Question

A product has a daily demand of 26 units per day. Ordering costs are $60 per order. The annual carrying costs are measured at 20% of item value. Your supplier has offered you three item cost/price and quantity scenarios (1) you pay $150 per unit if your order quantity is 199 units or less, (2) you pay $121 per unit if your order quantity is between 200 and 4999 units, and (3) you pay $114 per unit if your order quantity is 5000 units or more. Assume there are 365 days per year. Find the optimal order quantity and total cost for each of these plans and pick the one that is best.

Answer 1

We have following information

Daily demand = 26 units per day

Assume that 365 days in a year

Therefore, Annual demand D= 365 *26 = 9,490 units per year

Ordering cost S = $60 per order

Holding or carrying cost H = 20% of item value or purchase price

Scenario 1: The purchase price = $150 per unit if ordered less than 199

Scenario 2: The purchase price = $121 if ordered between 200 to 4999

Scenario 3: The purchase price = $114 if ordered 5000 units or more

Holding or carrying cost H in Case 1,                     

20% of $150 = $30

Holding or carrying cost H in Case 2,

20% of $121 = $24.20

Holding or carrying cost H in Case 3,

20% of $114 = $22.80

For minimum cost, first we have to calculate Optimum Order quantity per order which is EOQ for each scenario

Case 1: EOQ = sqrt (2* D*S/H) = sqrt(2*9490*60/30) = 194.83 or 195 units

Case 2: EOQ = sqrt (2* D*S/H) = sqrt(2*9490*60/24.20) = 216.93 or 217 units

Case 3: EOQ = sqrt (2* D*S/H) = sqrt(2*9490*60/22.80) = 223.49 units (but 5000 or more units can be ordered at this price, therefore it’s not possible)

Total annual cost = total ordering cost + total carrying cost +purchase cost

Total annual cost = (D/Q)* S + (H*Q)/2 + D * Purchase price

Case 1:

Total annual cost = (9490/195)*60 + (30*195)/2 + 9490 * $150 = $1,429,345

Where order size is Q =195 units (fewer than 199, maximum possible order at this price)

Case 2:

Total annual cost = (9490/217)*60 + (24.20*217)/2 + 9490 * $121 = $1,153,539.66

Where optimum order size is Q = 217 units (between 200 and 4999 maximum possible order at this price)

Case 3:

Total annual cost = (9490/5000)*60 + (22.80*5000)/2 + 9490 * $114 = $1,138,861.90

Where order size is Q =5000 units (minimum possible order at this price)

Conclusion: Case 3 is the best option because of lowest annual cost although it is not optimum quantity for order