Demand for a product is 25 tones / day and there are 200 working days / year. ==> D =
25(200) = 5000.
Ordering cost is €48 / order ==> S = 48
Carrying cost is €2 / unit / year ==> H = 2
Price schedule is as follows:
Quantity (Q) Price (P)
600-... 8
400-599 9
0-399 10
What is the best quantity that we could order to minimize our total annual cost?
To find the best quantity that minimizes the total annual cost, we need to find the Economic Order Quantity (EOQ).
The EOQ formula is given by:
EOQ = √(2DS / H)
where:
D = Demand per year (25 tons/day * 200 days/year = 5000 tons/year)
S = Ordering cost per order (€48)
H = Carrying cost per unit per year (€2)
Substituting the values into the formula:
EOQ = √(2 * 5000 * 48 / 2) = √(240000) = 489.897
The EOQ gives us the optimal quantity to order in order to minimize total annual cost. However, we need to consider the price schedule to find the best quantity to order.
From the price schedule, we can see that:
- For quantities of 600 or more, the price is €8 per unit.
- For quantities between 400 and 599, the price is €9 per unit.
- For quantities between 0 and 399, the price is €10 per unit.
Since the EOQ is approximately 489.897 units, it falls within the range of 400-599. Therefore, the best quantity to order to minimize the total annual cost is 400 units.
To calculate the total annual cost, we need to consider the ordering cost and the carrying cost. The total annual cost (TC) can be calculated as:
TC = DS + (Q/2) * H
where:
DS = Total ordering cost per year (D * S)
(Q/2) * H = Total carrying cost per year
Substituting the values:
DS = 5000 * 48 = €240,000
(Q/2) * H = (400/2) * 2 = €400
TC = 240,000 + 400 = €240,400
Therefore, the total annual cost for ordering 400 units is €240,400.