# Quantity discount problem:Bay Area Transit (BAT)

Bay Area Transit (BAT) is reevaluating its ordering policy for the tires used on its fleet of buses. Under BAT's current policy, an order of 1440 tires arrives every 90 days. As input to its ordering decision, BAT has made the following assumptions:

. There are 360 days per year

. Demand for new tires rarely deviates by much from an average of 16 tires per day

. The vendor that supplies tires to BAT charges $115 per tire regardless of quantity ordered. In addition, the supplier charges $250 to make a delivery, regardless of the number of tires delivered.

. Besides the vendor's fixed delivery charge of $250, BAT incurs a fixed cost of $70 to process and receive an order.

. The annual holding cost rate is 20 percent of its cost of the tire.

NOW assume that the vendor is offering the following discounts:

Quantity Discount

1 < 100 0%

100 < 250 1%

250 < 500 2%

500 < 1000 3%

1000 < 2000 4%

2000 plus 5%

a. If BAT continues to purchase 1440 tires every 90 days without consideration of the discounts, what is the total cost of purchasing the tires for the year?

b. Find the EOQs and determine the total cost for each price level (i.e., complete the table below) for tires.

Category

Price

EOQ

Q*

AHC

AOC

Cost

Total Cost

c. How many tires should BAT order each time it places an order [based on the information in the table]? Explain why you chose that quantity.

d. How many times will BAT place an order each year [based on your answer to c]?

e. How many days between placing orders [based on your answer to c]?

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#### Solution Preview

Bay Area Transit (BAT) is reevaluating its ordering policy for the tires used on its fleet of buses. Under BAT's current policy, an order of 1440 tires arrives every 90 days. As input to its ordering decision, BAT has made the following assumptions:

. There are 360 days per year

. Demand for new tires rarely deviates by much from an average of 16 tires per day

. The vendor that supplies tires to BAT charges $115 per tire regardless of quantity ordered. In addition, the supplier charges $250 to make a delivery, regardless of the number of tires delivered.

. Besides the vendor's fixed delivery charge of $250, BAT incurs a fixed cost of $70 to process and receive an order.

. The annual holding cost rate is 20 percent of its cost of the tire.

NOW assume that the ...

#### Solution Summary

This posting contains a detailed solution to the quantity discount-EOQ model for Bay Area Transit (BAT).