Question

A raw material normally used in batches of 30 units has annual deman of 150 units. the ordering cost is $145. The annulaized cost of adding a part number to the automated inventory tracking system is estimated at $400. The cost per order of delayed product delivery is estimated at $100. The cost to hold a part for one year is $2.00.

TCPUT = (AD)Q+CD+(hQ)/2+Cs

Make a model using lingo

Answer 1

Setup cost = A = 145

Demand = D = 150 units

Inventory monitoring cost = $400

Batch qty = Q = 30

Backorder cost , B = 100

We stock the item if:

Sqrt (2 *A*D*H) + Cs < (A+B) * D / Q

H < ( (A+B) * D / Q - Cs) ^2 / 2 * A * D

On equating the numbers

H < {(245 * 150) /30 – 400} ^ 2 / (2 *145 * 150) = 15.65

Since actual holding cost is $ 2 and less than the cost calculated above we will use the EOQ condition to determine Q.

Using the EOQ condition , Q = sqrt (2AD/H) = sqrt ( 2* 145 * 150 /2) = 147.47 units or 150 units