A firm has the following gross requirements for Item F. If ordering costs are $60 per order and carrying costs are $0.50 per period. If EOQ lot sizing is used to set the minimum order quantity, then the planned order releases is
A) 40 in period 1 and 0 in period 3
B) 0 in period 2 and 80 in period 3
C) 120 in period 2 and 120 in period 3
D) 100 in period 2 and 100 in period 3

Question

A firm has the following gross requirements for Item F. If ordering costs are $60 per order and carrying costs are $0.50 per period.  If EOQ lot sizing is used to set the minimum order quantity, then the planned order releases is
A) 40 in period 1 and 0 in period 3 
B) 0 in period 2 and 80 in period 3 
C) 120 in period 2 and 120 in period 3 
D) 100 in period 2 and 100 in period 3

Quizplus · Accepted Answer

To determine the planned order releases using EOQ lot sizing, we first need to calculate the economic order quantity (EOQ) using the formula:
EOQ = sqrt((2DS)/H)
where 
D = annual demand = 400 (sum of gross requirements)
S = ordering cost = $60 per order
H = carrying cost per unit per period = $0.50
Therefore, EOQ = sqrt((2*400*60)/0.50) = 489

Next, we need to determine the number of orders and order quantity for each period. Since the gross requirements are not evenly distributed, we need to use the production plan to determine when the orders will be placed.

The production plan shows:
Period 1: 40 units
Period 2: 280 units (120 from Period 1 + 160 from Period 2)
Period 3: 80 units (20 from Period 2 + 60 from Period 3)

Since the EOQ is 489, we need to order in multiples of this quantity. Therefore, we can order 2 lots of EOQ in Period 2 to cover the gross requirements for Periods 2 and 3. Each lot will be 489 units, so we will release 2 orders for a total of 978 units in Period 2. 
In Period 1, we will release 1 order for 489 units to cover the demand.
In Period 3, we will not release any orders since we have enough inventory from the orders placed in Period 2 to cover the demand.

Therefore, the planned order releases are as follows:
Period 1: 1 order for 489 units
Period 2: 2 orders for 978 units (489 units per order)
Period 3: 0 orders

A Firm Has the Following Gross Requirements for Item F