Logistics Management

Homework $\backslash$#$3$

Problem $1.($Chapter $4$: Logistics$/$Supply Chain Customer Service$)$ A food company is attempting to set the customer service level $($in$-$stock probability in its warehouse$)$ for a particular product line item. Annual sales for the items are $100,000$ boxes, or $3,846$ boxes biweekly. The product cost in inventory is $\backslash (\backslash$$ $10\backslash )$ per box, to which $\backslash (\backslash$$ $1\backslash )$ is added as profit margin. Stock replenishment is every two weeks and the demand during this time is assumed normally distributed with a standard deviation of $400$ boxes. Inventory carrying costs are $30$ percent per year of item value. Management estimates that a $0\mathrm{.}156$ percent change in total revenue would occur for each $1$ percent change in the in$-$stock probability. Based on the information, find the optimal in$-$stock probability for the item. $($Hint: see the similar example on Module $3$ Ch $04$ PPT file slides $19-22)$

$\backslash (\backslash$Delta S L $\backslash )$ Levels in $\backslash \%$ for Various $\backslash (\backslash$Delta z $\backslash )$ Values

$*$Developed from entries in a normal distribution table