Question

A construction equipment dealer is facing a difficult inventory problem. Low inventory turnover is squeezing profit margins and causing cash-flow problems. One of the top-selling SKUs in the storage is a special small appliance. Sales are 18 units per week, and the supplier charges $60 per unit. The cost of placing an order with the supplier is $45. Annual holding cost is 25 percent of a product’s value, and the shop operates 52 weeks per year. Management chose a 390-unit lot size so that new orders could be placed less frequently.

A)- Determine EOQ

B)- What is the annual cycle-inventory cost of the current policy of using a 390-unit lot size? Would a lot size of 468 be better?

C)- Suppose that the average demand is 18 units per week with a standard deviation of 5 units. The lead time is constant at 2 weeks. Determine the safety stock and reorder point if management wants a 90 percent cycle - service level.

Answer 1

Average weekly demand (d) = 18 units

Number of weeks per year = 52

Annual demand (D) = d x number of weeks per year = 18 x 52 = 936 units

Ordering cost (S) = $45

Holding cost (H) = 25% of cost = 25% of $60 = $15

Current order quantity = 390 units

A) Economic order quantity = √(2DS/H)

= √[2 X 936 X 45) /15]

= √(84240/15)

= √5616

= 75 units

B) With order quantity (Q) = 390 units

Annual ordering cost= (D/Q) S = (936/390) 45 = $108

Annual holding cost = (Q/2) H = (390/2) 15 = $2925

Annual cycle inventory cost with the current policy = $108 + $2925 = $3033

With order quantity(Q) = 468 units

Annual ordering cost = (D/Q) S = (936/468) 45 = $90

Annual holding cost (Q/2) H = (468/2) 15 = $3510

Total annual cost = $90+$3510 = $3600

So a lot size of 468 would not be better as it has a higher total cost than the lot size of 390 units

C) standard deviation of weekly demand (d) = 5 units

Lead time (L) = 2 weeks

At 90% service level value of Z = 1.28

Safety stock = Z x d x √L = 1.28 x 5 x √2 = 1.28 x 5 x 1.41 = 9.02 or rounded to 9 units

Reorder point = d x L + safety stock

= 18 x 2 + 9

= 36 + 9

= 45 units