material requirementsplanning mrp -...

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Material Requirements Planning ‐MRP

ENM308Production Planning and Control ‐ I

Spring 2013Haluk Yapıcıoğlu, PhD

Aggregate Planning

Master Production Schedule

Inventory Control

Operations Scheduling

Vehicle Routing

Forecast of Demand

Hierarchy of Production Decisions

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• 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.


• 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.

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Hierarchy of Production DecisionsMaster Production Schedule

Ladder‐back chair

Kitchen chair

Desk chair

1 2

April May

790

3 4 5 6 7 8

200

150

120

200

150

200

120

Aggregate production plan for chair family

550

200


• 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.

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Hierarchy of Production Decisions:Materials Requirement Planning

Back slats

Leg supports

Seat cushion

Seat‐frameboards

Frontlegs

Backlegs

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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Inventory without an MRP System

Inventory with an MRP System

Importance of 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 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 Output:

– Every required item is either produced or purchased. So, the report is sent to production or purchasing.

MRPcomputerprogram

Bill ofMaterials

file

Inventoryfile

Master Production Schedule

ReportsTo Production

To Purchasing

ForecastsOrders


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Level 1

Level 0

Level 2

Level 3

Bill of Materials: Product Structure Tree

BILL OF MATERIALSProduct Description: Ladder‐back chairItem: AComponent Quantity

RequiredSource

Item DescriptionB Ladder‐back 1 ManufacturingC Front legs 2 PurchaseD Leg supports 4 PurchaseE Seat 1 Manufacturing

Bill of Materials

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BILL OF MATERIALSProduct Description: SeatItem: EComponent Quantity

RequiredSource

Item DescriptionH Seat frame 1 ManufacturingI Seat cushion 1 Purchase

Bill of Materials

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 1251 = 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.

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Assume that 150 units of ladder‐back chairs are to be produced at the end of week 15

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

MRP Calculation

Assume that 150 units of ladder‐back chairs are to be produced at the end of week 15

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

MRP Calculation

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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

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

MRP Calculation: Time of Order Placement

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

Week

Complete order for seat subassembly 14

Minus lead time for seat subassembly 2

Place an order for seat subassembly 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

MRP Calculation: Time of Order Placement

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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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Level 0

Level 1

Level 2

MRP Calculation

Period 1 2 3 4 5 6 7 8 9 10Item

A

LT=

Q=

Gross Requirements

Scheduled receipts

On hand from prior period

Net requirementsTime‐phased Net Requirements

Planned order releases

Planned order delivery

MRP Calculation

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All the information above are given.

Period 1 2 3 4 5 6 7 8 9 10Item

A

LT= 1 wk

Q= L4L

Gross Requirements 30 30 40

Scheduled receipts

On hand from prior period 20

Net requirementsTime‐phased Net Requirements



MRP Calculation

20 units are just transferred from Period 1 to 2.

Period 1 2 3 4 5 6 7 8 9 10Item

A

LT= 1 wk

Q= L4L


Scheduled receipts

On hand from prior period 20 20

Net requirements

‐‐

Time‐phased Net Requirements



MRP Calculation

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Period 1 2 3 4 5 6 7 8 9 10Item

A

LT= 1 wk

Q= L4L


Scheduled receipts

On hand from prior period 20 20

Net requirements

‐‐ 10


10

Planned order releases 10

Planned order delivery 10

The net requirement of 30‐20=10 units must be ordered in week 1.

MRP Calculation

Period 1 2 3 4 5 6 7 8 9 10Item

A

LT= 1 wk

Q= L4L


Scheduled receipts

On hand from prior period 20 20 0 0 0

Net requirements

‐‐ 10


10

Planned order releases 10

Planned order delivery 10

The net requirement of 30‐20=10 units must be ordered in week 1.

MRP Calculation

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Period 1 2 3 4 5 6 7 8 9 10Item

A

LT= 1 wk

Q= L4L


Scheduled receipts

On hand from prior period 20 20 0 0 0

Net requirements

‐‐ 10 30


10 30

Planned order releases 10 30

Planned order delivery 10 30

The net requirement of 30‐00 = 30 units must be ordered in week 4.

MRP Calculation

Period 1 2 3 4 5 6 7 8 9 10Item

A

LT= 1 wk

Q= L4L


Scheduled receipts

On hand from prior period 20 20 0 0 0 0 0 0 0 0

Net requirements

‐‐ 10 30 40


10 30 40

Planned order releases 10 30 40

Planned order delivery 10 30 40

The net requirement of 40 – 0 = 40 units must be ordered in week 7.

MRP Calculation

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Period 1 2 3 4 5 6 7 8 9 10Item

B

LT= 1 wk

Q= L4L


Scheduled receipts 10

On hand from prior period 0 0 0 0 0 0

Net requirements

30 40


30 40



MRP Calculation

Period 1 2 3 4 5 6 7 8 9 10Item

C

LT= 1 wk

Q= 50


Scheduled receipts 50


Net requirements

20 50


20 50



MRP Calculation

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Period 1 2 3 4 5 6 7 8 9 10Item

D

LT= 2 wk

Q=100

Gross Requirements 10 100 30 100 40

Scheduled receipts


Net requirements

0 90 20 20 0


90 20 20

Planned order releases 100 100 100

Planned order delivery 100 100 100

MRP Calculation

Period 1 2 3 4 5 6 7 8 9 10Item

E

LT= 2

Q= 50

Gross Requirements 150 150

Scheduled receipts


Net requirements

140 130


140 130



MRP Calculation

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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

• Costs

– K = 100, h = 1, λ 30

– Method 1 = $1000

– Method 2 = $ 580

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

Lot sizing example (cont’d)

• EOQ

• 77

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 77 77 77 77 308

Setup 100 100 100 100 $400

Holding 57 7 74 24 51 41 21 58 38 $371

Total $771

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Silver‐Meal Heuristic

C(T): average setup and holding costs per period if the currentorder covers the next T periods.C(1) = KC(2) = (K + hr2)/2C(3) = (K + hr2 + 2hr3)/3C(4) = (K + hr2 + 2hr3 + 3hr4)/4C(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 80 110 80 30 300

Setup 100 100 100 100 $400

Holding 60 10 60 10 60 20 $220

Total $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 $250

Total $650

Part period balancing

• At each step, compute total holding cost Hk if we produce enough for the next k periods. Choose ksuch that Hk is as near as possible to K.

• For K = $100, y1 = 20 + 50 + 10 = 80, and we start over at t = 4.

Order Horizon Total Holding Cost

1 0

2 50

3 70

4 220

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Part Period Balancing 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 60 10 80 30 20 50 30 $280

Total $580

Wagner‐Whitin: an optimal algorithm

• 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.

1 2 3 4 5 6

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Wagner‐Whitin: an optimal algorithm

1 2 3 4 575 75 75 75

162208 376

131

98210

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 60 10 80 30 20 50 30 $280

Total $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

EOQ 77 77 77 77 $771

Silver‐Meal 80 110 80 30 $620

Least Unit Cost 80 100 70 50 $650

TotalPart Period Bal. 80 130 90 $580

Wagner‐Whitin 80 130 90 $580

LOT SIZING WITH CAPACITYCONSTRAINTS

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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.


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

Cumulative ct 32 64 96 128 160 192 224 256 288 320

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

ProductionRequirement

ProductionCapacity

June 10 15

July 14 11

August 15 12

September 16 17

Question: Is it possible to meet the production requirements of all the months?

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Checking feasibility


Cumulative ProductionCapacity

Cumulative

June 10 10 15 15

July 14 24 11 26

August 15 39 12 38

September 16 55 17 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.


• 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


ProductionCapacity

June 10 30

July 14 13

August 15 13

September 16 17

Question: Find a feasible production plan



ProductionCapacity

June 10 30

July 14 13

August 15 13

September 16 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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ProductionCapacity

June 11 30

July 13 13

August 15 13

September 16 17

Rule: Find the first period with less capacity. The first period with shortage is July when the capacity = 13 < 14 = production requirement.



ProductionCapacity

June 13 30

July 13 13

August 13 13

September 16 17

Rule: Find the first period with less capacity. The second period with shortage is Augustwhen 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

Question: Is it possible to improve the plan if K= $50, h=$2/unit/month?


ProductionCapacity

June 13 30

July 13 13

August 13 13

September 16 17

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Back‐shift September production to June?


ProductionCapacity

Excess

June 13 30 17

July 13 13 0

August 13 13 0

September 16 17 1


Back‐shift August production to June?


ProductionCapacity

Excess

June 13 30 17

July 13 13 0

August 13 13 0

September 16 17 1

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Back‐shift July production to June?


ProductionCapacity

Excess

June 13 30 17

July 13 13 0

August 13 13 0

September 16 17 1


Final Plan The above is the result of the improvement

procedure.


ProductionCapacity

Excess

June 26 30 4

July 0 13 13

August 13 13 0

September 16 17 1

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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.

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