The MRP Heuristic
 MRP stands for Materials Requirement Planning
 It is a widely used approach for production planning
and scheduling in industry
 It is the approach embedded in many commercially
available software applications
1
MRP Assumptions
 No capacity constraints
 A task initiated in period t completes in period t+ai
 Product structure is typically assumed to be of the
assembly type
2
Formulation
Minimize
z
  c Q
T
N
t 1
i 1
it
it
 Ait Yit    t 1  r 1 hrt I rt
T
R
subject to
I rt  I r ,t 1   i 1 ir Qit a i ,m   i 1 ir Qi ,t  Drt ,
N
N
Qit  MYit
Yit {0,1}
Qit , I rt  0
r , t
i, t , r
i, t
i, t , r
3
The MRP Solution Approach
 Solve the lot sizing problem for each item
independently starting with the end-items (finished
products) and working your way down the bill-ofmaterial (BOM)
 The selected production quantities for an item,
determine the demand for the items that are its
immediate predecessors (its input items)
4
Solving the Lot Sizing Problem
 Solve the problem for each item optimally (e.g., using
the Wagner-Whittin algorithm)
 Solve the problem approximately using a heuristic
(e.g., using a fixed order quantity, a fixed order
period, or a lot for lot heuristic)
5
Example
Item: Stool (Leadtime = 1 week)
Week
Gross Reqs
Sched Receipts
Proj Inventory
Net Reqs
Planned Orders
0
1
2
3
4
5
120
6
20
20
20
20
20
-100
100
-100
100
Item: Base (Leadtime = 1 week)
Week
Gross Reqs
Sched Receipts
Proj Inventory
Net Reqs
Planned Orders
0
1
2
3
4
100
5
6
0
0
0
0
-100
100
-100
-100
100
6
Example (Continued…)
Item: Legs (Leadtime = 2 weeks)
Week
Gross Reqs
Sched Receipts
Proj Inventory
Net Reqs
Planned Orders
0
0
1
2
3
4
400
5
6
0
200
0
0
-200
200
-200
-200
200
7
MRP Terminology
 Netting: determining net requirements against projected
inventory for each period
 Lot Sizing: determining order quantities
 Time Phasing: determining when production orders
should be initiated, given the production lead time
 BOM Explosion: determining gross requirements for
components
8
MRP Terminology (Continued…)
 Master Production Schedule (MPS): due dates and
quantities for all top level items (finished products)
 Bill of Material (BOM): the items that goes into each
sub-assembly and into the finished product
 Projected Inventory: (on hand plus scheduled receipts)
for all items
 Planned Lead times: production lead times
 Level code: a number assigned to an item depending on
the lowest position in the BOM where it can be found
9
The Netting Procedure

Dt: Gross requirements in period t for some item

St: Quantity currently scheduled to complete in period t
(i.e., a scheduled receipt)

It: projected on-hand inventory for the end of period t

Nt: Net requirement for period t

Qt: Planned orders in period t (production quantity
initiated in period t)
10
The Basic Steps
Step 1: Let t = 1
Step 2: It = It-1 - Dt
Step 3: If It  0, then let t = t + 1 and go back to step 2,
otherwise, let Nt = - It and set Nt’ = Dt’ for all t’ > t
Step 4: Use a lot sizing method to determine Qt for t=1,…, T,
taking into account the production leadtime
Step 5: Use the production quantities Qt in determining the
gross requirements for all items that are used by the item
under current consideration
11
Example - The Bill of Materials
A
100
200
(2)
300
B
500
400
100
300
300
600
400
12
Example – The Input Data
Part
Number
Current OnHand
Scheduled Receipts
Due
Lot Sizing
Rule
Lead Time
Quantity
A
20
FOP, 2 weeks
2 weeks
B
40
FOP, 2 weeks
2 weeks
100
40
Lot-for Lot
2 weeks
300
50
Lot-for-Lot
1 week
500
40
Lot-for-Lot
4 weeks
2
100
13
Example – Part A
Part A
1
2
3
4
5
6
7
8
Gross requirements
15
20
50
10
30
30
30
30
Scheduled receipts
10
10
15
-15
---
---
Net requirements
15
30
30
Planned order receipts
45
Adjusted SRs
Projected onhand
20
Planned order releases
5
100
20
100
5
55
45
45
30
30
14
Example – Part B
Part B
1
2
3
4
5
6
7
8
Gross requirements
10
15
10
20
20
15
15
15
---
---
---
---
Scheduled receipts
Adjusted SRs
Projected onhand
40
Net requirements
Planned order receipts
Planned order releases
15
Example – Part B
Part B
1
2
3
4
5
6
7
8
Gross requirements
10
15
10
20
20
15
15
15
30
15
5
-15
---
---
---
---
Net requirements
15
20
15
15
15
Planned order receipts
35
30
30
15
Scheduled receipts
Adjusted SRs
Projected onhand
40
Planned order releases
35
15
16
Example – Part 500
Part 500
1
Gross requirements
2
3
35
4
5
30
6
7
8
---
---
15
Scheduled receipts
Adjusted SRs
Projected onhand
40
40
5
5
-25
---
---
Net requirements
25
15
Planned order receipts
25
15
Planned order releases
25*
15
17
Example – Part 500
Part 500
1
2
3
4
5
6
7
8
---
---
---
---
Gross requirements
Scheduled receipts
Adjusted SRs
Projected onhand
40
Net requirements
Planned order receipts
Planned order releases
18
Example – Part 100
Part 100
Gross requirements from A
Gross requirements from 500
Gross Requirments
1
2
25
25
15
15
15
0
3
4
5
6
90
60
90
60
7
8
---
---
Scheduled receipts
Adjusted SRs
Projected onhand
40
-90
---
---
Net requirements
90
---
60
Planned order receipts
90
Planned order releases
90
0
60
60
19
Limitations of MRP
 Capacity-insensitive
 Assumes fixed lead times
 Incentive to inflate lead times
20
The MRP Planning Loop
1. Fixed lead times lead to poor due date performance
2. Management decides to increase lead time
3. Longer lead time requires longer forecasting horizon
4. Longer forecasting horizon creates errors in estimating
demand
5. Errors in estimating demand lead to poor due date
performance.
6. Management decides to increase lead time
21
Enhancements to MRP
 MRP II: The functionality of materials requirement
planning (MRP) + capacity requirement planning (CRP)
 APS: Advanced Planning Systems (software
applications with the ability to solve the underlying
optimization problem)
ERP: Enterprise Requirement Planning (MRP or APS
capabilities integrated into an enterprise-wide
information system)
22