Question

A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.40 per stone for quantities of 600 stones or more, $8.80 per stone for orders of 400 to 599 stones, and $9.30 per stone for lesser quantities. The jewelry firm operates 113 days per year. Usage rate is 20 stones per day, and ordering costs are $51. a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost. (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Order quantity stones b. If annual carrying costs are 33 percent of unit cost, what is the optimal order size? (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Optimal order size stones c. If lead time is 3 working days, at what point should the company reorder? (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Reorder quantity stones

Answer 1

Annual demand, D = 20*113 = 2260

Ordering cost, S = $ 51

Carrying cost, H = $ 2

EOQ = SQRT(2DS/H) = SQRT(2*2260*51/2) = 339

The applicable unit price (C) for this quantity is $ 9.30

So, total annual cost = Ordering cost + Carrying cost + Cost of stones

= (D/Q)*S + (Q/2)*H + D*C

= (2260/339)*51 + (339/2)*2 + 2260*9.3

= $ 21,697

Consider the next level price of $ 8.80, minimum order quantity for this = 400

Total annual cost = (2260/400)*51 + (400/2)*2 + 2260*8.8

= $ 20,576

Consider the next level price of $ 8.40, minimum order quantity for this = 600

Total annual cost = (2260/600)*51 + (600/2)*2 + 2260*8.4

= $ 19,776

Total annual cost is lower for order quantity of 600.

Therefore, optimal order quantity = 600

b) Carrying cost rate, h = 0.33

Consider the first level price of $ 9.3, Carrying cost, H = 9.3*.33 = $ 3.07, EOQ = SQRT(2*2260*51/3.07) = 274

Total annual cost = (2260/274)*51 + (274/2)*3.07 + 2260*9.3

= $ 21,859

Consider the next level price of $ 8.8, Carrying cost, H = 8.8*.33 = $ 2.90, minimum order quantity for this = 400

Total annual cost = (2260/400)*51 + (400/2)*2.90 + 2260*8.8

= $ 20,756

Consider the next level price of $ 8.4, Carrying cost, H = 8.4*.33 = $ 2.77, minimum order quantity for this = 600

Total annual cost = (2260/600)*51 + (600/2)*2.77 + 2260*8.4

= $ 19,827

Total annual cost is lowest for order quantity of 600, so optimal order quantity = 600

c) Reorder quantity = daily demand rate * lead time

= 20*3

= 60 stones