Question

Leaky​ Pipe, a local retailer of plumbing​ supplies, faces demand for one of its SKUs at a constant rate of 18 comma 700 units per year. It costs Leaky Pipe ​$35 to process an order to replenish stock and ​$6.00 per unit per year to carry the item in stock. Stock is received 12 working days after an order is placed. No backordering is allowed. Assume 250 working days a year. a. Leaky​ Pipe's optimal order quantity is 467 nothing units. ​(Enter your response rounded to the nearest whole​ number.) b. The optimal number of orders per year is 40 nothing orders. ​(Enter your response rounded to the nearest whole​ number.) c. The optimal interval​ (in working​ days) between orders is 31.6 nothing days. ​(Enter your response rounded to one decimal​ place.) d. The demand during lead time is 898 nothing units. ​(Enter your response rounded to the nearest whole​ number.) e. The reorder point is 898 nothing units. ​(Enter your response rounded to the nearest whole​ number.) f. The inventory position immediately after an order has been placed is 1395 nothing units. ​(Enter your response rounded to the nearest whole​ number.)

Answer 1

Annual demand (D) = 18700 units

Ordering cost(S) = $35 per order

Holding cost (H) = $6 per unit per year

Lead time(L) = 12 days

Number of days per year = 250 days

Average daily demand(d) = D/number of days per year = 18700/250 = 74.8 units

a) Optimal order quantity (Q) = √(2DS/H)

= √[(2 × 18700 × 35) / 6 ]

= √(1309000/6)

= √218166.67

= 467 units

b) Number of orders per year = D/Q = 18700/467 = 40 orders

C) Time between orders = (Q/D) number of days per year

= (467/18700) 250

= 6.2 days

d) Demand during lead time = d × L = 74.8 × 12 = 898 units

e) Reorder point = d × L = 74.8 × 12 = 898 units

f) Inventory position after an order is placed = Reorder point + Q = 898+467 = 1365 units