Question

1. A supermarket is open 360 days per year. Daily use of cash register tape averages 500 rolls. The cost of ordering tape is $85, and carrying costs are $4 per roll a year. Lead time is two days.
   

1. EOQ
2. Total annual carrying and ordering cost for EOQ
3. They currently order 5000 units each time. What is the current total annual carrying and ordering cost?
4. How much would they save annually in ordering and carrying costs if they change the current order quantity to EOQ?
5. Using EOQ, what is the number of orders per year and what is the interval between orders?
6. ROP (reorder point/quantity)

Answer 1

Average daily demand (d) = 500 rolls

Number of days per year = 360

Annual demand (D) = d × number of days per year = 500 × 360 = 180000 rolls

Ordering cost (S) = $85

Carrying cost (H) = $4

Lead time (L) = 2 days

a) Economic order quantity (EOQ) = √(2DS/H)

= √[(2 × 180000 × 85)/4]

= √(30600000/4)

= √7650000

= 2766 rolls

b) Annual ordering cost = (D/EOQ)S = (180000/2766)85 = $5531.45

Annual carrying cost (EOQ/2)H = (2766/2)4 = $5532

Total Annual cost with EOQ = Annual ordering cost + Annual carrying cost = $5531.45 + $5532 = $11063.45

C) If the order quantity (Q) = 5000 units

Annual ordering cost = (D/Q)S = (180000/5000)85 = $3060

Annual carrying cost (Q/2)H = (5000/2)4 = $10000

Total Annual cost with Q = Annual ordering cost + Annual carrying cost = $3060 + $10000 = $13060

d) Annual savings = Total annual cost with Q - Total annual cost with EOQ = $13060-$11063.45 = $1996.55

e) Number of orders per year = D/EOQ = 180000/2766 = 65.08

Time between orders = (EOQ/D) Number of days per year = (2766/180000)360 = 5.53 days

f) Reorder point = d × L = 500 × 2 = 1000 rolls