Chapter 12, Problem 5P

a. One hundred twenty units of end item Z are needed at the beginning of week 7. Prepare a material requirements plan for component C. Take into account that on hand there are 40 units of Z, 70 units of A, 100 units of B, and 30 units of C. Also, there is a scheduled receipt of 20 units of component C in week 4. Lead times are two weeks for Z and B, and one week for the other components. Lot-for-lot ordering will be used for all items.

b. Ninety-five units of end item E are needed at the beginning of week 7. Prepare a material requirements plan for component D. Take into account that 5 units of E are currently on hand, as well as 50 units of B, 100 units of C, and 80 units of D. Also, 30 units of C have been outsourced and are expected to arrive in week 4. Lead times are two weeks for E and C. and one week for the other components. Assume lot-for-lot ordering except for D. where multiples of 40 must be used.

Summary Introduction

To prepare: A material requirements plan for Component C.

Introduction: Materials Requirement Planning (MRP) is the planning or scheduling system, which can be used in the manufacturing process. It is used to plan the number of items required to produce one unit of finished goods (end item)

Explanation of Solution

Given information:

120 units of end item (Z) are required at the beginning of Week 7. It is given that 40 units of Component Z, 100 units of Component B, 70 units of Component A, and 30 units of Component C are available on hand. Scheduled receipt is 20 units of Component C in Week 4. Lead-time is given as 2 weeks for Component Z and Component B and 1 week for other components. Lot size is lot-for-lot.

In addition to the above information, the following diagram is given:

Prepare a Material Requirement Plan (MRP) for Component Z:

• Gross requirement is given as 120 units at the beginning of Week 7.
• On-hand inventory is 40 units. It remains same until Week 6, as there is no demand.
• Net requirement can be calculated by subtracting the projected on hand inventory of previous week from the gross requirement of current week.

$\begin{array}{c}\text{Net requirement}=\text{Gross requirement}-\text{On-hand units of previous week}\\ =120-40\\ =80\end{array}$

• 80 units are required at the beginning of Week 7. Hence, they need to order for 80 units (as the lot size is lot-for-lot) before two weeks (as the lead-time is 2 weeks), which means on Week 5.
• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\text{Projected on-hand}=\left(\begin{array}{l}\text{Projected on-hand of Week 6}+\\ \text{Planned order receipt of Week 6}-\\ \text{Gross requirement of Week 6}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(40+0-0\right)+0\\ =40\end{array}$

Prepare a Material Requirement Plan (MRP) for Component A (2):

• Component Z is the parent item of Component A (2). As the number of Component A is 2, the planned order release should be multiplied with 2 to determine the gross requirement of Component A.
• On-hand inventory is 70 units. It remains same until Week 4, as there is no demand.
• Net requirement can be calculated by subtracting the projected on hand inventory of previous week from the gross requirement of current week.

$\begin{array}{c}\text{Net requirement}=\text{Gross requirement}-\text{On-hand units of previous week}\\ =160-70\\ =90\end{array}$

• 90 units are required at the beginning of Week 5. Hence, they need to order for 90 units (as the lot size is lot-for-lot) on previous week (as the lead-time is 1 weeks), which means on Week 4.
• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 6}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 5}+\\ \text{Planned order receipt of Week 5}-\\ \text{Gross requirement of Week 5}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(70+90-160\right)+0\\ =0\end{array}$

Prepare a Material Requirement Plan (MRP) for Component B (4):

• Component Z is the parent item of Component B (4). As the number of Component B is 4, the planned order release should be multiplied with 4 to determine the gross requirement of Component B.
• On-hand inventory is 100 units. It remains same until Week 4, as there is no demand.
• Net requirement can be calculated by subtracting the projected on hand inventory of previous week from the gross requirement of current week.

$\begin{array}{c}\text{Net requirement}=\text{Gross requirement}-\text{On-hand units of previous week}\\ =320-100\\ =220\end{array}$

• 220 units are required at the beginning of Week 5. Hence, they need to order for 220 units (as the lot size is lot-for-lot) on two weeks before (as the lead-time is 2 weeks), which means on Week 3.
• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 6}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 5}+\\ \text{Planned order receipt of Week 5}-\\ \text{Gross requirement of Week 5}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(100+220-320\right)+0\\ =0\end{array}$

Prepare a Material Requirement Plan (MRP) for Component C (3) and C (2):

• Component A (2) is the parent item of Component C (3) and Component B (4) is the parent item of Component C (2). As the number of Component C is 3, the planned order release of Component A should be multiplied with 3 to determine the gross requirement of Component C. The same should be followed for Component C (2) with its parent item B (4).
• On-hand inventory is 30 units. It remains same until Week 3, as there is no demand.
• Net requirement can be calculated by subtracting the projected on hand inventory of previous week from the gross requirement of current week.

$\begin{array}{c}\text{Net requirement}=\text{Gross requirement}-\text{On-hand units of previous week}\\ =440-30\\ =410\end{array}$

• 410 units are required at the beginning of Week 3. Hence, they need to order for 410 units (as the lot size is lot-for-lot) on previous week (as the lead-time is 1 week), which means on Week 2.
• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 4}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 3}+\\ \text{Planned order receipt of Week 3}-\\ \text{Gross requirement of Week 3}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(30+410-440\right)+20\\ =20\end{array}$

• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 5}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 4}+\\ \text{Planned order receipt of Week 4}-\\ \text{Gross requirement of Week 4}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(20+250-270\right)+0\\ =0\end{array}$

Summary Introduction

To prepare: A material requirements plan for Component D.

Introduction: Materials Requirement Planning (MRP) is the planning or scheduling system, which can be used in the manufacturing process. It is used to plan the number of items required to produce one unit of finished goods (end item)

Explanation of Solution

Given information:

95 units of end item (E) are required at the beginning of Week 7. It is given that 5 units of Component E, 50 units of Component B, 80 units of Component D, and 100 units of Component C are available on hand. Scheduled receipt is 30 units of Component C in Week 4. Lead-time is given as 2 weeks for Component E and Component C and 1 week for other components. Lot size is lot-for-lot for all the components except Component D. Lot size for Component C is multiples of 40.

In addition to the above information, the following diagram is given:

Prepare a Material Requirement Plan (MRP) for Component E:

• Gross requirement is given as 95 units at the beginning of Week 7.
• On-hand inventory is 5 units. It remains same until Week 6, as there is no demand.
• Net requirement can be calculated by subtracting the projected on hand inventory of previous week from the gross requirement of current week.

$\begin{array}{c}\text{Net requirement}=\text{Gross requirement}-\text{On-hand units of previous week}\\ =95-5\\ =90\end{array}$

• 90 units are required at the beginning of Week 7. Hence, they need to order for 90 units (as the lot size is lot-for-lot) before two weeks (as the lead-time is 2 weeks), which means on Week 5.
• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\text{Projected on-hand}=\left(\begin{array}{l}\text{Projected on-hand of Week 6}+\\ \text{Planned order receipt of Week 6}-\\ \text{Gross requirement of Week 6}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(5+0-0\right)+0\\ =5\end{array}$

Prepare a Material Requirement Plan (MRP) for Component B (3):

• Component E is the parent item of Component B (3). As the number of Component B is 3, the planned order release should be multiplied with 3 to determine the gross requirement of Component 3.
• On-hand inventory is 50 units. It remains same until Week 4, as there is no demand.
• Net requirement can be calculated by subtracting the projected on hand inventory of previous week from the gross requirement of current week.

$\begin{array}{c}\text{Net requirement}=\text{Gross requirement}-\text{On-hand units of previous week}\\ =270-50\\ =220\end{array}$

• 220 units are required at the beginning of Week 5. Hence, they need to order for 220 units (as the lot size is lot-for-lot) on previous week (as the lead-time is 1 weeks), which means on Week 4.
• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 6}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 5}+\\ \text{Planned order receipt of Week 5}-\\ \text{Gross requirement of Week 5}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(50+220-270\right)+0\\ =0\end{array}$

Prepare a Material Requirement Plan (MRP) for Component C (2):

• Component E is the parent item of Component C (2). As the number of Component C is 2, the planned order release should be multiplied with 2 to determine the gross requirement of Component C.
• On-hand inventory is 100 units. It remains same until Week 3, as there is no demand. Scheduled receipts of 30 units arrived on Week 4. Hence, the on-hand inventory is 130 units on Week 4.
• Net requirement can be calculated by subtracting the projected on hand inventory of previous week from the gross requirement of current week.

$\begin{array}{c}\text{Net requirement}=\text{Gross requirement}-\text{On-hand units of previous week}\\ =180-130\\ =50\end{array}$

• 50 units are required at the beginning of Week 5. Hence, they need to order for 50 units (as the lot size is lot-for-lot) on two weeks before (as the lead-time is 2 weeks), which means on Week 3.
• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 5}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 4}+\\ \text{Planned order receipt of Week 4}-\\ \text{Gross requirement of Week 4}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(130+0-0\right)+0\\ =130\end{array}$

• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 6}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 5}+\\ \text{Planned order receipt of Week 5}-\\ \text{Gross requirement of Week 5}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(130+50-180\right)+0\\ =0\end{array}$

Prepare a Material Requirement Plan (MRP) for Component D (2) and D (2):

• Component B (3) is the parent item of Component D (2) and Component C (2) is the parent item of Component D (2). As the number of Component D is 2, the planned order release of Component B should be multiplied with 2 to determine the gross requirement of Component D. The same should be followed for Component D (2) with its parent item C (2).
• On-hand inventory is 80 units. It remains same until Week 3, as there is no demand.
• Net requirement can be calculated by subtracting the projected on hand inventory of previous week from the gross requirement of current week.

$\begin{array}{c}\text{Net requirement}=\text{Gross requirement}-\text{On-hand units of previous week}\\ =100-80\\ =20\end{array}$

• 20 units are required at the beginning of Week 3. Hence, they need to order for 40 units (as the lot size is multiples of 40) on previous week (as the lead-time is 1 week), which means on Week 2.
• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 4}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 3}+\\ \text{Planned order receipt of Week 3}-\\ \text{Gross requirement of Week 3}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(80+40-100\right)+0\\ =20\end{array}$

• Projected on-hand inventory is calculated by adding the scheduled receipts and the value attained by subtracting gross requirements from the sum of projected on-hand of previous week and planned order receipt of previous week.

$\begin{array}{c}\begin{array}{l}\text{Projected on-}\\ \text{hand on Week 5}\end{array}\}=\left(\begin{array}{l}\text{Projected on-hand of Week 4}+\\ \text{Planned order receipt of Week 4}-\\ \text{Gross requirement of Week 4}\end{array}\right)+\text{Scheduled receipt of current week}\\ =\left(20+440-440\right)+0\\ =20\end{array}$