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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 manufacturer overseas, 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 $85. 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 2% per month (24% per year) of the purchase price paid by MPBC. The retail price (paid by the customers) for the AirWing is $210 per bicycle.
MPBC is interested in making an inventory plan for 2015. 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 table below. A forecast for AirWing model sales in the upcoming year, 2014 has been developed and will be used to make an inventory plan for MPBC.
Discussion Questions
1. Develop an inventory plan to help MPBC.
2. Discuss ROPs and total costs.
3. How do you handle the fact that the Reorder Point is larger than the EOQ?
4. How can you address demand that is not at the level of the planning horizon?
Demand for AirWing Model
Month 2012 2013 Forecast for2014
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
Solution:
All the given information for 2014 are the forecasted values. As the forecast often does not give the exact value so to deal with that problem I would suggest to keep 5-10% extra stock than as forecasted. However of we perform our analysis based on the forecasted values the following are the obtained solutions.
Total demand for the year = 439
Monthly forecasted demand = 439/12 = 36.5833.
Standard deviation of monthly demand = 24.5814.
Order cost = $85/order
Retail price = $210/unit
Purchase price = 60% of the retail price = $210*0.60 = $126/unit
Holding cost = 24% per year of the purchase price = $126*0.24 = $30.24/year per unit.
Service level to be maintained = 95%
Lead time = 4 weeks
1) We can use the Economic order quantity to develop the most basic inventory plan. Though as we are using yearly plan here but we can see that the month to month demand changes significantly. This means the developed EOQ for the complete year might not be the best plan to follow however that is the easiest option to choose.
EOQ = ; Number of units cant be fraction
The solution is giving the optimal number of units to order is 50.
2) For 95% service level Z = 1.645 as obtained from the tables. So,
ROP = Average demand during lead time + Z*Sd.
= 36.5833+1.645*24.5814 = 77.0197= 77
Number of annual orders = 439/50 = 8.78 = 9; Number of orders cant be fraction
Annual inventory cost = Annual holding cost + Annual Ordering cost + Annual Purchase cost
=Holding cost *Average inventory + Number of orders*Ordering cost + Total demand*Unit cost
= $30.24*50/2 + 9*$85 + 439*$126
= $56,835.00
3) The ROP is larger than EOQ due to the fact that the monthly demand varies. As for example January demand is 8 and may demand is 97. We can also see that 1st three months has demand less than EOQ so an extra stock is expected to be present each time we order. And also as I suggested, this is a forecasted values so it would be better to keep another 5-10% stock to satisfy customers. That would also help to solve this situation.
4) Here the demand varies which clearly indicates that the demand is not at the planning horizon. And as we developed the EOQ inventory level based on yearly demand which would not same as monthly demand due to variation. To develop more sophisticated inventory plan we can analyze the data more rigorously. We can calculate the seasonality, or smoothen the data and make analysis based on smoother data. Or we can also shorten the interval for EOQ.
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