CEE6100 HW9

3. The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 40 cars per month. The cars cost $60 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%. a. Determine the economic order quantity and total annual cost under the assumption that no backorders are permitted. Q * = √ 2 D c o c h . = √ 2 ∗ 4 0 ∗ 12 ∗ 15 0.2 ∗ 60 = 34.64 TC= 1 2 Q c h + D Q c o =207.85+207.85=415.70 b. Using a $45 per-unit per-year backorder cost, determine the minimum cost inventory policy and total annual cost for the model racing cars. Q * = √ 2 D c o c h . ( c h + c b c b ) = √ 2 ∗ 480 ∗ 15 0.2 ∗ 60 . ( 0.2 ∗ 60 + 45 45 ) =39 S * = Q * . ( c h c h + c b ) =8.21 TC= ¿¿ =145.80+184.68+38.88=369.36 c. What is the maximum number of days a customer would have to wait for a backorder under the policy in part (b)? Assume that the Hobby Shop is open for business 300 days per year. Length of backorder period = S d = 8.21 480 / 300 = 5.13 days d. Would you recommend a no-backorder or a backorder inventory policy for this product? Explain. Backorder case since the maximum wait is only 5.13 and the cost savings is 415.70-369.36=46.34 (11.1%) e. If the lead time is six days, what is the reorder point for both the no-backorder and backorder inventory policies? EQQ: r=dm= 480 300 ∗ 6 = 9.6 Backorder: r=dm-S=1.39