Assignment:
Trace the inventory behavior with the forecasted demand (assume they are accurate and there are no forecasting errors)
1. Identify the amount of total stockout
2. Calculate the lost profit due to the stockout
3. Recalculate the total cost
Martin-Pullin Bicycle Corporation
Martin-Pullin Bicycle Corp. (MPBC), located in Dallas, is a wholesale distributor of bicycles and bicycle parts. Formed in 1981 by cousins Ray martin and Jim Pullin, the firm's primary retail outlets are located within a 400-mile radius of the distribution center. Theses retail outlets receive the order from Martin-Pullin within two days after notifying the distribution center, provided that the stock is available. However, if an order is not fulfilled by the company, no backorder is placed; the retailers arrange to get their shipment from other distributors, and MPBC loses that amount of business.
The company distributes a wide variety of bicycles. The most popular model, and the major source of revenue to the company, is the AirWing. MPBC receives all the models from a single manufacturer overseas, and the shipment takes as long as four weeks from the time an order is placed. With the cost of communication, paperwork, and customer clearance included, MPBC estimates that each time an order is placed, it incurs a cost of $65. The purchase price paid by MPBC , per bicycle, is roughly 60% of the suggested retail price for all the styles available, and the inventory carrying cost is 1% per month (12% per year) of the purchase price paid by MPBC. The retail price (paid by the customers) for AirWing is $170 per bicycle.
MPBC is interested in making an inventory plan for 2002. The firm wants to maintain a 95% service level with its customers to minimize the losses on the lost orders. The data collected for the past two years are summarized in the following table. A forecast for AirWing model sales in the upcoming year 2000 has been developed and will be used to make an inventory plan for MPBC.
AirWing - MPBC Popular model
annual demand = 439 units
cost of each valve = $170.00
inventory carrying cost ~ 1% p/month = 12% p/year
average ordering cost = $65.00 p/order
order arrival time ~ 4 weeks = 1month
service Level desired is 95%
carrying cost Ch = $12.24
Z value, area under the normal curve for service level of 95% = 1.6449 (Taken from Appendix A, in the text)
EOQ = 68.2831
ROP = Average demand during lead time + Z (Standard deviation of demand during lead time)
Stand Deviation = 24.581 Data represents the entire population
Avg Demand p/mth = 36.583
Z = 1.6449
EOQ = 68
ROP = 36.583 + (1.6449)(24.581) = 36.583 + 41.74 = 77.0162869
Carrying cost = 12.24
SS = 24.581*1.6449 = 40.4332869 safety stock
SS Carrying cost = 494.9034317
| Carrying Cost/Unit/Year |
Ch = $12.24 |
0.12*102=$12.24 p/bicycle/year |
| Cost/Unit (to Customer) |
CuC = $170.00 |
$170.00 p/bicycle |
| Cost/Unit (MPBC) |
Cu = $102.00 |
0.6*170 = $102.00 p/bicycle |
| Cost/Order |
Co = $65.00 |
$65.00 p/order |
| Delivery Time/Order |
L = 1 Month |
1 month |
| Demand for AirWing Model: |
|
| Month |
Yr 2000 |
Yr 2001 |
Forecast 2002 |
| Jan |
6 |
7 |
8 |
| Feb |
12 |
14 |
15 |
| Mar |
24 |
27 |
31 |
| Apr |
46 |
53 |
59 |
| May |
75 |
86 |
97 |
| Jun |
47 |
54 |
60 |
| Jul |
30 |
34 |
39 |
| Aug |
18 |
21 |
24 |
| Sep |
13 |
15 |
16 |
| Oct |
12 |
13 |
15 |
| Nov |
22 |
25 |
28 |
| Dec |
38 |
42 |
47 |
| Total |
343 |
391 |
439
|