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Material Requirements Planning ‐ MRP
ENM308
Production Planning and Control ‐ I
Spring 2013
Haluk Yapıcıoğlu, PhD
Hierarchy of Production Decisions
Forecast of Demand
Aggregate Planning
Master Production Schedule
Inventory Control
Operations Scheduling
Vehicle Routing
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Hierarchy of Production Decisions
• Forecasting: First, a firm must forecast demand for aggregate sales over the planning horizon. • Aggregate planning: The forecasts provide inputs for determining aggregate production and workforce levels over the planning horizon.
• Master production schedule (MPS): Recall, that the aggregate production plan does not consider any “real” product but a “fictitious” aggregate product. The MPS translates the aggregate plan output in terms of specific production goals by product and time period. Hierarchy of Production Decisions
• Suppose that a firm produces three types of chairs: ladder‐
back chair, kitchen chair and desk chair. The aggregate production considers a fictitious aggregate unit of chair and find that the firm should produce 550 units of chairs in April. The MPS then translates this output in terms of three product types and four work‐weeks in April. The MPS suggests that the firm produce 200 units of desk chairs in Week 1, 150 units of ladder‐back chair in Week 2, and 200 units of kitchen chairs in Week 3. • Material Requirements Planning (MRP): A product is manufactured from some components or subassemblies. For example a chair may require two back legs, two front legs, 4 leg supports, etc. 2
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Hierarchy of Production Decisions
Master Production Schedule
April
1
Ladder‐back chair Aggregate production plan for chair family
3
4
5
150
6
7
8
150
200
Kitchen chair Desk chair
2
May
200
120
200
550
120
200
790
Hierarchy of Production Decisions
• While forecasting, aggregate plan and MPS consider the volume of finished products, MRP plans for the components, and subassemblies. A firm may obtain the components by in‐house production or purchasing. MRP prepares a plan of in‐house production or purchasing requirements of components and subassemblies.
• Scheduling: Scheduling allocates resource over times in order to produce the products. The resources include workers, machines and tools. • Vehicle Routing: After the products are produced, the firm may deliver the products to some other manufacturers, or warehouses. The vehicle routing allocates vehicles and prepares a route for each vehicle. 3
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Hierarchy of Production Decisions:
Materials Requirement Planning
Back
legs
Back slats
Seat cushion
Leg supports
Seat‐frame
boards
Front
legs
Material Requirements Planning
• The demands for the finished goods are obtained from forecasting. These demands are called independent demand.
• The demands for the components or subassemblies depend on those for the finished goods. These demands are called dependent demand. • Material Requirements Planning (MRP) is used for dependent demand and for both assembly and manufacturing
• If the finished product is composed of many components, MRP can be used to optimize the inventory costs.
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Importance of an MRP System
Inventory without an MRP System
Inventory with an MRP System
Importance of an MRP System
• Without an MRP system:
– Component is ordered at time A, when the inventory level of the component hits reorder point, R
– So, the component is received at time B. – However, the component is actually needed at time C, not B. So, the inventory holding cost incurred between time B and C is a wastage.
• With an MRP system:
– We shall see that given the production schedule of the finished goods and some other information, it is possible to predict the exact time, C when the component will be required. Order is placed carefully so that it is received at time C.
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MRP Input and Output
• MRP Inputs:
– Master Production Schedule (MPS): The MPS of the finished product provides information on the net requirement of the finished product over time.
– Inventory file: For each item, the number of units on hand is obtained from the inventory file.
MRP Input and Output
• MRP Inputs:
– Bill of Materials: For each component, the bill of materials provides information on the number of units required, source of the component (purchase/ manufacture), etc. There are two forms of the bill of materials:
• Product Structure Tree: The finished product is shown at the top, at level 0. The components assembled to produce the finished product is shown at level 1 or below. The sub‐components used to produce the components at level 1 is shown at level 2 or below, and so on. The number in the parentheses shows the requirement of the item. For example, “G(4)” implies that 4 units of G is required to produce 1 unit of B.
• For each item, the name, number, source, and lead time of every component required is shown on the bill of materials in a tabular form.
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MRP Input and Output
• MRP Output:
– Every required item is either produced or purchased. So, the report is sent to production or purchasing.
MRP Input and Output
Orders
Bill of
Materials
file
To Production
Master Production Schedule
Forecasts
MRP
computer
program
Inventory
file
Reports
To Purchasing
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Bill of Materials: Product Structure Tree
Level 0
Level 1
Level 2
Level 3
Bill of Materials
Item
B
C
D
E
BILL OF MATERIALS
Product Description: Ladder‐back chair
Item: A
Quantity Component
Source
Description
Required
Ladder‐back 1
Manufacturing
Front legs
2
Purchase
Leg supports
4
Purchase
Seat 1
Manufacturing
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Bill of Materials
Item
H
I
BILL OF MATERIALS
Product Description: Seat
Item: E
Quantity Component
Source
Description
Required
Seat frame 1
Manufacturing
Seat cushion
1
Purchase
On Hand Inventory and Lead time
Component
Units in Inventory
Lead Time (weeks)
Seat aubassembly
25
2
Seat Frame
50
3
Seat Frame Boards
75
1
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MRP Calculation
• Suppose that 150 units of ladder‐back chair is required.
• The previous slide shows a product structure tree with seat subassembly, seat frames, and seat frame boards. For each of the above components, the previous slide also shows the number of units on hand.
• The net requirement is computed from top to bottom. Since 150 units of ladder‐back chair is required, and since 1 unit of seat subassembly is required for each unit of ladder‐
back chair, the gross requirement of seat‐subassembly is 150x1 =150 units. Since there are 25 units of seat‐
subassembly in the inventory, the net requirement of the seat‐subassembly is 150 – 25 = 125 units.
MRP Calculation
• Since 1 unit of seat frames is required for each unit of seat subassembly, the gross requirement of the seat frames is 1251 = 125 units. (Note that although it follows from the product structure tree that 1 unit of seat frames is required for each unit of ladder‐back chair, the gross requirement of seat frames is not 150 units because each of the 25 units of seat‐subassembly also contains 1 unit of seat frames.) Since there are 50 units of seat frames in the inventory, the net requirement of the seat frames is 125‐50 = 75 units. The detail computation is shown in the next two slides.
• A similar logic is used to compute the time of order placement. 10
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MRP Calculation
Units
Quantity of ladder‐back chairs to be produced
150
Gross requirement, seat subassembly
Less seat subassembly in inventory
25
Net requirement, seat subassembly
Gross requirement, seat frames
Less seat frames in inventory
50
Net requirement, seat frames
Gross requirement, seat frame boards
Less seat frame boards in inventory
75
Net requirement, seat frame boards
Assume that 150 units of ladder‐back chairs are to be produced at the end of week 15
MRP Calculation
Units
Quantity of ladder‐back chairs to be produced
150
Gross requirement, seat subassembly
150
Less seat subassembly in inventory
25
Net requirement, seat subassembly
125
Gross requirement, seat frames
125
Less seat frames in inventory
50
Net requirement, seat frames
75
Gross requirement, seat frame boards
300
Less seat frame boards in inventory
75
Net requirement, seat frame boards
225
Assume that 150 units of ladder‐back chairs are to be produced at the end of week 15
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MRP Calculation: Time of Order Placement
Week
Complete order for seat subassembly
14
Minus lead time for seat subassembly
2
Place an order for seat subassembly
Complete order for seat frames
Minus lead time for seat frames
3
Place an order for seat frames
Complete order for seat frame boards
Minus lead time for seat frame boards
1
Place an order for seat frame boards
Assume that 150 units of ladder‐back chairs are to be produced at the end of week 15 and that there is a one‐week lead time for ladder‐back chair assembly
MRP Calculation: Time of Order Placement
Week
Complete order for seat subassembly
Minus lead time for seat subassembly
Place an order for seat subassembly
14
2
12
Complete order for seat frames
12
Minus lead time for seat frames
3
Place an order for seat frames
9
Complete order for seat frame boards
9
Minus lead time for seat frame boards
1
Place an order for seat frame boards
8
Assume that 150 units of ladder‐back chairs are to be produced at the end of week 15 and that there is a one‐week lead time for ladder‐back chair assembly
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MRP Calculation: Some Definitions
• Scheduled Receipts: – Items ordered prior to the current planning period and/or
– Items returned from the customer
• Lot‐for‐lot (L4L)
– Order quantity equals the net requirement – Sometimes, lot‐for‐lot policy cannot be used. There may be restrictions on minimum order quantity or order quantity may be required to multiples of 50, 100 etc.
MRP Calculation
• Example 1: Each unit of A is composed of one unit of B, two units of C, and one unit of D. C is composed of two units of D and three units of E. Items A, C, D, and E have on‐hand inventories of 20, 10, 20, and 10 units, respectively. Item B has a scheduled receipt of 10 units in period 1, and C has a scheduled receipt of 50 units in Period 1. Lot‐for‐lot (L4L) is used for Items A and B. Item C requires a minimum lot size of 50 units. D and E are required to be purchased in multiples of 100 and 50, respectively. Lead times are one period for Items A, B, and C, and two periods for Items D and E. The gross requirements for A are 30 in Period 2, 30 in Period 5, and 40 in Period 8. Find the planned order releases for all items.
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MRP Calculation
Level 0
Level 1
Level 2
MRP Calculation
Period
Item
A
LT=
Q=
1
2
3
4
5
6
7
8
9 10
Gross Requirements
Scheduled receipts
On hand from prior period
Net requirements
Time‐phased Net Requirements
Planned order releases
Planned order delivery
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MRP Calculation
Period
Item
A
LT= 1 wk
1
Gross Requirements
2
3
4
30
5
6
7
30
8
9 10
40
Scheduled receipts
On hand from prior period 20
Net requirements
Time‐phased Net Q= L4L Requirements
Planned order releases
Planned order delivery
All the information above are given.
MRP Calculation
Period
Item
A
LT= 1 wk
1
Gross Requirements
2
3
4
30
5
30
6
7
8
9 10
40
Scheduled receipts
On hand from prior period 20 20
Net requirements
Time‐phased Net Q= L4L Requirements
‐‐
Planned order releases
Planned order delivery
20 units are just transferred from Period 1 to 2.
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MRP Calculation
Period
Item
A
LT= 1 wk
1
Gross Requirements
2
3
4
30
5
6
7
30
8
9 10
40
Scheduled receipts
On hand from prior period 20 20
Net requirements
Time‐phased Net Q= L4L Requirements
Planned order releases
‐‐ 10
10
10
Planned order delivery
10
The net requirement of 30‐20=10 units must be ordered in week 1.
MRP Calculation
Period
Item
A
LT= 1 wk
1
Gross Requirements
2
3
4
30
5
30
6
7
8
9 10
40
Scheduled receipts
On hand from prior period 20 20 0
Net requirements
Time‐phased Net Q= L4L Requirements
Planned order releases
Planned order delivery
0
0
‐‐ 10
10
10
10
The net requirement of 30‐20=10 units must be ordered in week 1.
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MRP Calculation
Period
Item
A
LT= 1 wk
1
Gross Requirements
2
3
4
30
5
6
7
30
8
9 10
40
Scheduled receipts
On hand from prior period 20 20 0
Net requirements
Time‐phased Net Q= L4L Requirements
Planned order releases
0
‐‐ 10
30
10
30
10
30
Planned order delivery
0
10
30
The net requirement of 30‐00 = 30 units must be ordered in week 4.
MRP Calculation
Period
Item
A
LT= 1 wk
1
Gross Requirements
2
3
4
30
5
6
7
30
8
9 10
40
Scheduled receipts
On hand from prior period 20 20 0
Net requirements
Time‐phased Net Q= L4L Requirements
Planned order releases
Planned order delivery
0
‐‐ 10
0
0
0
30
30
40
10
30
40
30
0
0
40
10
10
0
40
The net requirement of 40 – 0 = 40 units must be ordered in week 7.
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MRP Calculation
Period
Item
B
LT= 1 wk
1
Gross Requirements
10
Scheduled receipts
10
On hand from prior period
2
3
4
5
6
30
0
Net requirements
Time‐phased Net Q= L4L Requirements
0
0
0
0
9 10
0
40
30
40
30
40
Planned order delivery
8
40
30
Planned order releases
7
30
40
MRP Calculation
Period
Item
C
LT= 1 wk
1
Gross Requirements
20
Scheduled receipts
50
2
3
Planned order releases
Planned order delivery
5
6
60
On hand from prior period 10 40 40
Net requirements
Time‐phased Net Q= 50 Requirements
4
40
8
9 10
80
30 30
20
30
0
0
0
50
20
50
50
50
50
7
50
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MRP Calculation
Period
Item
D
LT= 2 wk
Q=
100
1
Gross Requirements
2
3
4
5
6
10
100 30
20 10
10
10
80 80
90
20
20
7
8
9 10
100 40
Scheduled receipts
On hand from prior period
Net requirements
Time‐phased Net Requirements
Planned order releases
0
90
20
0
20
100 100
Planned order delivery
80 40 40 40
100
100 100
100
MRP Calculation
Period
Item
E
LT= 2
1
Gross Requirements
2
3
4
150
5
6
7
8
9 10
150
Scheduled receipts
On hand from prior period 10
Net requirements
Q= 50 Time‐phased Net Requirements
Planned order releases
Planned order delivery
10 10
20
140
20 20 20 20
130
140
130
150
150
150
20 20
150
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MATERIAL REQUIREMENTS PLANNING: LOT SIZING
Lot‐sizing models
Lot‐for‐lot – "chase" demand
EOQ – fixed quantity, different intervals
Silver‐Meal
Least Unit Cost
Part period balancing try to make setup/ordering cost equal to holding cost
• Wagner‐Whitin "optimal" method
•
•
•
•
•
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Lot‐sizing example
Week
1
2
3
4
5
6
7
8
9
10
Net Reqs
20
50
10
50
50
10
20
40
20
30
Planned Order 1
20
50
10
50
50
10
20
40
20
30
Planned Order 2
80
130
90
• Costs
30
– K = 100, h = 1, λ
– Method 1 = $1000
– Method 2 = $ 580
Lot sizing example (cont’d)
• EOQ
77
•
Week
1
2
Net Req
20
50
Qt
77
77
77
77
308
Setup
100
100
100
100
$400
Holding
Total
57
3
4
10
50
7
74
5
6
7
50
10
20
24
51
41
8
9
10
40
20
30
21
58
38
Total
300
$371
$771
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Silver‐Meal Heuristic
C(T): average setup and holding costs per period if the current
order covers the next T periods.
C(1) = K
C(2) = (K + hr2)/2
C(3) = (K + hr2 + 2hr3)/3
C(4) = (K + hr2 + 2hr3 + 3hr4)/4
C(j) = (K + hr2 + 2hr3 +…+ (j ‐ 1)rj ) = j
∑
Rule: Iterate until C(j) > C(j ‐ 1), set
, and begin again at period j .
Silver Meal Example
C(1) = 100
C(2) = (100 + 1(50))/2 = 75
C(3) = (100 + 1(50) + 2(1)(10))/3 = 56.67
C(4) = (100 + 1(50) + 2(1)(10) + 3(1)(50))/4 = 80
So y1 = 20 + 50 + 10 = 80, and we start over at t = 4.
Week
1
2
3
4
5
6
7
8
9
10
Total
Net Req
20
50
10
50
50
10
20
40
20
30
300
Qt
80
30
300
Setup
100
100
$400
Holding
Total
110
80
100
60
10
100
60
10
60
20
$220
$620
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Least Unit Cost Example
C(1) = 100/20 = 5
C(2) = (100 + 1(50))/(20+50) = 2,143
C(3) = (100 + 1(50) + 2(1)(10))/(20+50+10) = 2,125
C(4) = (100 + 1(50) + 2(1)(10) + 3(1)(50)) /(20+50+10+50)
= 2,462
So y1 = 20 + 50 + 10 = 80, and we start over at t = 4.
Week
1
2
3
4
5
6
7
8
9
10
Total
Net Req
20
50
10
50
50
10
20
40
20
30
300
Qt
80
100
70
50
300
Setup
100
100
100
100
$400
Holding
60
10
50
60
40
30
Total
$250
$650
Part period balancing
• At each step, compute total holding cost Hk if we produce enough for the next k periods. Choose k
such that Hk is as near as possible to K.
Order Horizon Total Holding Cost
1
0
2
50
3
70
4
220
• For K = $100, y1 = 20 + 50 + 10 = 80, and we start over at t = 4.
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Part Period Balancing Example
Week
1
2
3
Net Req
20
50
10
Qt
80
130
90
300
Setup
100
100
100
$300
Holding
60
10
4
5
6
7
50
50
10
20
80
30
8
9
10
40
20
30
20
50
30
Total
300
$280
Total
$580
Wagner‐Whitin: an optimal algorithm
1
2
3
4
5
6
• Define fk as the minimum cost starting at node k, assuming we start a lot at node k. Then,
fk = min j>k (ckj + fj );
• where ckj is the setup and holding costs of setting up in period k and producing to meet demand through period j ‐ 1, and fn+1 = 0.
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Wagner‐Whitin: an optimal algorithm
208
162
1
2
75
75
376
131
3
4
75
5
75
98
210
Wagner‐Whitin Example
Week
1
2
3
4
5
6
7
8
9
10
Total
Net Req
20
50
10
50
50
10
20
40
20
30
300
Qt
80
130
90
300
Setup
100
100
100
$300
Holding
Total
60
10
80
30
20
50
30
$280
$580
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Summary of Lot‐sizing Methods
Week
1
2
3
4
5
6
7
8
9
10
Total
Net Req
20
50
10
50
50
10
20
40
20
30
300
30
$620
EOQ
77
Silver‐Meal
80
77
77
77
110
$771
80
Least Unit Cost
80
100
70
50
$650
TotalPart Period Bal.
80
130
90
$580
Wagner‐Whitin
80
130
90
$580
LOT SIZING WITH CAPACITY
CONSTRAINTS
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Lot sizing with capacity constraints
• So far we have assumed that there is no capacity constraint on production. However, often, the production capacity is limited. • Here we assume that it is required to develop a production plan (i.e., production quantities of various periods) that minimizes total inventory holding and ordering costs.
• Capacity constraints make the problem more realistic. • At the same time, capacity constraints make the problem difficult.
Lot sizing with capacity constraints
Week
1
2
3
4
5
6
7
8
9
10
Total
Net Req rt
20
50
10
50
50
10
20
40
20
30
300
Capacity ct
32
32
32
32
32
32
32
32
32
32
320
Cumulative rt
20
70
80
130
180
190 210
250
270
300
128
160
192
256
288
320
Cumulative ct
32
64
96
224
In general, we require that
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Feasibility check
• For every period, compute the cumulative requirement and the cumulative capacity. – If for every period, the cumulative capacity is larger than (or equal to) the cumulative requirement, then there exists a feasible solution. – Else, if there is a period in which cumulative capacity is smaller than the cumulative requirement, then there will be a shortage in that period, and, therefore, there is no feasible solution. Checking feasibility
Production
Requirement
June
10
July
14
August
15
September
16
Production
Capacity
15
11
12
17
Question: Is it possible to meet the production requirements of all the months? 28
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Checking feasibility
Production
Cumulative
Requirement
June
July
August
September
10
14
15
16
10
24
39
55
Production Cumulative
Capacity
15
11
12
17
15
26
38
55
Answer: The August requirement cannot be met even after full production in June, July and August. Hence, it is not possible to meet the production requirements of all the months.
Lot sizing with capacity constraints
• Two methods:
– the lot shifting technique, a heuristic procedure that constructs a production plan, and – another procedure that improves a given production plan.
• At times, capacity may be so low that it may not be possible to meet the demand of all periods. How to check feasibility?
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Lot shifting technique
• Lot shifting technique constructs a feasible production plan, if there exists one or provides a proof that there is no feasible solution.
• Lot shifting method is a heuristic. The production plan obtained from the lot shifting technique is not necessarily optimal. It is possible to improve the production plan. • An improvement procedure will be discussed after the lot shifting technique.
Lot shifting technique
• The lot shifting method repeatedly does the following:
– Find the first period with less capacity. • If possible, back‐shift the excess capacity to some prior periods. Continue.
• If it is not possible to back‐shift the excess capacity to some prior periods, stop. There is no feasible solution.
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Lot shifting technique: example
Production
Requirement
June
10
July
14
August
15
September
16
Production
Capacity
30
13
13
17
Question: Find a feasible production plan
Lot shifting technique: example
Production
Requirement
June
10
July
14
August
15
September
16
Production
Capacity
30
13
13
17
Rule: Find the first period with less capacity. The first period with shortage is July when the capacity = 13 < 14 = production requirement.
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Lot shifting technique: example
Production
Requirement
June
11
July
13
August
15
September
16
Production
Capacity
30
13
13
17
Rule: Find the first period with less capacity. The first period with shortage is July when the capacity = 13 < 14 = production requirement.
Lot shifting technique: example
Production
Requirement
June
13
July
13
August
13
September
16
Production
Capacity
30
13
13
17
Rule: Find the first period with less capacity. The second period with shortage is August
when the capacity = 13 < 15 = production requirement.
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Improvement rule
Rule: Beginning at the last period, shift the entire production lot to the nearest time periods having excess capacity, if the savings in setup cost is greater than the additional holding costs.
Improvement rule: example
Production
Requirement
June
13
July
13
August
13
September
16
Production
Capacity
30
13
13
17
Question: Is it possible to improve the plan if K= $50, h=$2/unit/month?
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Improvement rule: example
Production
Production Excess
Requirement Capacity
June
13
30
17
July
13
13
0
August
13
13
0
September
16
17
1
Back‐shift September production to June? Improvement rule: example
Production
Production Excess
Requirement Capacity
June
13
30
17
July
13
13
0
August
13
13
0
September
16
17
1
Back‐shift August production to June? 34
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Improvement rule: example
Production
Production Excess
Requirement Capacity
June
13
30
17
July
13
13
0
August
13
13
0
September
16
17
1
Back‐shift July production to June? Improvement rule: example
Production
Production Excess
Requirement Capacity
June
26
30
4
July
0
13
13
August
13
13
0
September
16
17
1
Final Plan The above is the result of the improvement
procedure.
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5/8/2013
Shortcomings of MRP
• Uncertainty. MRP ignores demand uncertainty, supply uncertainty, and internal uncertainties that arise in the manufacturing process. • Capacity Planning. Basic MRP does not take capacity constraints into account. • Rolling Horizons. MRP is treated as a static system with a fixed horizon of n periods. The choice of n is arbitrary and can affect the results. • Lead Times Dependent on Lot Sizes. In MRP lead times are assumed fixed, but they clearly depend on the size of the lot required.
Shortcomings of MRP, cont.
• Quality Problems. Defective items can destroy the linking of the levels in an MRP system.
• Data Integrity. Real MRP systems are big (perhaps more than 20 levels deep) and the integrity of the data can be a serious problem.
• Order Pegging. A single component may be used in multiple end items, and each lot must then be pegged to the appropriate item. 36