A mail-order house uses 16,260 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. |
Number of Boxes | Price per Box |
1,000 to 1,999 | $1.25 |
2,000 to 4,999 | 1.20 |
5,000 to 9,999 | 1.15 |
10,000 or more | 1.10 |
a. |
Determine the optimal order quantity. (Round your answer to the nearest whole number.) |
Optimal order quantity | boxes |
b. |
Determine the number of orders per year. (Round your answer to 2 decimal places.) |
Number of order | per year |
DEMAND = 16260
HOLDING COST = 0.6
ORDERING COST = 96
EOQ = SQRT(2DS/H)
Optimal order quantity = Quantity with lowest total annual cost of inventory
TCI = annual holding cost + annual ordering cost + annual material cost
Annual holding = adjusted quantity / 2 * holding cost
Annual ordering = demand / adjusted quantity * ordering cost
Annual material cost = demand * cost per unit
ADJUSTED Q = EOQ IF EOQ > LOWER LIMIT, < UPPER LIMIT
LOWER LIMIT IF EOQ < LOWER LIMIT
UPPER LIMIT IF EOQ > UPPER LIMIT
NO. |
LOWER BRACKET |
UPPER BRACKET |
PER UNIT |
HC |
EOQ |
Q* |
TOTAL COST |
FORMULA |
1 |
1 |
1999 |
1.25 |
0.6 |
2281 |
1999 |
21705.57 |
(16260 * 1.25) + ((1999 / 2) * 0.6) + ((16260 / 1999) * 96) = 21706 |
2 |
2000 |
4999 |
1.2 |
0.6 |
2281 |
2281 |
20880.63143 |
(16260 * 1.2) + ((2281 / 2) * 0.6) + ((16260 / 2281) * 96) = 20881 |
3 |
5000 |
9999 |
1.15 |
0.6 |
2281 |
5000 |
20511.19 |
(16260 * 1.15) + ((5000 / 2) * 0.6) + ((16260 / 5000) * 96) = 20511 |
4 |
10000 |
MORE |
1.1 |
0.6 |
2281 |
10000 |
21042.1 |
(16260 * 1.1) + ((10000 / 2) * 0.6) + ((16260 / 10000) * 96) = 21042 |
OPTIMAL ORDER QUANTITY = 5000
TOTAL COST OF INVENTORY = 20511
2. NO. OF ORDERS PER YEAR = D / Q = 16260 / 5000 = 3.25
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