A manager just received a new price list from a supplier. It will now cost 1$ a

Question

A manager just received a new price list from a supplier. It will now cost 1$ a box for order quantities of 801 or more boxes, 1.10$ a box for 200 to 800 boxes, and 1.20$

a box for smaller quantities. ordering and carrying costs are 10$ per box a year. the firm uses 3,600 boxes a year. the manager has suggested a "round number"

order size of 800 boxes. the manager's rationale is that with u shaped cost curve that is fairly flat at its minimum, the difference in total cost between 800 and 801 units would be small anyway. how would you reply to the manager's suggestion? what order size would you recommend

Explanation / Answer

Annual demand, D = 3600 boxes

Ordering cost, S = $ 10

Carrying cost, H = $ 10

Total annual cost of ordering policy of Q=800 boxes = Ordering cost + Carrying cost + cost of boxes = (D/Q)*S + (Q/2)*H + D*C = (3600/800)*10 + (800/2)*10 + 3600*1.1 = $ 8005

Total annual cost of ordering policy of Q=801 boxes = Ordering cost + Carrying cost + cost of boxes = (D/Q)*S + (Q/2)*H + D*C = (3600/801)*10 + (801/2)*10 + 3600*1 = $ 7650

Total annual cost with order quantity of 801 boxes is lesser. Therefore, the manager is wrong in his judgment.

I would recommend an order size of 801 boxes.

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