In: Statistics and Probability
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. These 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 overseas manufacturer, and shipment takes as long as four weeks from the time an order is placed. With the cost of communication, paperwork, and customs 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 bike models available. The inventory carrying cost is 1% per month (12% per year) of the purchase price paid by MPBC. The retail price (paid by the customer) for the AirWing is $170 per bicycle.
MPBC is interested in making an inventory plan for 2011. The firm wants to maintain a 95% service level with its customers to minimize the impact of lost orders. The data collected for the past two years is summarized in the following table. A forecast for AirWing model sales in upcoming year 2011 has been developed and will be used to make an inventory plan for MPBC.
MONTH |
2009 |
2010 |
FORECAST FOR 2011 |
||||
January |
6 |
7 |
8 |
||||
February |
12 |
14 |
15 |
||||
March |
24 |
27 |
31 |
||||
April |
46 |
53 |
59 |
||||
May |
75 |
86 |
97 |
||||
June |
47 |
54 |
60 |
||||
July |
30 |
34 |
39 |
||||
August |
18 |
21 |
24 |
||||
September |
13 |
15 |
16 |
||||
October |
12 |
13 |
15 |
||||
November |
22 |
25 |
28 |
||||
December |
38 |
42 |
47 |
||||
Total |
343 |
391 |
439 |
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