A company buys tractors at a cost of $6,500 and sells them for $10,000. A charge

Question

A company buys tractors at a cost of $6,500 and sells them for $10,000. A charge of $2500 is incurred for each order of tractors, regardless of the size of the order. The company estimates the holding charge for one tractor to be $500 per tractor per month 8 If there is a monthly demand for 15 tractors what is the optimal ordering policy, and the resulting monthly inventory (i.e. holding and ordering) cost? a. If instead the demand is not constant and the forecast for the next 4 months is 20, 25, 12 and 3, use dynamic programming to determine the optimal ordering policy and the minimal cost over the four-month period. b.

Explanation / Answer

A.

B.

D Demand 15 Units K Ordering cost 2500 $ h Holding cost/unit 500 $ P Cost per unit 6500 $ Currently per month 2000 units W Working days 30 days d Daily demand 0.5 Q Economic lot size 12.24744871 Optimal Prod quantity Sqtr((2*Annual Demand*order cost)/Annual inventory carrying cost) (sqrt(2*KD/h) Avg S Avg Stock (Q/2) 6.123724357 6 Avg Stock N Optimal no of orders 1.224744871 (Demand/EOQ) 1 No of Orders DBO Days between order (Days/N) 24.49489743 24.49 Days Cycle time TC Total cost ((KD/Q)+(hQ/2)) 6123.72 $ Total cost OC Ordering cost (KD/Q) 3061.86 HC Holding cost (hQ/2)) 3061.86 PC Production cost (P*D) 97500.00 TC 103623.72

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