Bell Computers purchases integrated chips at $350 per chip. The holding cost is

Question

Bell Computers purchases integrated chips at $350 per chip. The holding cost is $33 per unit per year, the ordering cost is $121 per order, and sales are steady at 395 per month. The company's supplier, Rich Blue Chip Manufacturing, Inc., decides to offer price concessions in order to attract larger orders. The price structure is shown below. Rich Blue Chip's Price Structure Price/Unit Quantity Purchased 1-99 units 100-199 units 200 or more units $325 $300 a) What is the optimal order quantity and the minimum annual cost for Bell Computers to order, purchase, and hold these integrated chips? The optimal order quantity after the change in pricing structure is 200 units (enter your response as a whole number) The total annual cost for Bell computers to order, purchase, and hold the integrated chips is S 1,428,168 (round your response to the nearest whole number). b) Bell Computers wishes to use a 10% holding cost rather than the fixed $33 holding cost in part a, what is the optimal order quantity, and what is the optimal annual cost? The optimal order quantity after the change in the holding cost calculation is units (enter your response as a whole number) The total annual cost for Bell computers to order, purchase, and hold the integrated chips is S(round your response to the nearest whole number)

Explanation / Answer

The formula to be used is Economic Order Quantity EOQ = SQRT(2AD/h) where A is the demand for fixed time period. D is ordering cost per order irrespective of size of the order, and 'h' is the holding cost per unit per period of time.

In the question holding cost is $33 per unit per year, therefore fixed time period is a year, hence A = 395*12=4740

The minimum total cost 142167.70 including ordering, holding, and purchase cost is corresponding to order size of 200 units.

Part b, changing holding cost as 10% calculations are as follows:

Minimum total annual cost is 1427867.70 for order size of 200 units.

EOQ 1-99 units 100-199 units 200 or more Annual sales-A 4740 4740 4740 4740 4740 Ordering cost-D 121 121 121 121 121 Holding cost-h 33 33 33 33 33 Purchase/price /unit 325 350 325 300 300 2AD/h 34760 EOQ-SQRT(2AD/h) 186.440339 Analysis of annual costs Order Quantity-Q 186 99 199 200 201 No. of order= A/Q        (n) 25.483871 47.87878788 23.81909548 23.7 23.58209 Average inventory=Q/2 (I) 93 49.5 99.5 100 100.5 Ordering cost-D*n 3083.55 5793.33 2882.11 2867.70 2853.43 Holding cost-h*I 3069 1633.5 3283.5 3300 3316.5 Purchase cost-p*A 1540500 1659000 1540500 1422000 1422000 Total annual cost 1546652.55 1666426.83 1546665.61 1428167.70 1428169.93

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