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 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)

6 Example

7 Example (Continued…)

8 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

9 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

10 The Netting Procedure  D t : Gross requirements in period t for some item  S t : Quantity currently scheduled to complete in period t (i.e., a scheduled receipt)  I t : projected on-hand inventory for the end of period t  N t : Net requirement for period t  Q t : Planned orders in period t (production quantity initiated in period t )

11 The Basic Steps Step 1: Let t = 1 Step 2: I t = I t- 1 - D t Step 3: If I t  0, then let t = t + 1 and go back to step 2, otherwise, let N t = - I t and set N t’ = D t’ for all t ’ > t Step 4: Use a lot sizing method to determine Q t for t =1,…, T, taking into account the production leadtime Step 5: Use the production quantities Q t in determining the gross requirements for all items that are used by the item under current consideration

12 Example - The Bill of Materials A 100 (2) B

13 Example – The Input Data Part Number Current On- Hand Scheduled ReceiptsLot Sizing Rule Lead Time DueQuantity A20FOP, 2 weeks2 weeks B40FOP, 2 weeks2 weeks 10040Lot-for Lot2 weeks Lot-for-Lot1 week 50040Lot-for-Lot4 weeks

14 Example – Part A Part A Gross requirements Scheduled receipts Adjusted SRs20100 Projected on- hand Net requirements1530 Planned order receipts4530 Planned order releases4530

15 Example – Part B Part B Gross requirements Scheduled receipts Adjusted SRs Projected on- hand Net requirements Planned order receipts Planned order releases

16 Example – Part B Part B Gross requirements Scheduled receipts Adjusted SRs Projected on- hand Net requirements Planned order receipts Planned order releases353015

17 Example – Part 500 Part Gross requirements Scheduled receipts Adjusted SRs Projected on- hand Net requirements2515 Planned order receipts2515 Planned order releases25*15

18 Example – Part 500 Part Gross requirements Scheduled receipts Adjusted SRs Projected on- hand Net requirements Planned order receipts Planned order releases

19 Example – Part 100 Part Gross requirements from A Gross requirements from 500 Gross Requirments Scheduled receipts Adjusted SRs Projected on- hand Net requirements Planned order receipts9060 Planned order releases9060

20 Limitations of MRP  Capacity-insensitive  Assumes fixed lead times  Incentive to inflate lead times

21 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

22 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)