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

Begin by selecting the formula used to calculate EOQ. $($DequalsDemand in units for one$$ year, PequalsOrdering cost per purchase$$ order, CequalsCarrying cost of one unit in$$ stock, QequalsAny order$$ quantity.$)$

ModifyingAbove EOQ equals StartRoot StartFraction $2$ DP Over Upper C EndFraction EndRoot With Subscript

Part $2$

The optimal number of pairs of shoes per order is

$6,000$

pair.

Part $3$

Requirement $2.$ Assume each month consists of approximately $4$ weeks. If it takes $1$ week to receive an$$ order, at what point should warehouse OR$2$ reorder$$ shoes?

Determine the formula used to calculate the reorder point for reordering shoes in warehouse$$ OR$2,$ then calculate the reorder point.

Demand per week

$$

Purchasing lead time $($wks$)$

$=$

Reorder point

$3,125$

$$

$1$

$=$

$3,125$

pairs

Part $4$

Requirement $3.$ Although$$ OR$2\text{'}$s average weekly demand is $3$ comma $125$ pairs of shoes $(150$ comma $00012$ months$4$ weeks$),$ demand each week may vary with the following probability$$ distribution:

Total demand for $1$ week

$1,600$ pairs

$2,650$ pairs

$3,125$ pairs

$3,415$ pairs

$3,665$ pairs

Probability $($sums to $1\mathrm{.}00)$

$0\mathrm{.}02$

$0\mathrm{.}20$

$0\mathrm{.}56$

$0\mathrm{.}20$

$0\mathrm{.}02$

If a store wants shoes and OR$2$ has none in$$ stock, OR$2$ can$$ "rush" them to the store at an additional cost of $ $4$ per pair. How much safety stock should Warehouse OR$2$ hold? How will this affect the reorder point and reorder$$ quantity?

The relevant total stockout and carrying costs are the

$$

when a safety stock of

pairs

of shoes is maintained. Therefore, Warehouse OR$2$

hold that number as safety stock.

This will

the reorder point to

pairs of shoes. The reorder quantity will