At a recent trade show, a Canadian company unveiled its radical new product for the sports equipment industry - a graphite hockey stick! The company, known as"He Shoots, He Scores" has enthusiastic plans for the stick. As owner of a medium-sized retail sporting goods store, you are aware of the various costs involved in ordering and holding inventory. Taking into account the respective costs, you are to develop an appropriate ordering policy for this brand-new item.

Since this is a new product, you have no historical data on which to base your forecast of demand. However, you have data on the number of sticks sold for other new, state-of-the-art sticks from prior years:

	2 years ago	Last year			2 years ago	Last year
Jul	20	24		Jan	34	68
Aug	35	44		Feb	41	62
Sep	59	49		Mar	38	33
Oct	79	100		Apr	19	26
Nov	42	51		May	27	26
Dec	83	81		Jun	25	21

As in any business, sales for any given month could be extremely volatile (or not). In this game, the demand for the next year is generated from a Normal distribution (which ranges from negative infinity to infinity). It is not necessary to know the parameters of the Normal distribution for this game, but they are given at the end of these instructions.

"He Shoots, He Scores" will allow you to purchase hockey sticks for $20. Marketing research results given at the recent trade show indicated that potential customers would pay up to $30 for the item. Thus, you plan to use $30 as your selling price. Note that the amount you sell in a given month is always the lowest of either monthly demand or (beginning inventory + quantity ordered).

Placing an order costs you $60 (note that the manufacturer allows at most one replenishment per month). Any unsatisfied demand (a stockout, or should we call it a "stick" out?) costs you $7 per unit short. Backorders are not allowed (since customers will most likely purchase the hockey stick from a competitor if you don't have enough on-hand). Inventory remaining at the end of a month costs you $1 per unit.

Your task is to plan replenishments (when to order, how much to order) on a month-by-month basis for the next 12 months. Assume that the first month in the planning horizon is July, and that there is no inventory on-hand. After you make your replenishment decision, assume the demand for that month is 30. Then, you may make the decision for next month. Use the attached table to indicate your monthly replenishments, and to tabulate the results of your respective strategy. If a stockout occurs, write "0" for the ending inventory, and put a "0" for the beginning inventory of the subsequent month. Add your explanation based on the problem-solving rubric below the worksheet.

For example, assume that there were no units in beginning inventory, and that you ordered 15 sticks at the beginning of July. Assuming a demand of 23 sticks, you would face the following costs:

revenue: $30 * min(0+15,23) = $30 * 15 = $450

ordering cost: $60 + ($20 * 15) = $360

shortage cost: $7 * 8 = $56

holding cost: 0 (since there is no ending inventory - i.e. we had a stockout)

monthly profit = $450 - ($360 + $56) = $34

Parameters for Normal Distribution:

Normal( (D2+D1*3) / 4 , Absvalue (D1-D2) )

where: D1 is demand last year

D2 is demand 2 years ago

Thus, demand for July is calculated from: Normal ((20+24*3) / 4, Absvalue (24-20))

Normal (23,4)

Worksheet

July

Aug

Sept

Oct

Nov

Dec

Jan

Feb

March

April

May

June

1

Beg. Inventory

0

2

Order quantity

3

Number available = (1) + (2)

4

Demand

5

End. Inventory = max[(3)-(4), 0]

Revenue:

6

Sales = $30 * min [(3), (4)]

Costs:

7

Ordering If (2)>0, = $60 + ($20* (2)), If (2)=0, = 0

8

Shortage = - $7 * min[0, (3)-(4)]

9

Holding = $1 * (5)

10

Total Costs = (7) + (8) + (9)

11

Monthly Profit = (6) - (10)

12

Annual Profit