A company (The manufacturer) is experiencing high variability in orders from a distributor, who again receives orders from a retailer.

The manufacturer suspects the high variability is due to the bullwhip effect. Initial discussions with the distributor indicate that it is also experiencing high variability in incoming orders from the retailer, although not as high as the manufacturer.

The distributor agrees to share a 20-period demand forecast with the manufacturer.

Both the retailer and the distributor use a 20-period rolling horizon when planning how much to order.

At the beginning of a period, they review the inventory on hand and decide how much to order.
Orders are placed and arrive immediately (without time lag) and can be sold in the same period.

Both the retailer and the distributor use (S,Q)-policies, where all orders have the same quantity Q. The retailer and the distributor, both use the EOQ formula to find the order quantity Q, based on the forecasted demand over 20 time periods. The holding cost for the 20 periods is $1 per unit for the retailer, and $0.5 per unit for the distributor. The ordering cost is $1,000 for the retailer and $2,000 for the distributor.

For both the retailer and the distributor, an order is placed when the inventory on hand in the beginning of a period is below certain level, S. This level is given by the average sales forecasted over a 20-period snapshot plus a safety stock. For the retailer, the safety stock is 5,000 units. For the distributor the safety stock is 10,000 units.

The manufacturer wants to measure the "size" of bullwhip effect as the ratio between the variance in incoming orders (to The manufacturer) over the variance of the demand.

QUESTION:

Using EOQ ordering at both the retailer and the distributor, what is the size of the bullwhip effect at The manufacturer?
Answer without commas or decimals. Hint: Size of the bullwhip at The manufacturer is the ratio of variance of orders placed on The manufacturer and variance of actual customer orders the retailer sees in the market.

Time period	Demand	Retailer orders	Retailer Inventory	Distributor orders	Distributor Inventory
			12000		25000
1	10580
2	11501
3	9778
4	12804
5	12033
6	10102
7	10995
8	9880
9	9750
10	10200
11	12956
12	9909
13	10002
14	12034
15	11444
16	7899
17	10223
18	10433
19	10563
20	9797

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