Problem statement
A retailer faces constant annual demand D, pays ordering cost S per order and holding cost H per unit per year. Orders arrive after a lead time of L days. Find the EOQ, the number of orders per year, the cycle time, the reorder point and the total annual inventory cost.
- Q* = √(2DS / H)
- TC = (D/Q)·S + (Q/2)·H
- ROP = d·L + safety stock, d = D / working days
Optimal order qty
774.6
Total inventory cost / yr
$1,549.19
Orders (runs) per year
15.49
Cycle time (days)
19.4
Ordering / setup cost
$774.60
Holding cost
$774.60
Max inventory
774.6
Reorder point
200
Purchase cost D·C
$120,000.00
Grand total incl. purchase
$121,549.19
Inventory level over time
What are we learning?
At the EOQ, annual ordering cost equals annual holding cost. The cost curve is flat near the optimum, so small rounding errors in Q barely change total cost.
Daily demand d = 40 units/day. Reorder when on-hand stock falls to 200 units.