# A company uses a product that must be delivered by special trucks. As such, ordering (and...

## Question:

A company uses a product that must be delivered by special trucks. As such, ordering (and delivery) costs are relatively high, at $3,600 per order. The product is packaged in four-liter containers. The cost of holding the product in storage is$90 per four-liter container per year. The annual demand for the product, which is constant over time, is 3,000 four-liter containers per year. The lead time from order placement to receipt is 16 days. The company operates 320 working days per year. Compute the optimal order quantity, the total minimum inventory cost, and the reorder point.

## Economic order quantity:

Economic order quantity is the level of unit to be ordered at a time. It provides minimum inventory cost, so it is considered as most economic level of quantity. It includes annual cost, ordering cost and carrying cost.

{eq}\textrm{Economic order Quantity }= \sqrt{\dfrac{2\times A\times O}{C}} {/eq}

A- Annual Demand, $3,000 O - Ordering cost,$ 3600

C0- Carrying cost $90 {eq}\textrm{Economic order Quantity }= \sqrt{\dfrac{2\times 3000\times 3600}{90}} {/eq} = 489.8 or 490 four-liter Total minimum inventory cost Ordering cost 3000 /490 = 6 order( 6 *$3,600) = 21,600

Carrying cost{ (490/2)* $90} =$22,050

Total cost = \$43,650

Reorder point.

= average daily unit sales * delivery lead time

Average daily sales = 3000/320 = 9.375

Reorder point = 9.375*16