Bell Computers purchases integrated chips at $350 per chip. The holding cost is 35 percent of the unit price per year, the ordering cost is $120 per order and sales are steady at 5,000 per year. The company’s supplier, Rich Blue Chip Manufacturing Inc., decides to offer price discounts to attract larger orders. The price structure is shown below:
Quantity Purchases Price/Unit
1-99 units $350
100-199 units $325
200 or more units $300
What is the optimal order quantity?
Annual demand D = 5000
Ordering cost S = 120
Holding cost = 0.35
Quantity range | Price C | Holding cost H |
1-99 | 350 | 0.35*350 = 122.5 |
100-199 | 325 |
0.35*325 = 113.75 |
200 or more | 300 |
0.35*300 = 105 |
We calculate EOQ for all the ranges
H = 122.5
EOQ = 99 units
It is feasible as it is with in the range
H = 113.75
EOQ = 103 units
It is feasible as it is with in the range
H = 105
EOQ = 107
It is not feasible but we get more discount. So we calculate total cost at Q = 99, Q = 103 and Q = 200
Total cost = Purchasing cost + Annual holding cost + Annual ordering costs = CD+(Q/2)H + (D/Q)S
Q = 99
Total cost = (350*5000)+(99/2)*122.5 + (5000/99)*120 = 1762124.36
Q = 103
Total cost = (325*5000)+(103/2)*113.75 + (5000/103)*120 = 1636683.37
Q = 200
Total cost = (300*5000)+(200/2)*105 + (5000/200)*120 = 1513500
Total cost is less at Q = 200 units
Optimal order quantity = 200
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