$

KVS Pharmacy fills prescriptions for a popular children$$s antibiotic, Amoxcycilin. The daily demand for Amoxycillin is normally distributed with a mean of $250$ ounces and a standard deviation of $50$ ounces.

The vendor for the pharmaceutical firm that supplies the drug calls the drugstore$$s pharmacist every $30$ days and checks the inventory of Amoxcycilin.

During the last call, the druggist indicated that the store had $60$ ounces of the antibiotic in stock. The lead time to receive an order is four days.

A$)$ Determine the order size that will enable the druggist to maintain a $95\%$ customer service level.

Note: Customer service $95\%$ level determines the z$-$value, see example $7-11.$ z$-$value is determined from a table of cumulative probabilities of the normal distribution, Table $7-2$ states the most common z$-$values and the service level.TABLE $7-2$ Standard Deviations and Probabilities

$=$ Number of

Devlations Required

Probability of Being in Stock

Table $7-3$ displays the inventory carrying cost incurred for Trexoid across a range of different service level policies. Notice that the difference in inventory canrying coss is

increasing at an increasing rate. To go from a stockout probability of $15$ percent to a probability of $10$ percent costs an incremental $$26\mathrm{.}60($ $$125\mathrm{.}40-$$$98\mathrm{.}80).$ From a stockiont

probability of $10$ percent to a $5$ percent probability costs another $$34\mathrm{.}20($$$159\mathrm{.}60-$$$125\mathrm{.}40).$ But look at the cost differential to move from the stockout probability af $5$

percent to $1$ percent $-$ this will cost an additional $-$ $$159\mathrm{.}60.$

The general relationship between required inventory and increasing service level is depicted in Figure $7-4.$ As it shows, as companies attempt to offer higher levels of in$-$

stock performance to their customers, inventory carrying costs become increasingly burdensome. The burden may not seem so large when you think about the inventory af a

single item such as Trexoid, but consider that your store may carry hundreds of different computer games. Could you afford the extra expense of a $99$ percent in$-$stock policy

on all of them? Ultimately, the decision about how much safety stock to carry requires managers to balance carrying costs with the costs of stockouts, including lost profit, laet

future sales, and lost goodwill of customers who cannot buy what they want when they want it$.$