$21-30$ EOQ, uncertainty, safety stock, reorder point. FootLove Shoe Co$.$ produces and sells excellent quality walking shoes. After production, these shoes are distributed to $30$ warehouses around the country. Each warehouse services approximately $120$ stores in its region. FootLove uses an EOQ model to determine the number of pairs of shoes to order for each warehouse from the factory. Annual demand for warehouse WH$1$ is approximately $180,000$ pairs of shoes. The ordering cost is $$200$ per order. The annual carrying cost of a pair of shoes is $$3\mathrm{.}20$ per pair.

$1.$ Use the EOQ model to determine the optimal number of pairs of shoes per order.

$2.$ Assume each month consists of approximately $4$ weeks. If it takes $1$ week to receive an order, at what

point should warehouse WH$1$ reorder shoes?

$3.$ Although WH$1$s average weekly demand is $3,750$ pairs of shoes $(180,000-$: $12$ months $-$: $4$ weeks$),$ de$-$

mand each week may vary with the following probability distribution:

Total demand for $1$ week $3,250$ pairs $3,500$ pairs $3,750$ pairs $4,000$ pairs $4,250$ pairs

Probability $($sums to $1\mathrm{.}00)0\mathrm{.}050\mathrm{.}150\mathrm{.}550\mathrm{.}200\mathrm{.}05$

If a store wants shoes and WH$1$ has none in stock, WH$1$ can $$rush$$ them to the store at an additional cost of $$3\mathrm{.}00$ per pair. How much safety stock should warehouse WH$1$ hold? How will this affect the reorder point and reorder quantity?