A small manufacturer orders shafts and bearings from its suppliers with the cost

Question

A small manufacturer orders shafts and bearings from its suppliers with the cost of 20 and 27 cents respectively. There is a fixed setup cost of 120 $ for all orders. 9900 shafts and 12000 bearings are needed annually. The holding cost is based on a 30 percent annual interest rate. a. Determine the optimal size of the orders of shafts and bearings and the optimal time between placement of orders of these two items. b. If both items are ordered simultaneously, the setup cost of 120 $ applies to the combined order. Compare the average annual cost of holding and setup if these items are ordered separately; if they are both ordered when the bearings would normally be ordered; and if they are both ordered when the shafts would normally be ordered

Explanation / Answer

Shafts Bearings Separate total Combined D Demand Total Annual 9900 12000 21900 p Purchase cost 20.00 27.00 23.84 K Set up cost cost 120 120 120 h Holding cost 6 8.1 7.150684932 Working days 365 365 365 EOQ (Sqrt(2*k*D/h) 629.29 596.28 857.34 629 Ans A 596 Ans A 857 AI = EOQ/2 Average inventory 315 298 429 (AI*h) Holding cost 1887.86 2414.95 3065.29 (p*AI) Purchasing cost for 6292.85 8049.84 10217.63 No of orders 15.73 20.12 25.54 D*K/EOQ Toc Total ordering cost annualy 1887.86 2414.95 4302.81 3065.29 Ans B EOQ*h/2 Thc Annual Holding cost 1887.86 2414.95 4302.81 3065.29 Toc+Thc THOC Total Inv cost 3775.71 4829.91 8605.62 6130.58 D*P Tpc Purchasing cost annual 198000 324000 522000.00 522000 Toc+Thc+Tpc TC Total cost 201776 328830 530605.62 528131 Length of order cycle (Days) 23.20 Ans A 18.14 Ans A 14.29

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