Harriet is the purchasing manager for High Tech Company. She is faced now with t
ID: 346482 • Letter: H
Question
Harriet is the purchasing manager for High Tech Company. She is faced now with the following dilemma. Her operation uses 10,000 units a year of copper cable connectors. She knows it can be manufactured internally at the rate of 100,000 units per year and at a cost of $40 per unit. However, associated with each production run there is a set-up cost of $5000, and the annual inventory holding cost is i = 20 percent.
Harriet is cost conscious and decided to get a price from two external suppliers. Electronic Hardware Company offered a price of $44 per unit, provided that the minimum quantity shipped is 1000 units; they could supply up to 6000 units per year.
Metstamp Company fixed the price of $43.50 per unit, with a fixed cost of $200 per shipment, regardless of the quantity; they could supply up to 4000 units per year. What is the optimal policy Harriet should use, assuming no shortages are allowed?
Explanation / Answer
Let us find the total cost function for production and the two suppliers.
For production only
p = rate of production = 100,000 per year
d = deamand rate = 10,000 per year
S = setup cost = $5,000
H = holding cost of inventory = 20% x $40 = $8
EOQ = Q* = SQRT(2.d.S/H) x SQRT(p/(p - d))
= SQRT(2*10000*5000/8) * SQRT(100000/(100000 - 10000)) = 3726
Total cost = Q*.H.(p - d)/2.p + (D/Q*).S + $40.d = $426,833
For the first supplier=6000, rest 4000 production
dp = 4000; ds = 6000
Qp* = SQRT(2*4000*5000/8) * SQRT(100000/(100000 - 4000)) = 2282
Total cost from production = Qp*.H.(p - dp)/2.p + (dp/Qp*).S + $40.dp = $177,527
Total cost from the first supplier = (1000*20%*44)/2 + 6000*44 = $268,400
Total cost of this plan = $177,527 + $268,400 = $445,927
For the first supplier=6000, rest 4000 from second supplier
Total cost from the first supplier = (1000*20%*44)/2 + 6000*44 = $268,400
Q* for the second supplier = SQRT(2*4000*200/(20%*43.5)) = 429
Total cost for the second supplier = Q*.H./2 + (D/Q*).S + $43.5.d = $177,731
Total cost of this plan = $177,731 + $268,400 = $446,131
For the second supplier=4000, rest 6000 from production
dp = 6000; ds = 4000
Qp* = SQRT(2*6000*5000/8) * SQRT(100000/(100000 - 6000)) = 2825
Total cost from production = Qp*.H.(p - dp)/2.p + (dp/Qp*).S + $40.dp = $261,241
Total cost from the second supplier = $177,731
Total cost of this plan = $177,527 + $261,241 = $438,768
So, the minimum total cost will be realized for the 'production only' option. The total cost will be $426,833 which is less than any other mix of cobination.
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