Question

The Roadking Tire Company produces the Roadrunner tire. The annual demand at its DC is 17,400 tires. The transport and handling costs are $2,600 each time a shipment of tires is ordered at the distribution center. Orders are filled in 10 days. The annual carrying cost is $3.75 per tire. Assume the company works 260 days per year.

1. Determine the optimal order quantity, and the minimum total annual cost.
2. Compute the optimal number of orders to place per year.
3. Compute the number of operating days between orders, based on optimal ordering policy.
4. Determine the reorder point.

Answer 1

Question: The Roadking Tire Company produces the Roadrunner tire. The annual demand at its DC is 17,400 tires. The transport and handling costs are $2,600 each time a shipment of tires is ordered at the distribution center. Orders are filled in 10 days. The annual carrying cost is $3.75 per tire. Assume the company works 260 days per year.

Answer:

Given that:

Annual Demand (D) = 17400

Order Cost (S) = 2600

Holding Cost (H) = 3.75

Number of working days (N) = 260

Lead Time (Lt) = 10 days

a. Determine the optimal order quantity and the minimum total annual cost.

Economic Order Quantity (EOQ) is given by:

EOQ = Sqrt(2 x D x S / H)

Therefore:

EOQ = Sqrt(2 x 17400 x 2600 / 3.75)

EOQ = Sqrt(24128000)

EOQ = 4912.03

Now:

Total Annual Cost is given by:

Total Annual Cost (TC) = (D x S) / EOQ + (EOQ x H) / 2

Therefore:

Total Annual Cost (TC) = (17400 x 2600) / 4912.03 + (4912.03 x 3.75) / 2

Total Annual Cost (TC) = 18420.0977196

Total Annual Cost (TC) = 18420.10

b. Compute the optimal number of orders to place per year.

Number of orders per year is given by:

Number of orders per year = D / EOQ

Therefore:

Number of orders per year = 17400 / 4912.03 = 3.54232364216

Number of orders per year = 4

c. Compute the number of operating days between orders, based on optimal ordering policy.

Time between orders (TBO) is given by:

Time between orders (TBO) = (EOQ / D) x N

Therefore:

Time Between Orders (TBO) = (4912.03 / 17400) x 260

Time Between Orders (TBO) = 73.3981494253

Time Between Orders (TBO) = 73.40

d. Determine the reorder point.

Reorder Point (ROP) is given by:

ROP = d x Lt

Here: d = D / 260 = 17400 / 260 = 66.9230769231 = 66.92

Therefore:

ROP = 66.92 x 10

ROP = 669.2

ROP = 669