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Quantity Discount Problem - Graduate Level

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A company will begin stocking remote control devices. Expected monthly demand is 800 units. The controllers can be purchased from either supplier A or supplier B. Their price lists are as follows.

Supplier A
Quantity/Unit Price
1-199 / $14
200-499 / $13.80
500+ / $13.60

Supplier B
Quantity/Unit Price
1-149 / $14.10
150-349 / $13.90
350+ / $13.70

Ordering cost is $40 and annual holding cost is 25% of unit price per unit. Which supplier should be used and what order quantity is optimal if the intent is to minimize the total annual cost?

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Solution Preview

The attached file gives the Economic Order Quantity (EOQ) Calculation. The EOQ uses ordering cost which is $40, Annual Usage which is 800*12=9,600 and the carrying cost. The carrying cost ...

Solution Summary

The solution explains how to choose between two suppliers so as to minimize the total cost

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Supply Chain Management Exercise Question

Supply Chain Management exercise questions

1. Mike Johnson went back to work in his family business after graduating. The family business, Johnson Bicycles, is a bike shop that specializes in high quality bikes. They carried a full line of bikes, ranging from touring bikes to mountain bikes and aimed to be the premiere, full service bike shop.

Currently, Johnson Bicycles has three retail outlets that it stocks individually (and hence manages inventory separately for each location). Mike thinks that the operation is big enough to take advantage of scale economies and wants to investigate the possibility of consolidating inventory at a centralized distribution point. Mike thinks that centralizing inventory should lead to a substantial reduction in inventory costs.

The basic idea would be to stock the bikes centrally (excluding the token display model) and expedite delivery to the stores on an as needed basis. He figured if the principal of aggregation would work for the series 200 bike, then it should provide costs savings for all styles of bikes. Table 1, below, shows last year's sales history for the model 200 series at each retail location.

Series 200 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Std Dev Total
Outlet 1 9 5 15 10 12 5 3 12 23 12 8 5 5.5 119
Outlet 2 10 10 30 12 22 15 17 30 11 14 12 15 7.1 198
Outlet 3 12 22 5 15 14 23 10 4 9 15 3 5 6.7 137
Total Sales 31 37 50 37 48 43 30 46 43 41 23 25 8.9 454

As can be seen, monthly sales varied, but generally, sales remained fairly constant from year to year. Mike estimated it cost $65 every time the company placed an order for a given model at each location. The supplier's lead time is a hefty two months, but fortunately it has been constant over time. Historically, they've stocked to a 98% service level. Each bike model cost $75 per bike and Mike figures that holding cost to be 25% of the purchase price on an annual basis. With their high service level, there was naturally, a lot of extra safety stock in inventory. Mike knew every additional unit of safety stock (recall safety stock is any inventory held in excess of average demand) added directly to the total cost of inventory in the form of added holding cost. That is, total cost is equal to the cost of ordering plus the cost of holding inventory, where the cost of holding inventory is equal to the cost of holding average inventory plus safety stock.

a. Using the s, S model, what are the order quantities, reorder points, and total annual inventory costs associated with inventory management of the Series 200 line of bikes at each location?

b. What would be the order quantity, reorder point, and total annual inventory cost for a consolidated plan where bikes are stored at a central distribution center?

c. Would you recommend switching to centralized inventory management? What other factors besides costs should Mike consider?

Please see attached for full question.

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