Question

A manufacturing facility replaces its industrial light fixtures at a rate of 100 units per day. The plant orders the lights periodically and it costs $100 to initiate a purchase order. A light unit kept in storage is estimated to cost about $.02 per day. The lead time between placing and receiving an order is 12 days. Determine the optimal inventory policy for ordering and include the order quantity, frequency of orders (in days), reorder point (in units) and expected non purchase costs associated with this order practice (per day).

Answer 1

Solution:

It is given that –

1. Daily demand of industrial light fixtures =            D            =              100 Units per day
2. Ordering Cost of light fixtures                  =            S            =            $ 100 per order
3. Holding cost of each light fixture              =            H            =            $ 0.02 per day per unit

To optimize total cost (ordering and holding costs), Economic Order Quantity would be:

Q           =           

              =           

              =            1,000 units per order     ANSWER

Frequency of order (in days)would be:

N            =            Order quantity / Demand per day

              =            Q / D

              =            1,000 / 100

              =            10 Days               ANSWER

Now it is also given that the lead time    =            L             =            12 days

Please note that this is a case, in which order lead time (12 days) is more than one order cycle (10 days), but less than two order cycles (20 days). Hence the reorder will happen one order cycle advance and the reorder level would be would be:

R            =            (Order lead time * Demand per day) – Order quantity

              =            (L * D) - Q

              =            (12 * 100) – 1,000

              =            200 units            ANSWER

This reorder level can be graphically shown as below:

Now minimum inventory = 0 units

And maximum inventory = Q = 1000 units

So, the average inventory would be = ( 0 + 1000 ) / 2 = 500

So expected non purchase cost will be the inventory holding cost per day, i.e.

Inventory holding cost = average inventory * holding cost per unit

              =            500        *            0.02       =            $ 10 per day ANSWER

ANSWER: The inventory policy (as shown graphically above) will be as follows:

Ordering Quantity = 1,000 units per order

Ordering frequency = 10 days

Reorder level = 200 units

Non purchase costs (holding costs) = $ 10 per day