Question

ProTech Electronics supplies microcomputer circuitry to a company that incorporates microprocessors into refrigerators and other home appliances. One of the components has an annual demand of 250 units, and this is constant throughout the year. Carrying cost is estimated to be $1 per unit per year, and the ordering (setup) cost is $20 per order. To minimize cost, how many units should be ordered each time an order is placed? How many orders per year are needed with the optimal policy? What will be the maximum inventory level? What is the cycle length (time between orders) when orders are placed using the EOQ quantity? What is the average inventory if costs are minimized? Suppose that the ordering (setup) cost is not $20, and ProTech has been ordering 150 units each time an order is placed. For this order policy (of Q = 150) to be optimal, determine what the ordering (setup) cost would have to be

Answer 1

To minimize cost, the optimal order quantity is 100 units per order. The number of orders per year is 3. The maximum inventory level is 100 units.

Step-by-step explanation:

To minimize cost, we can use the Economic Order Quantity (EOQ) formula which is:

EOQ = √(2 * D * S / H)

Where:

EOQ is the Economic Order Quantity

D is the annual demand (250 units)

S is the setup (ordering) cost ($20 per order)

H is the carrying cost per unit per year ($1 per unit per year)

Plugging in the values:

EOQ = √(2 * 250 * 20 / 1) = √(10,000) ≈ 100 units

So, the optimal order quantity is 100 units per order.

Next, we can calculate the number of orders per year with the optimal policy:

Number of orders per year = D / EOQ = 250 / 100 = 2.5 = 3 orders (round to the nearest whole number)

The maximum inventory level can be calculated using the formula:

Maximum inventory level = EOQ = 100 units

The cycle length, or time between orders, when orders are placed using the EOQ quantity is:

Cycle length = 1 / Number of orders per year = 1 / 3 ≈ 0.333 years (or approximately 4 months)

To find the average inventory, we can divide the EOQ by 2:

Average inventory = EOQ / 2 = 100 / 2 = 50 units

If ProTech has been ordering 150 units each time an order is placed, for this order policy (of Q = 150) to be optimal, the ordering (setup) cost would have to be:

Setup cost = (2 * D * S) / Q

Plugging in the values:

20 = (2 * 250 * S) / 150

Solving for S:

S = (20 * 150) / (2 * 250) = 15

So, the ordering (setup) cost would have to be $15 for the order policy of ordering 150 units to be optimal.