Trial-and-Error (Approximate) Method 1. Approximately what quantity Q minimizes

Question

Trial-and-Error (Approximate) Method

1. Approximately what quantity Q minimizes total annual ordering & holding costs? _____ boxes

Please show work.

Lastly, should question #1 (trial and error (approx.) method) and question #2 (eoq exact formula) should those 2 answers be different? what formulas do you use for each?

The situation: Rachel is responsible for purchasing the paper used in all copy machines and laser printers at Costco. After looking at her records, Roxie has found demand for paper averages 600 boxes per month. The price of a box of paper is $20 (regardless of the number ordered). Placing and handling an order costs $70. Annual unit holding costs per box are 25% of the unit price. Last year, Rachel ordered paper once every 2 months, but she wants to know if another ordering policy would be cheaper.

Explanation / Answer

Trial-and-Error method

1. As per current ordering policy, order quantity is equal to two months demand, Q = 600*2 = 1200 boxes

Annual demand, D = 600*12 = 7200 boxes

Setup cost, S = 70

Holding cost, H = 20*25% = 5

Total annual Cost = (D/Q)*S + (Q/2)*H = (7200/1200)*70+(1200/2)*5 = 420+3000 = $ 3420

At this order quantity, holding cost is substantially higher. So decreasing the order quantity might result in cost reduction

Trial #1: Q = 600, Total annual cost = (7200/600)*70+(600/2)*5 = 840+1500 = $ 2340

Trial #2: Q = 400, Total annual cost = (7200/400)*70+(400/2)*5 = 1260+1000 = $ 2260

Order quantity of 400 yields ordering cost and holding cost very close. So this is a fairly good estimate of lot size to use.

B)

2. Using EOQ formula, Optimal Order quantity, Q* = SQRT(2DS/H) = SQRT(2*7200*70/5) = 449 boxes

3. If cell F5 calculates total annual cost, then formula is =(B1/E5)*B3+(E5/2)*B4

4. At Q*, total annual ordering +holding cost =(7200/449)*70+(449/2)*5 = $ 2245

5. Number of times she will place order of size Q* per year = D/Q = 7200/449 = 16

6. Last year total annual ordering +holding cost = (7200/1200)*70+(1200/2)*5 = $ 3420

7. Percentage reduction in annual ordering+holding cost by following optimal ordering policy = (3420-2245)/3420 = 34.36 %

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