Mrp Algorithm

Material Requirements Planning
Lecturer: Stanley B. Gershwin

MRP Overview

• Primary source: Factory Physics by Hopp and
Spearman.
• Basic idea: Once the final due date for a product is known, and the time required for each production step is known, then intermediate due dates and material requirement times can be determined.
• Original goal: To determine when material for production is required.

MRP Overview

Demand

Demand
• ... from outside the system is independent demand.

• ... for components or raw material is dependent demand. Before MRP, buyers were not synchronized with producers. MRP Overview

Planning Algorithm

• Start at the due date for a finished product (or end item ) (Tk).

• Determine the last operation, the time required for that operation (tk−1), and the material required for that operation.
• The material may come from outside, or from earlier operations inside the factory.
• Subtract the last operation time from the due date to determine when the last operation should start.

MRP Overview

Planning Algorithm

Tk−1 = Tk − tk−1
• The material required must be present at that time.

• Continue working backwards.

• However, since more than one component may be needed at an operation, the planning algorithm must work its way backwards along each branch of a tree
— the bill of materials.

MRP Overview

Planning Algorithm
Time

• In some MRP systems, time is divided into time buckets — days, weeks, or whatever is convenient.
• In others, time may be chosen as a continuous variable. MRP Overview

Discussion

• What assumptions are being made here ...
� ... about predictability?
� ... about capacity?

• How realistic are those assumptions?

• Is it more flexible to use time buckets or continuous time? MRP Overview

Jargon

• Push system: one in which material is loaded based

on planning or forecasts, not on current demand.

� MRP is a push system.
• Pull system: one in which production occurs in response to the consumption of finished goods inventory by demand.
• Which is better?

Bill of Materials

(BOM)

Level 0

Level 1

Level 2

• Top level is end item.

• Items are given a low-level code corresponding to the lowest level they appear at, for any end item in the factory.

The BOM must be maintained as the product mix changes. Master

Production

Schedule

• Information concerning independent demand.

• Gross requirements: What must be delivered in the future, and when.
• On-hand inventory: Finished good already available.

• Net requirements: (Gross requirements) – (On-hand inventory). Master
Production

Schedule
1
Gross requirements 15
Projected on-hand 30 15
Net requirements
0

Example

Netting

Week
2 3 4 5 6 7 8
20 50 10 30 30 30 30
-5
5 50 10 30 30 30 30

• 15 of the initial 30 units of inventory are used to satisfy Week 1 demand.
• The remaining 15 units are 5 less than required to satisfy Week 2 demand.

Master
Production
Schedule

Example
Lot Sizing

• Lot sizes are 75. The first arrival must occur in Week 2.
• 75 units last until Week 4, so plan arrival in Week 5.
• Similarly, deliveries needed in Weeks 5 and 7.
1
Gross requirements
15
Cumulative gross
15
Planned order receipts 30 0
Cumulative receipts
30

Week
2
3
4
5
6
7
8
20 50 10 30 30 30 30
35 85 95 125 155 185 215
75 0
0 75 0 75 0
105 105 105 180 180 255 255

Master

Production

Schedule

Example
Cumulatives

300

cumulative gross cumulative receipts

250
200
150
100
50
00

1

2

3

4

5

6

7

8 week Material requirements are determined by considering whether inventory would otherwise become negative. Master
Production
Schedule

Example
Time Phasing

• Lead times are 1 week. Therefore, order release

must occur one week before delivery is required.

1
Gross requirements 15
Cumulative gross
15
Planned receipts 30 0
Cumulative receipts 30
Planned release
75

2
20
35
75
105
0

3
50
85
0
105
0

Week
4
5
10 30
95 125
0 75
105 180
75 0

6
30
155
0
180
75

7
30
185
75
255
0

8
30
215
0

255

0

Master
Production
Schedule

Example
BOM Explosion

• Now, do exactly the same thing for all the components required to produce the finished goods
(level 1).
• Do it again for all the components of those components (level 2).
• Et cetera.

Data

Inputs

• Master Production Schedule — demand – quantities and due dates
• Item Master File — for each part number: description, BOM, lot-sizing, planning lead times
• Inventory Status – finished goods, work-in-progress

Data

Outputs

• Planned order releases
• Change notices

• Exception reports — discrepancies, consequences of unexpected events

Master
Production

Schedule

• Define

Definitions

� Dt = Demands, or gross requirements for week t
� St = Quantity that will be completed in week t
� It = Projected finished inventory in week t
� Nt = Net requirements in week t

Master
Production

Schedule

Netting

• Inventory dynamics: Starting with t = 1 (where

t = 0 means now ) and incrementing t by 1,

It = It−1 − Dt, as long as It−1 − Dt � 0
It = It−1 − Dt + St, if It−1 − Dt < 0 where St is minimal amount needed to make the inventory positive, which is consistent with lot-sizing requirements. Master
Production

Schedule

Netting

• Net requirements: Let t� be the first time when It−1 − Dt < 0.
Then,
�

⎧ if t < t�

�0
Nt = It−1 − Dt < 0 if t = t�
⎧
� Dt if t > t�
• From net requirements, we calculate required production
(scheduled receipts) St, t > t�.
• St is adjusted for new orders or new forecasts.
• Then procedure is repeated for the next T �.

Master

Production

Schedule

Netting
Example

Week

1 2 3 4 5 6 7 8
Gross requirements

15 20 50 10 30 30 30 30
Projected on-hand
20

5 5 55 45 15 -15

20 100

Adjusted scheduled receipts

0 0 0 0 0 15 30 30
Net requirements

Master

Production

Schedule

1
15
Gross requirements
5
Projected on-hand
20
0
Net requirements
10
Scheduled receipts�
Adjusted scheduled receipts 0

Netting

Example

2 3

20 50

5 55

0 0

10
20 100

Week
4
5
10
30
45
15
0
0
100

6 7 8
30 30 30
-15
15 30 30

* original plan

• The 10 units planned for week 1 were deferred to week 2.
• The 100 units planned for week 4 were expedited to week 3.

Master
Production

Schedule

Lot Sizing

Possible rules:
• Lot-for-lot: produce in a period the net requirements for that period. Maximum setups.
• Fixed order period: produce in a period the net requirements for P periods.
• Fixed order quantity: always produce the same quantity, whenever anything is produced. EOQ formula can be used to determine lot size.
Which satisfy the Wagner-Whitin property?

Master
Production

Schedule

Lot Sizing

300

cumulative gross cumulative receipts −− fixed batch cumulative receipts−− fixed period

250

200

150

100

50

00 c 1

2

3

4

5

6

7

8

week

Master
Production

Schedule

BOM Explosion

• After scheduling production for all the top level (Level
0) items, do the same for Level 1 items.
• The planned order releases for Level 0 are the gross requirements for Level 1.
• Do the same for Level 2, 3, etc.

Reality

Uncertainty/Variability

• MRP is deterministic but reality is not. Therefore, the

system needs safety stock and safety lead times .

• Safety stock protects against quantity uncertainties.

� You don’t know how much you will make, so plan to make a little extra.
• Safety lead time protects against timing uncertainties. � You don’t know exactly when you will make it, so plan to make it a little early.

Reality

Uncertainty/Variability
Safety Stock

• Instead of having a minimal planned inventory of zero, the (positive) safety stock is the planned minimal inventory level.
• Whenever the actual minimal inventory differs from the safety stock, adjust planned order releases accordingly. Reality

Uncertainty/Variability
Safety Lead Time

• Add some extra time to the planned lead time.

Reality

Uncertainty/Variability
Yield Loss

• Yield = expected fraction of parts started that are successfully produced.
• Actual yield is random.

• If you need to end up with N items, and the yield is y, start with N/y.
• However, the actual production may differ from N , so safety stock is needed.

Reality

Other problems

• Capacity is actually finite.

• Planned lead times tend to be long (to compensate for variability).
� Also, workers should start work on a job as soon as it is released, and relax later (usually possible because of safety lead time). Often, however, they relax first, so if a disruption occurs, the job is late.

Reality

Other problems
Nervousness

• Nervousness — drastic changes in schedules due to small deviations from plans — (chaos?)
• Nervousness results when a deterministic calculation is applied to a random system, and local perturbations lead to global changes.

Other problems

Reality

Nervousness

300

cumulative gross cumulative receipts −− original cumulative receipts −− perturbed

250

200

150

100

50

00 c 1

2

3

4

5

6

7

8

week

Reality

Other problems
Nervousness

• Possible consequences:

� Drastic changes in plans for the near future, which will

confuse workers;

� Excessive setups, consuming excess expense or capacity.

• Solution: Freeze the early part of the schedule (ie, the near future). Do not change the schedule even if there is a change in requirements; or do not accept changes in requirements.
� But: What price is paid for freezing?

Reality

Fundamental problem

• MRP is a solution to a problem whose formulation is based on an unrealistic model, one which is
� deterministic
� infinite capacity

• As a result,

� it frequently produces non-optimal or infeasible schedules, and � it requires constant manual intervention to compensate for poor schedules.

• On top of that, nervousness amplifies inevitable variability. MRP II

• Manufacturing Resources Planning

� MRP, and correction of some its problems,
� demand management,
� forecasting,
� capacity planning,
� master production scheduling,
� rough-cut capacity planning,
� capacity requirements planning (CRP),
� dispatching,
� input-output control.

MRP II Hierarchy

Cumulative
Production

Hierarchical Planning and Scheduling

Short range

Medium range
Long range t Hierarchical Planning

MRP II Hierarchy

and Scheduling

Planning/Scheduling/Control Hierarchy
Level 1

a

b

c

Level 2

E

d

e

f

C

g

h

F

Level 3

H

Level 4

1

A

2

B

3

C

4

D

5

E

6

F

7

G

8

H

9

I 10

J 11 K 12

MRP II Hierarchy

Hierarchical Planning
General ideas

• Higher levels deal with longer time scales and more of the system (scope).
• Higher levels use more aggregated (coarse-grained) models. • Higher levels send production targets down to lower levels. � Each level refines the target for the level below,

with reduced time scale and reduced scope.

� The bottom level actually implements the schedule.

MRP II Hierarchy

Hierarchical Planning
General ideas

Production targets

Capacity reports
Level k−1

Production targets

Uncontrolled events

Capacity reports
Level k

Material movement commands MRP II Hierarchy

Hierarchical Planning
Long-Range Planning

• Range: six months to five years.

• Recalculation frequency: 1/month to 1/year.

• Detail: part family.

• Forecasting

• Resource planning — build a new plant?

• Aggregate planning — determines rough estimates of production, staffing, etc.

MRP II Hierarchy

Hierarchical Planning
Intermediate-Range Planning

• Demand management — converts long range forecast and actual orders into detailed forecast.
• Master production scheduling

• Rough-cut capacity planning — capacity check for feasibility. • CRP — better than rough cut, but still not perfect.
Based on infinite capacity assumption.

MRP II Hierarchy

Hierarchical Planning
Short-Term Control/Scheduling

• Daily Plan

� Production target for the day

• Shop Floor Control

� Job dispatching — which job to run next?
� Input-output control — release
� Often based on simple rules
� Sometimes based on large deterministic mixed

(integer and continuous variable) optimization

MRP II Hierarchy

Hierarchical Planning
Issues

• The high level and low level models sometimes don’t match. � The high level aggregation is not done accurately.

� Actual events make the production target obsolete.

� Consequence: Targets may be infeasible or too

conservative.

• The short-term schedule may be recalculated too frequently. � Consequence: Instability.

MIT OpenCourseWare http://ocw.mit.edu 2.854 / 2.853 Introduction to Manufacturing Systems
Fall 2010

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