Question

A juice company purchases components from a variety of sources through their global network of suppliers. They are looking to determine their order quantity for PET bottles. They have forecast their demand for PET bottles for the next year to be 1195295 cases. Being a standard component, sales are expected to be constant/uniform over the course of the year. They operate 5 days per week so each year is made up of 260 days. The lead time for PET bottles (time from order to receipt is 3 days. They have also determined that the cost to carry a case of PET bottles in inventory is $0.84 per case per year and that order costs are estimated at $143.99 per order.  (Note: when working with inventory problems demand and carrying costs must be stated in the same time frame, annual in this case) The PET bottles purchased for $2.58 per case.  Given that the assumptions for the basic EOQ model apply, calculate the optimal order quantity (in cases) for this item.

1. What is the annual holding cost? Note: just the annual holding cost, not the total annual cost.  

2. What is the total annual cost, including ordering, holding and purchase costs? Note: the total annual cost including ordering, holding and purchase costs.  

Answer 1

1. EOQ = sqroot{(2*Annual Demand*Ordering cost)/Carrying cost}

= sqroot{(2*1195295*143.99)/0.84}

= 20243.2

Annual Holding cost = Average Inventory * Holdinhg cost per unit

= (20243.2/2)*0.84

= $8502.14

2. Ordering cost = (Annual Demand/EOQ)*Ordering cost per order

= (1195295/20243.2)*143.99

= $8502.14

Purchasing cost = Annual demand * Unit Price

= 1195295*2.58

= $3083861.1

Total cost = $8502.14 + $8502.14 + $3083861.1

= $3100865.38