Given the following MRP matrix for Item C:

If each order cost $500 and the holding cost is $0.75 per item per period,then using the Periodic Order Quantity lot sizing technique,the Projected on Hand at the end of period 7 would be
A)330
B)270
C)0
D)140

Question

Given the following MRP matrix for Item C:

If each order cost $500 and the holding cost is $0.75 per item per period,then using the Periodic Order Quantity lot sizing technique,the Projected on Hand at the end of period 7 would be
A)330 
B)270 
C)0 
D)140

Quizplus · Accepted Answer

To use the Periodic Order Quantity lot sizing technique, we need to first find the Total Gross Requirements (TGR) for each period by summing up the gross requirements and any planned receipts for that period. Using the given MRP matrix, we can calculate the TGR for each period as follows:

Period 1: 50
Period 2: 70
Period 3: 130
Period 4: 200
Period 5: 280
Period 6: 230
Period 7: 270

Next, we need to determine the order quantity that will satisfy the TGR for each period. Since we are using Periodic Order Quantity lot sizing, we will place orders at regular intervals (in this case, every 7 periods). We want to minimize the total cost, which includes ordering cost (fixed at $500 per order) and holding cost ($0.75 per item per period).

To determine the optimal order quantity, we can use the following formula:

Order Quantity = sqrt(2DS/H)

where
D = annual demand = TGR for 7 periods = 1130
S = ordering cost = $500
H = holding cost = $0.75 per item per period

Plugging in the values, we get:

Order Quantity = sqrt(2 * 1130 * 500 / 0.75) = 5051

This means we should place an order of 5051 units at the beginning of Period 1, and then again at the beginning of Period 8, Period 15, and so on.

Now we can calculate the Projected on Hand (POH) for each period, which tells us the expected inventory level at the end of that period. We start with an initial inventory of 5051 units, and subtract the gross requirements for each period, while adding any planned receipts. The POH for each period is shown below:

Period 1: 5001
Period 2: 4931 (5001 - 50)
Period 3: 4861 (4931 - 70)
Period 4: 4731 (4861 - 130)
Period 5: 4451 (4731 - 280)
Period 6: 4221 (4451 - 230)
Period 7: 3951 (4221 - 270)

Therefore, the answer is (C) 0, because the projected on hand at the end of Period 7 is 3951 units, which is still above zero.

Given the Following MRP Matrix for Item C