1

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

2

MRP Assumptions

No capacity constraints A task initiated in period t completes in period

t+i

Product structure is typically assumed to be of the assembly type

3

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Formulation

4

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-of-material (BOM)

The selected production quantities for an item, determine the demand for the items that are its immediate predecessors (its input items)

5

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)

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Example

Item: Stool (Leadtime = 1 week)

Week 0 1 2 3 4 5 6Gross Reqs 120Sched ReceiptsProj Inventory 20 20 20 20 20 -100 -100Net Reqs 100Planned Orders 100

Item: Base (Leadtime = 1 week)

Week 0 1 2 3 4 5 6Gross Reqs 100Sched ReceiptsProj Inventory 0 0 0 0 -100 -100 -100Net Reqs 100Planned Orders 100

7

Example (Continued…)

Item: Legs (Leadtime = 2 weeks)

Week 0 1 2 3 4 5 6Gross Reqs 400Sched Receipts 200Proj Inventory 0 0 0 0 -200 -200 -200Net Reqs 200Planned Orders 200

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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

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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

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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)

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The Basic Steps

Step 1: Let t = 1Step 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

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Example - The Bill of Materials

A

100 (2) 200

300 400

B

500

300

100 600

300 400

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Example – The Input Data

Part Number

Current On-Hand

Scheduled Receipts Lot Sizing Rule

Lead Time

Due Quantity

A 20 FOP, 2 weeks 2 weeks

B 40 FOP, 2 weeks 2 weeks

100 40 Lot-for Lot 2 weeks

300 50 2 100 Lot-for-Lot 1 week

500 40 Lot-for-Lot 4 weeks

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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 10 100

Adjusted SRs 20 100

Projected on-hand

20 5 5 55 45 15 -15 --- ---

Net requirements 15 30 30

Planned order receipts 45 30

Planned order releases 45 30

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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 on-hand

40 --- --- --- ---

Net requirements

Planned order receipts

Planned order releases

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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 on-hand

40 30 15 5 -15 --- --- --- ---

Net requirements 15 20 15 15 15

Planned order receipts 35 30 15

Planned order releases 35 30 15

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Example – Part 500

Part 500 1 2 3 4 5 6 7 8

Gross requirements 35 30 15

Scheduled receipts

Adjusted SRs

Projected on-hand

40 40 5 5 -25 --- --- --- ---

Net requirements 25 15

Planned order receipts 25 15

Planned order releases 25* 15

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Example – Part 500

Part 500 1 2 3 4 5 6 7 8

Gross requirements

Scheduled receipts

Adjusted SRs

Projected on-hand

40 --- --- --- ---

Net requirements

Planned order receipts

Planned order releases

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Example – Part 100

Part 100 1 2 3 4 5 6 7 8

Gross requirements from AGross requirements from 500

Gross Requirments2525

1515

90

90

60

60

Scheduled receipts

Adjusted SRs

Projected on-hand

40 15 0 0 -90 --- --- --- ---

Net requirements 90 --- 60

Planned order receipts 90 60

Planned order releases 90 60

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Limitations of MRP

Capacity-insensitive

Assumes fixed lead times

Incentive to inflate lead times

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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

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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)