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Production Planning Solution
Techniques Part 1 MRP, MRP-IIMads Kehlet Jepsen
Production Planning Solution Techniques Part 1 MRP, MRP-II p.1/3
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Overview
Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/3
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Overview
Material Requirement Planning(MRP)
Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/3
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Overview
Material Requirement Planning(MRP)
MRP Procedure
Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/3
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Overview
Material Requirement Planning(MRP)
MRP Procedure
Issues with MRP
Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/3
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Overview
Material Requirement Planning(MRP)
MRP Procedure
Issues with MRPManufacturing Resource Planning MRP II
Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/3
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Overview
Material Requirement Planning(MRP)
MRP Procedure
Issues with MRPManufacturing Resource Planning MRP II
Time driven Rough-Cut Capacity Planning
Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/3
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Overview
Material Requirement Planning(MRP)
MRP Procedure
Issues with MRPManufacturing Resource Planning MRP II
Time driven Rough-Cut Capacity Planning
Heuristic for Time driven Rough-Cut Capacity Planning
Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/3
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Overview
Material Requirement Planning(MRP)
MRP Procedure
Issues with MRPManufacturing Resource Planning MRP II
Time driven Rough-Cut Capacity Planning
Heuristic for Time driven Rough-Cut Capacity Planning
Neighborhood for Time driven Rough-Cut CapacityPlanning
Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/3
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Material Requirement Planning(MRP)
Production Planning Solution Techniques Part 1 MRP, MRP-II p.3/3
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Material Requirement Planning(MRP)
Originally system was based on reorder point.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.3/3
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Material Requirement Planning(MRP)
Originally system was based on reorder point.
Reorder point is suited for independent demand.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.3/3
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Material Requirement Planning(MRP)
Originally system was based on reorder point.
Reorder point is suited for independent demand.
But not for dependent demand.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.3/3
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Material Requirement Planning(MRP)
Originally system was based on reorder point.
Reorder point is suited for independent demand.
But not for dependent demand.MRP works backwards from independent demand toderive a schedule.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.3/3
M i l R i Pl i (MRP)
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Material Requirement Planning(MRP)
Originally system was based on reorder point.
Reorder point is suited for independent demand.
But not for dependent demand.MRP works backwards from independent demand toderive a schedule.
MRP is called a push system since it pushes items inthe production chain.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.3/3
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Overview of MRP
Production Planning Solution Techniques Part 1 MRP, MRP-II p.4/3
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Overview of MRP
External orders is called Purchase orders.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.4/3
O i f MRP
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Overview of MRP
External orders is called Purchase orders.
Internal orders is called Jobs.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.4/3
O i f MRP
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Overview of MRP
External orders is called Purchase orders.
Internal orders is called Jobs.
Time is divided into buckets.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.4/3
O i f MRP
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Overview of MRP
External orders is called Purchase orders.
Internal orders is called Jobs.
Time is divided into buckets.The bill of material(BOM) describes relationship
Production Planning Solution Techniques Part 1 MRP, MRP-II p.4/3
O i f MRP
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Overview of MRP
External orders is called Purchase orders.
Internal orders is called Jobs.
Time is divided into buckets.The bill of material(BOM) describes relationship
The routing describes the work processes.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.4/3
S h ti f MRP
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Schematic of MRP
Production Planning Solution Techniques Part 1 MRP, MRP-II p.5/3
MRP Inputs and Outputs
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MRP Inputs and Outputs
Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/3
MRP Inputs and Outputs
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MRP Inputs and Outputs
Master Production Schedule:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/3
MRP Inputs and Outputs
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MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and duedates.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/3
MRP Inputs and Outputs
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MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and duedates.
Erp Database:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/3
MRP Inputs and Outputs
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MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and duedates.
Erp Database: BOM, Routing, lot-sizing rule(LSR),
lead time(PLT) and On-Hand Inventory.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/3
MRP Inputs and Outputs
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MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and duedates.
Erp Database: BOM, Routing, lot-sizing rule(LSR),
lead time(PLT) and On-Hand Inventory.
Scheduled Receipts: Out standing orders and Jobs.Work in process.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/3
MRP Inputs and Outputs
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MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and duedates.
Erp Database: BOM, Routing, lot-sizing rule(LSR),
lead time(PLT) and On-Hand Inventory.
Scheduled Receipts: Out standing orders and Jobs.Work in process.
MRP outputs: Planned order release, Change noticesand Exception reports.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/3
MRP Procedure
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MRP Procedure
Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/3
MRP Procedure
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MRP Procedure
Tis the number of time periods.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/3
MRP Procedure
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MRP Procedure
Tis the number of time periods.
Dt gross requirements (demand) for periodt
Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/3
MRP Procedure
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MRP Procedure
Tis the number of time periods.
Dt gross requirements (demand) for periodt
Stquantity currently scheduled to complete in period
t
Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/3
MRP Procedure
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MRP Procedure
Tis the number of time periods.
Dt gross requirements (demand) for periodt
Stquantity currently scheduled to complete in period t
It Projected on-hand inventory in period t
Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/3
MRP Procedure
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MRP Procedure
Tis the number of time periods.
Dt gross requirements (demand) for periodt
Stquantity currently scheduled to complete in period t
It Projected on-hand inventory in period t
Nt net requirements for periodt
Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/3
MRP Procedure: Netting
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g
Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/3
MRP Procedure: Netting
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g
1. ComputeIt=It1 Dt t
Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/3
MRP Procedure: Netting
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g
1. ComputeIt=It1 Dt t
2. Findtm={min1tT :It
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g
1. ComputeIt=It1 Dt t
2. Findtm={min1tT :It tm
. Generate Change Notice andadjust SR andSt.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/3
MRP Procedure: Netting
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g
1. ComputeIt=It1 Dt t
2. Findtm={min1tT :It tm
. Generate Change Notice andadjust SR andSt. Continue untilIm>0or no moreSRs.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/3
MRP Procedure: Netting
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1. ComputeIt=It1 Dt t
2. Findtm={min1tT :It tm
. Generate Change Notice andadjust SR andSt. Continue untilIm>0or no moreSRs.
4. Adjust projected on-hand inventory toIt=It+ St
Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/3
MRP Procedure: Netting
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1. ComputeIt=It1 Dt t
2. Findtm={min1tT :It tm
. Generate Change Notice andadjust SR andSt. Continue untilIm>0or no moreSRs.
4. Adjust projected on-hand inventory toIt=It+ St
5. Findt ={t|It
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Netting example
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Gross requierments 15 20 50 50
Scheduled receipts 10 10
Adjusted SRs
Projected on-hand 20
Net requirements
Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/3
Netting example
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Gross requierments 15 20 50 50
Scheduled receipts 10 10
Adjusted SRs
Projected on-hand 20 5
Net requirements
I1=D1 I0= 5
Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/3
Netting example
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Gross requierments 15 20 50 50
Scheduled receipts 10 10
Adjusted SRs 20
Projected on-hand 20 5
Net requirements
I1=D1 I0= 5I1>0AdjustS1. S2=S2+ S1 = 20
Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/3
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Netting example
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Gross requierments 15 20 50 50
Scheduled receipts 10 10
Adjusted SRs 20
Projected on-hand 20 5 5 -45 -
Net requirements 45
I1=D1 I0= 5I1>0AdjustS1. S2=S2+ S1 = 20
I2=I1 D2= 5 20
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Gross requierments 15 20 50 50
Scheduled receipts 10 10
Adjusted SRs 20
Projected on-hand 20 5 5 -45 -
Net requirements 45 50
I1=D1 I0= 5I1>0AdjustS1. S2=S2+ S1 = 20
I2=I1 D2= 5 20
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
MRP Procedure continued
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Lot sizing:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
MRP Procedure continued
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Lot sizing:Wagner Whitin
Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
MRP Procedure continued
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Lot sizing:Wagner Whitin
lot for lot
Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
MRP Procedure continued
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Lot sizing:Wagner Whitin
lot for lot
fixed order period
Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
MRP Procedure continued
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Lot sizing:Wagner Whitin
lot for lot
fixed order periodFixed order Quantity and EOQ.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
MRP Procedure continued
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Lot sizing:Wagner Whitin
lot for lot
fixed order periodFixed order Quantity and EOQ.
Part-Period Balancing. Balancing inventory cost and
Setup Cost.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
MRP Procedure continued
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Lot sizing:Wagner Whitin
lot for lot
fixed order periodFixed order Quantity and EOQ.
Part-Period Balancing. Balancing inventory cost and
Setup Cost.Time fasing. All lead times are considered for items, notfor status on floor
Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
MRP Procedure continued
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Lot sizing:Wagner Whitin
lot for lot
fixed order periodFixed order Quantity and EOQ.
Part-Period Balancing. Balancing inventory cost and
Setup Cost.Time fasing. All lead times are considered for items, notfor status on floor
Bom Explosion. Netting and lot sizing is done for eachsub item.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/3
Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10
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Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10
Quantity 1 setup cost Part-Periods Inventory cost
10 30 0 0
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10
Quantity 1 setup cost Part-Periods Inventory cost
10 30 0 0
25
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
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Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10Quantity 1 setup cost Part-Periods Inventory cost
10 30 0 0
25 30 15
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10Quantity 1 setup cost Part-Periods Inventory cost
10 30 0 0
25 30 15 15
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10Quantity 1 setup cost Part-Periods Inventory cost
10 30 0 0
25 30 15 15
35
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10Quantity 1 setup cost Part-Periods Inventory cost
10 30 0 0
25 30 15 15
35 30
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10Quantity 1 setup cost Part-Periods Inventory cost
10 30 0 0
25 30 15 15
35 30 35
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
Part Period Balancing
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Number of itemsnNumber of Periodspthe item is carried in the inventory.
Part Period cost isn p
Example:
Period 1 2 3
Net Requirements 10 15 10Quantity 1 setup cost Part-Periods Inventory cost
10 30 0 0
25 30 15 15
35 30 35 35
Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/3
Issues with MRP
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.12/3
Issues with MRP
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Assume constant lead times. To take care of variationSafety Stock and Safety Lead time is used.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.12/3
Issues with MRP
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Assume constant lead times. To take care of variationSafety Stock and Safety Lead time is used.
Capacity Infeasibility, there is no capacity check.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.12/3
Issues with MRP
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Assume constant lead times. To take care of variationSafety Stock and Safety Lead time is used.
Capacity Infeasibility, there is no capacity check.
Long Planned Lead time due to variation in deliverytime.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.12/3
Issues with MRP
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Assume constant lead times. To take care of variationSafety Stock and Safety Lead time is used.
Capacity Infeasibility, there is no capacity check.
Long Planned Lead time due to variation in deliverytime.
System Nervousness. Plans that are feasible can
become infeasible.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.12/3
Questians or comments to MRP
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Are there any questians or comments ?
Production Planning Solution Techniques Part 1 MRP, MRP-II p.13/3
Manufacturing Resource Planning
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.14/3
Manufacturing Resource Planning
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Address deficiencies in MRP
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Manufacturing Resource Planning
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Address deficiencies in MRPBrings in new functionalities including:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.14/3
Manufacturing Resource Planning
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Address deficiencies in MRPBrings in new functionalities including:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.14/3
Long-Range Planning
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.15/3
Long-Range Planning
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Forecasting seeks to predict demands of the future.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.15/3
Long-Range Planning
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Forecasting seeks to predict demands of the future.Resource Planning. Determines long time capacityneed. Is used to decide is knew facilities must be build
or old facilities must be expanded.
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Long-Range Planning
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Forecasting seeks to predict demands of the future.Resource Planning. Determines long time capacityneed. Is used to decide is knew facilities must be build
or old facilities must be expanded.Aggregate Planning. Determines how inventory is build.Do we use overtime or do we carry inventory over a
long period.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.15/3
Intermidiate Planning
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.16/3
Intermidiate Planning
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Demand management Converts long-term forecast intoactual customer orders and forecast of anticipatedorders.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.16/3
Intermidiate Planning
D d C l f i
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Demand management Converts long-term forecast intoactual customer orders and forecast of anticipatedorders.
Available to promise Secures that an order can be meetat a given due date. This can be done by using forwardloading.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.16/3
Intermidiate Planning
D d t C t l t f t i t
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Demand management Converts long-term forecast intoactual customer orders and forecast of anticipatedorders.
Available to promise Secures that an order can be meetat a given due date. This can be done by using forwardloading.
Master Production Schedule Generates an anticipatedproduction schedule.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.16/3
Intermidiate Planning
D d t C t l t f t i t
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Demand management Converts long-term forecast intoactual customer orders and forecast of anticipatedorders.
Available to promise Secures that an order can be meetat a given due date. This can be done by using forwardloading.
Master Production Schedule Generates an anticipatedproduction schedule.
Rough-cut Planning Provides a schedule where thecapacity on critical resources is meet.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.16/3
Intermidiate Planning
D d t C t l t f t i t
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Demand management Converts long-term forecast intoactual customer orders and forecast of anticipatedorders.
Available to promise Secures that an order can be meetat a given due date. This can be done by using forwardloading.
Master Production Schedule Generates an anticipatedproduction schedule.
Rough-cut Planning Provides a schedule where thecapacity on critical resources is meet.
Capacity Requirements Planning Does not preformactual capacity check. CRP assumes infinite capacityon resources. Basically it just calculates finish dates
based on fixed lead times.Production Planning Solution Techniques Part 1 MRP, MRP-II p.16/3
Short-term control
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.17/3
Short-term control
Job release Converts jobs to scheduled receipts
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Job release Converts jobs to scheduled receipts.Resolves conflicts if several high-level items uses samelow-level item.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.17/3
Short-term control
Job release Converts jobs to scheduled receipts
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Job release Converts jobs to scheduled receipts.Resolves conflicts if several high-level items uses samelow-level item.
Job dispatching Maintains queue in front of eachworkstation and try to maintain due date.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.17/3
Short-term control
Job release Converts jobs to scheduled receipts
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Job release Converts jobs to scheduled receipts.Resolves conflicts if several high-level items uses samelow-level item.
Job dispatching Maintains queue in front of eachworkstation and try to maintain due date.
Shortest process time Chooses the shortest job
Production Planning Solution Techniques Part 1 MRP, MRP-II p.17/3
Short-term control
Job release Converts jobs to scheduled receiptsfl f
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Job release Converts jobs to scheduled receipts.Resolves conflicts if several high-level items uses samelow-level item.
Job dispatching Maintains queue in front of eachworkstation and try to maintain due date.
Shortest process time Chooses the shortest job
Earliest due date dispatches job with nearest duedate
Production Planning Solution Techniques Part 1 MRP, MRP-II p.17/3
Short-term control
Job release Converts jobs to scheduled receiptsR l fli if l hi h l l i
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Job release Converts jobs to scheduled receipts.Resolves conflicts if several high-level items uses samelow-level item.
Job dispatching Maintains queue in front of eachworkstation and try to maintain due date.
Shortest process time Chooses the shortest job
Earliest due date dispatches job with nearest duedate
Least slack Choose job where, the due date minusremaining process time is lowest.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.17/3
Short-term control
Job release Converts jobs to scheduled receiptsR l fli t if l hi h l l it
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Job release Converts jobs to scheduled receipts.Resolves conflicts if several high-level items uses samelow-level item.
Job dispatching Maintains queue in front of eachworkstation and try to maintain due date.
Shortest process time Chooses the shortest job
Earliest due date dispatches job with nearest duedate
Least slack Choose job where, the due date minusremaining process time is lowest.
Least slack per remaining operation Divide slackwith number of operation remaining on routing.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.17/3
Questians or comments to MRP II
Are there any questians or comments ?
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Are there any questians or comments ?
Production Planning Solution Techniques Part 1 MRP, MRP-II p.18/3
Rough-Cut Capacity Planning(RCCP)
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/3
Rough-Cut Capacity Planning(RCCP)
Considers aggregated work
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Considers aggregated work
Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/3
Rough-Cut Capacity Planning(RCCP)
Considers aggregated work
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Considers aggregated workAllocates work in time buckets
Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/3
Rough-Cut Capacity Planning(RCCP)
Considers aggregated work
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Co s de s agg egated oAllocates work in time buckets
Determines resources in order to reach due dates
Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/3
Rough-Cut Capacity Planning(RCCP)
Considers aggregated workAll k i i b k
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gg gAllocates work in time buckets
Determines resources in order to reach due dates
Both regular and nonregular (outsourcing over timeetc.) is considered
Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/3
Rough-Cut Capacity Planning(RCCP)
Considers aggregated workAll t k i ti b k t
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gg gAllocates work in time buckets
Determines resources in order to reach due dates
Both regular and nonregular (outsourcing over timeetc.) is considered
Time driven RCCP is when project dates must be meet.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/3
Rough-Cut Capacity Planning(RCCP)
Considers aggregated workAll t k i ti b k t
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gg gAllocates work in time buckets
Determines resources in order to reach due dates
Both regular and nonregular (outsourcing over timeetc.) is considered
Time driven RCCP is when project dates must be meet.
In resource-driven RCCP only regular capacity can beused
Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/3
Rough-Cut Capacity Planning(RCCP)
Considers aggregated workAllocates work in time buckets
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gg gAllocates work in time buckets
Determines resources in order to reach due dates
Both regular and nonregular (outsourcing over timeetc.) is considered
Time driven RCCP is when project dates must be meet.
In resource-driven RCCP only regular capacity can beused
This session will consider the time driven
Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/3
Some notation
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobsJ1, J2, , Jn
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobsJ1, J2, , Jnk resources R1 R
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kresourcesR1, , Rn
Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobsJ1
, J2
, , Jnk resources R1 R
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kresourcesR1, , Rn
Ttime buckets
Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobsJ1
, J2
, , Jnk resources R1 R
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kresourcesR1, , Rn
Ttime buckets
Qkt is the regular capacity for resourcekin periodt
Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobsJ1
, J2
, , Jnk resources R1 Rn
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kresourcesR1, , Rn
Ttime buckets
Qkt is the regular capacity for resourcekin periodt
JobJj requiresqjk units of resourcek
Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobsJ1
, J2
, , Jnk resources R1, , Rn
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kresourcesR1, , Rn
Ttime buckets
Qkt is the regular capacity for resourcekin periodt
JobJj requiresqjk units of resourcek
xkt
denotes the fraction of jobJj
performed in periodt
Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobsJ1
, J2
, , Jnk resources R1, , Rn
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kresourcesR1, , Rn
Ttime buckets
Qkt is the regular capacity for resourcekin periodt
JobJj requiresqjk units of resourcek
xkt
denotes the fraction of jobJj
performed in periodt
Jj must be performed in time window[rj , dj ]
Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobsJ1
, J2
, , JnkresourcesR1, , Rn
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1, , n
Ttime buckets
Qkt is the regular capacity for resourcekin periodt
JobJj requiresqjk units of resourcek
xkt
denotes the fraction of jobJj performed in periodt
Jj must be performed in time window[rj , dj ]
pj is the minimum number of periods jobJj can use.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Some notation
njobs
J1
, J2
, , JnkresourcesR1, , Rn
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1, , n
Ttime buckets
Qkt is the regular capacity for resourcekin periodt
JobJj requiresqjk units of resourcek
xkt
denotes the fraction of jobJj performed in periodt
Jj must be performed in time window[rj , dj ]
pj is the minimum number of periods jobJj can use.
1pj
is the maximum fraction of a job that can be
completed in a week.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/3
Precedence constraints
If jobJimust finish beforeJj there is a precedence relation.For a periodthis can be modelled as:
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.21/3
Precedence constraints
If jobJi
must finish beforeJj
there is a precedence relation.For a periodthis can be modelled as:
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xj >0
1t=dt
xit= 1
Production Planning Solution Techniques Part 1 MRP, MRP-II p.21/3
Precedence constraints
If jobJi
must finish beforeJj
there is a precedence relation.For a periodthis can be modelled as:
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xj >0
1t=dt
xit= 1
There will bedj rj constraints per precedence relation.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.21/3
Precedence constraints
If jobJimust finish beforeJ
jthere is a precedence relation.
For a periodthis can be modelled as:
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xj >0
1t=dt
xit= 1
There will bedj rj constraints per precedence relation.
Time windows can in some cases be tightened, due to
precedence constraints.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.21/3
Nonregular capacity
LetQkt
denote the nonregular capacity for resourcekinperiodt. Then for each resource and time period:
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.22/3
Nonregular capacity
LetQkt
denote the nonregular capacity for resourcekinperiodt. Then for each resource and time period:
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Ukt = max{0,
n
j=1 qjkxjt Qkt
Production Planning Solution Techniques Part 1 MRP, MRP-II p.22/3
Nonregular capacity
LetQkt
denote the nonregular capacity for resourcekinperiodt. Then for each resource and time period:
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Ukt = max{0,
n
j=1 qjkxjt Qkt
The cost of using nonregular capacity for resource kin time
period t is ckt
Production Planning Solution Techniques Part 1 MRP, MRP-II p.22/3
Nonregular capacity
LetQkt
denote the nonregular capacity for resourcekinperiodt. Then for each resource and time period:
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Ukt = max{0,
n
j=1 qjkxjt Qkt
The cost of using nonregular capacity for resource kin time
period t is ckt It is assumed that there is no limit on the
nonregular resources.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.22/3
Mathematical Model
min T
t=1
Kk=1 cktUkt
bj t t
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subject to
djt=rj xjt = 1 1j nxjt
1
pj1j n, 1tT
nj=1 qjkxjt Ukt 0 1j n, 1tT
xjt, Ukt 0 1j n, 1tT
Production Planning Solution Techniques Part 1 MRP, MRP-II p.23/3
Controlling feasibility
Allowed To Work window for jobJj is defined as[Sj , Cj ].
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/3
Controlling feasibility
Allowed To Work window for jobJj is defined as[Sj , Cj ].
JobJj cannot start beforeSj or afterCj
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/3
Controlling feasibility
Allowed To Work window for jobJj is defined as[Sj , Cj ].
JobJj cannot start beforeSj or afterCj
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A ATW for jobJj is feasible if:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/3
Controlling feasibility
Allowed To Work window for jobJj is defined as[Sj , Cj ].
JobJj cannot start beforeSj or afterCj
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A ATW for jobJj is feasible if:
1. Sj rj andCj dj
2. Cj Sj pj1
Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/3
Controlling feasibility
Allowed To Work window for jobJj is defined as[Sj , Cj ].
JobJj cannot start beforeSj or afterCj
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A ATW for jobJj is feasible if:
1. Sj rj andCj dj
2. Cj Sj pj1
A setSof ATW windows is feasible if:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/3
Controlling feasibility
Allowed To Work window for jobJj is defined as[Sj , Cj ].
JobJj cannot start beforeSj or afterCj
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A ATW for jobJj is feasible if:
1. Sj rj andCj dj
2. Cj Sj pj1
A setSof ATW windows is feasible if:
1. Every ATW window is feasible
2. Sj > Cj ifJiJj
Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/3
Mathematical Model ATW windows
sjt=
1 Sj tCj0 otherwise
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0 otherwise
(PS)min T
t=1
Kk=1 cktUkt
subjectto djt=rj xjt = 1 1j n
xjt sjpj
1j n, 1tT
nj=1 qjkxjt Ukt 0 1j n, 1tTxjt, Ukt 0 1j n, 1tT
Production Planning Solution Techniques Part 1 MRP, MRP-II p.25/3
Constructive heuristics(HBASIC)
Construct a feasible setSof ATW windows.
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/3
Constructive heuristics(HBASIC)
Construct a feasible setSof ATW windows.
Solve problemPS
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/3
Constructive heuristics(HBASIC)
Construct a feasible setSof ATW windows.
Solve problemPS
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To obtain a feasible set of ATW windows construct them as
follows:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/3
Constructive heuristics(HBASIC)
Construct a feasible setSof ATW windows.
Solve problemPS
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To obtain a feasible set of ATW windows construct them as
follows:SetSj =rj
Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/3
Constructive heuristics(HBASIC)
Construct a feasible setSof ATW windows.
Solve problemPS
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To obtain a feasible set of ATW windows construct them as
follows:SetSj =rj
SetCj = min{dj , mink|jiJkrk1}
Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/3
Constructive heuristics(HBASIC)
Construct a feasible setSof ATW windows.
Solve problemPS
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To obtain a feasible set of ATW windows construct them as
follows:SetSj =rj
SetCj = min{dj , mink|jiJkrk1}
Have I forgotten an important assumption ?
Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
{Ji1, Ji2, , Jik}is a ordered set if:
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
{Ji1, Ji2, , Jik}is a ordered set if:
Ji Ji Ji Ji Ji Ji
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Ji1 Ji2, Ji3 Ji4, , Jik1 Jik
Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
{Ji1, Ji2, , Jik}is a ordered set if:
Ji1 Ji2, Ji3 Ji4, , Jik 1 Jik
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Ji1 Ji2, Ji3 Ji4, , Jik1 Jik
A critical path is a path where:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
{Ji1, Ji2, , Jik}is a ordered set if:
Ji1 Ji2, Ji3 Ji4, , Jik 1 Jik
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Ji1 Ji2, Ji3 Ji4, , Jik1 Jik
A critical path is a path where:
Lj1 =Lj2== min1n Lj
Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
{Ji1, Ji2, , Jik}is a ordered set if:
Ji1 Ji2, Ji3 Ji4, , Jik 1 Jik
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i1 i2, i3 i4, , ik1 ik
A critical path is a path where:
Lj1 =Lj2== min1n Lj
Sji =Sji1+pi1 for2iR
Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
{Ji1, Ji2, , Jik}is a ordered set if:
Ji1 Ji2, Ji3 Ji4, , Jik1 Jik
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i1 i2, i3 i4, , ik1 ik
A critical path is a path where:
Lj1 =Lj2== min1n Lj
Sji =Sji1+pi1 for2iRCji =Cji+1pji+1 for1iR
Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
{Ji1, Ji2, , Jik}is a ordered set if:
Ji1 Ji2, Ji3 Ji4, , Jik1 Jik
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1 2,
3 4, ,
k 1 k
A critical path is a path where:
Lj1 =Lj2== min1n Lj
Sji =Sji1+pi1 for2iRCji =Cji+1pji+1 for1iR
A critical path is maximal if for allJl:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
Constructive heuristics (HCP M)
Define the slack of jobJj asLj =Cj(Sj+pj)
{Ji1, Ji2, , Jik}is a ordered set if:
Ji1 Ji2, Ji3 Ji4, , Jik1 Jik
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1 2 3 4 k 1 k
A critical path is a path where:
Lj1 =Lj2== min1n Lj
Sji =Sji1+pi1 for2iRCji =Cji+1pji+1 for1iR
A critical path is maximal if for allJl:{Ji1, Ji2, , Jik , Jil}is critical
{Jil, Ji1, Ji2 , , Jik}is critical
Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/3
(HCP M) continued
InitializeSj =rj andCj =dj for allJj
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/3
(HCP M) continued
InitializeSj =rj andCj =dj for allJj
Compute the slack for all jobs
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/3
(HCP M) continued
InitializeSj =rj andCj =dj for allJj
Compute the slack for all jobs
Find a maximal critical path{Ji1 , Ji2, , Jik}
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/3
(HCP M) continued
InitializeSj =rj andCj =dj for allJj
Compute the slack for all jobs
Find a maximal critical path{Ji1 , Ji2, , Jik}
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Compute the total slack L=CjR(Sj1+
Ri=1pji
Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/3
(HCP M) continued
InitializeSj =rj andCj =dj for allJj
Compute the slack for all jobs
Find a maximal critical path{Ji1 , Ji2, , Jik}
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Compute the total slack L=CjR(Sj1+
Ri=1pji
SetSji =Sj1+
i1k=1pik+ |L
i1k=1pik/
Rk=1pik |
Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/3
(HCP M) continued
InitializeSj =rj andCj =dj for allJj
Compute the slack for all jobs
Find a maximal critical path{Ji1 , Ji2, , Jik}
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Compute the total slack L=CjR(Sj1+
Ri=1pji
SetSji =Sj1+
i1k=1pik+ |L
i1k=1pik/
Rk=1pik |
Change toCik =Sik+11
Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/3
HCP Mexample
1 2 3 4
S 0 5 15 20
C 10 15 25 30
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p 5 5 10 5
Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/3
HCP Mexample
1 2 3 4
S 0 5 15 20
C 10 15 25 30
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p 5 5 10 5L=C4(0 + 20) = 5
Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/3
HCP Mexample
1 2 3 4
S 0 5 15 20
C 10 15 25 30
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p 5 5 10 5L=C4(0 + 20) = 5
Recall Sji =Sji+i1k=1pjk+ |Li1k=1 /Rk=1pjk|
Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/3
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HCP Mexample
1 2 3 4
S 0 5 15 20
C 10 15 25 30
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p 5 5 10 5L=C4(0 + 20) = 5
Recall Sji =Sji+i1k=1pjk+ |Li1k=1 /Rk=1pjk|S2= 0 + 5 +
5525
= 6
S3= 0 + 10 + 10525
= 12
Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/3
HCP Mexample
1 2 3 4
S 0 5 15 20
C 10 15 25 30
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p 5 5 10 5L=C4(0 + 20) = 5
Recall Sji =Sji+i1k=1pjk+ |Li1k=1 /Rk=1pjk|S2= 0 + 5 +
5525
= 6
S3= 0 + 10 + 10525
= 12
S4= 0 + 20 + 20525
= 24
Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/3
HCP Mexample
1 2 3 4
S 0 5 15 20
C 10 15 25 30
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p 5 5 10 5L=C4(0 + 20) = 5
Recall Sji =Sji+i1k=1pjk+ |Li1k=1 /Rk=1pjk|S2= 0 + 5 +
5525
= 6
S3= 0 + 10 + 10525
= 12
S4= 0 + 20 + 20525
= 24
C1=S21 = 5,C2= 11,C3= 23
Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/3
Neighbourhoods
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.30/3
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Neighbourhoods
For jobJj increaseSj or decreaseCj
DecreaseSj impliesSj > rj,Ck =Sj1for anypreceding jobJk andCk Sk pk
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.30/3
Neighbourhoods
For jobJj increaseSj or decreaseCj
DecreaseSj impliesSj > rj,Ck =Sj1for anypreceding jobJk andCk Sk pk
Neighbourhood can be ordered after the greedy choice
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e g bou ood ca be o de ed a te t e g eedy c o ceor the steepest edge rule.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.30/3
Exercises
Ex 1 Suggest some improvements for 2-3 of the
modules in the MRP II model. You should describewhat additional data the system and need and whatvalue it would add for the users.
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Production Planning Solution Techniques Part 1 MRP, MRP-II p.31/3
Exercises
Ex 1 Suggest some improvements for 2-3 of the
modules in the MRP II model. You should describewhat additional data the system and need and whatvalue it would add for the users.
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Ex 2 For RCCP we have focused on the time drivencase in this exercise we consider the resource drivencase:
Production Planning Solution Techniques Part 1 MRP, MRP-II p.31/3
Exercises
Ex 1 Suggest some improvements for 2-3 of the
modules in the MRP II model. You should describewhat additional data the system and need and whatvalue it would add for the users.
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Ex 2 For RCCP we have focused on the time drivencase in this exercise we consider the resource drivencase:
Ex 2.1 Give a mathematical model for the Resourcedriven RCCP without precedence constraints.
Production Planning Solution Techniques Part 1 MRP, MRP-II p.31/3
Exercises
Ex 1 Suggest some improvements for 2-3 of the
modules in the MRP II model. You should describewhat additional data the system and need and whatvalue it would add for the users.
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Ex 2 For RCCP we have focused on the time drivencase in this exercise we consider the resource drivencase:
Ex 2.1 Give a mathematical model for the Resourcedriven RCCP without precedence constraints.
Ex 2.2 If we useHBASICto solve the resource drivenRCCP will it result in a feasible solution ? Justify you
answer
Production Planning Solution Techniques Part 1 MRP, MRP-II p.31/3
Exercises
Ex 1 Suggest some improvements for 2-3 of the
modules in the MRP II model. You should describewhat additional data the system and need and whatvalue it would add for the users.
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Ex 2 For RCCP we have focused on the time drivencase in this exercise we consider the resource drivencase:
Ex 2.1 Give a mathematical model for the Resourcedriven RCCP without precedence constraints.
Ex 2.2 If we useHBASICto solve the resource drivenRCCP will it result in a feasible solution ? Justify you
answer
Ex 2.3 Describe a heuristic for the resource drivenRCCP. The heuristic should include a constructive
heuristic and a improvement heuristic.Production Planning Solution Techniques Part 1 MRP, MRP-II p.31/3
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