Production Planning Solution Techniques Part 1 MRP, MRP-II
Mads Kehlet Jepsen

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.1/31

Overview

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.2/31

Overview
Material Requirement Planning(MRP)

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.2/31

Overview
Material Requirement Planning(MRP) MRP Procedure

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.2/31

Overview
Material Requirement Planning(MRP) MRP Procedure Issues with MRP

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.2/31

Overview
Material Requirement Planning(MRP) MRP Procedure Issues with MRP Manufacturing Resource Planning MRP II

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.2/31

Overview
Material Requirement Planning(MRP) MRP Procedure Issues with MRP Manufacturing Resource Planning MRP II Time driven Rough-Cut Capacity Planning

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.2/31

Overview
Material Requirement Planning(MRP) MRP Procedure Issues with MRP Manufacturing 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.2/31

Overview
Material Requirement Planning(MRP) MRP Procedure Issues with MRP Manufacturing Resource Planning MRP II Time driven Rough-Cut Capacity Planning Heuristic for Time driven Rough-Cut Capacity Planning Neighborhood for Time driven Rough-Cut Capacity Planning

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.2/31

Material Requirement Planning(MRP)

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.3/31

Material Requirement Planning(MRP)
Originally system was based on reorder point.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.3/31

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.3/31

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.3/31

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 to derive a schedule.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.3/31

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 to derive a schedule. MRP is called a push system since it pushes items in the production chain.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.3/31

Overview of MRP

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.4/31

Overview of MRP
External orders is called Purchase orders.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.4/31

Overview of MRP
External orders is called Purchase orders. Internal orders is called Jobs.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.4/31

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.4/31

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.4/31

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.4/31

Schematic of MRP

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.5/31

MRP Inputs and Outputs

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.6/31

MRP Inputs and Outputs
Master Production Schedule:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.6/31

MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and due dates.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.6/31

MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and due dates. Erp Database:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.6/31

MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and due dates. 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.6/31

MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and due dates. 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.6/31

MRP Inputs and Outputs
Master Production Schedule: Item, Quantity and due dates. 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 notices and Exception reports.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.6/31

MRP Procedure

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.7/31

MRP Procedure
T is the number of time periods.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.7/31

MRP Procedure
T is the number of time periods. Dt gross requirements (demand) for period t

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.7/31

MRP Procedure
T is the number of time periods. Dt gross requirements (demand) for period t St quantity currently scheduled to complete in period t

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.7/31

MRP Procedure
T is the number of time periods. Dt gross requirements (demand) for period t St quantity 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.7/31

MRP Procedure
T is the number of time periods. Dt gross requirements (demand) for period t St quantity currently scheduled to complete in period t It Projected on-hand inventory in period t Nt net requirements for period t

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.7/31

MRP Procedure: Netting

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.8/31

MRP Procedure: Netting
1. Compute It = It−1 − Dt
∀t

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.8/31

MRP Procedure: Netting
1. Compute It = It−1 − Dt
∀t

2. Find tm = {min1≤t≤T : It < 0}

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.8/31

MRP Procedure: Netting
1. Compute It = It−1 − Dt
∀t

2. Find tm = {min1≤t≤T : It < 0} 3. If the first SR has t > tm . Generate Change Notice and adjust SR and St .

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.8/31

MRP Procedure: Netting
1. Compute It = It−1 − Dt
∀t

2. Find tm = {min1≤t≤T : It < 0} 3. If the first SR has t > tm . Generate Change Notice and adjust SR and St . Continue until Im > 0 or no more SRs.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.8/31

MRP Procedure: Netting
1. Compute It = It−1 − Dt
∀t

2. Find tm = {min1≤t≤T : It < 0} 3. If the first SR has t > tm . Generate Change Notice and adjust SR and St . Continue until Im > 0 or no more SRs. 4. Adjust projected on-hand inventory to It = It + St

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.8/31

MRP Procedure: Netting
1. Compute It = It−1 − Dt
∀t

2. Find tm = {min1≤t≤T : It < 0} 3. If the first SR has t > tm . Generate Change Notice and adjust SR and St . Continue until Im > 0 or no more SRs. 4. Adjust projected on-hand inventory to It = It + St 5. Find t∗ = {t|It < 0}

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.8/31

MRP Procedure: Netting
1. Compute It = It−1 − Dt
∀t

2. Find tm = {min1≤t≤T : It < 0} 3. If the first SR has t > tm . Generate Change Notice and adjust SR and St . Continue until Im > 0 or no more SRs. 4. Adjust projected on-hand inventory to It = It + St 5. Find t∗ = {t|It < 0} Net requirement follows as:   0 t < t∗  Nt = −It t = t∗   D t > t∗ t

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.8/31

Netting example
Gross requierments 15 20 50 Scheduled receipts 10 10 Adjusted SRs Projected on-hand 20 Net requirements 50

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.9/31

Netting example
Gross requierments 15 20 50 Scheduled receipts 10 10 Adjusted SRs Projected on-hand 20 5 Net requirements
I1 = D1 − I0 = 5

50

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.9/31

Netting example
Gross requierments 15 20 50 Scheduled receipts 10 10 Adjusted SRs 20 Projected on-hand 20 5 Net requirements
I1 = D1 − I0 = 5 I1 > 0 Adjust S1 . S2 = S2 + S1 = 20

50

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.9/31

Netting example
Gross requierments 15 20 50 Scheduled receipts 10 10 Adjusted SRs 20 Projected on-hand 20 5 5 Net requirements
I1 = D1 − I0 = 5 I1 > 0 Adjust S1 . S2 = S2 + S1 = 20 I2 = I1 − D2 = 5 − 20 < 0 I2 = I2 + S2 = 5 − 20 + 20 = 5

50

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.9/31

Netting example
Gross requierments 15 20 50 50 Scheduled receipts 10 10 Adjusted SRs 20 Projected on-hand 20 5 5 -45 Net requirements
I1 = D1 − I0 = 5 I1 > 0 Adjust S1 . S2 = S2 + S1 = 20 I2 = I1 − D2 = 5 − 20 < 0 I2 = I2 + S2 = 5 − 20 + 20 = 5 I3 = I2 − D3 = −45

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.9/31

Netting example
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 = 5 I1 > 0 Adjust S1 . S2 = S2 + S1 = 20 I2 = I1 − D2 = 5 − 20 < 0 I2 = I2 + S2 = 5 − 20 + 20 = 5 I3 = I2 − D3 = −45 N3 = −I3 = 45

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.9/31

Netting example
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 = 5 I1 > 0 Adjust S1 . S2 = S2 + S1 = 20 I2 = I1 − D2 = 5 − 20 < 0 I2 = I2 + S2 = 5 − 20 + 20 = 5 I3 = I2 − D3 = −45 N3 = −I3 = 45 N4 = D4 = 50

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.9/31

MRP Procedure continued

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

MRP Procedure continued
Lot sizing:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

MRP Procedure continued
Lot sizing: Wagner Whitin

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

MRP Procedure continued
Lot sizing: Wagner Whitin lot for lot

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

MRP Procedure continued
Lot sizing: Wagner Whitin lot for lot fixed order period

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

MRP Procedure continued
Lot sizing: Wagner Whitin lot for lot fixed order period Fixed order Quantity and EOQ.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

MRP Procedure continued
Lot sizing: Wagner Whitin lot for lot fixed order period Fixed order Quantity and EOQ. Part-Period Balancing. Balancing inventory cost and Setup Cost.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

MRP Procedure continued
Lot sizing: Wagner Whitin lot for lot fixed order period Fixed order Quantity and EOQ. Part-Period Balancing. Balancing inventory cost and Setup Cost. Time fasing. All lead times are considered for items, not for status on floor

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

MRP Procedure continued
Lot sizing: Wagner Whitin lot for lot fixed order period Fixed order Quantity and EOQ. Part-Period Balancing. Balancing inventory cost and Setup Cost. Time fasing. All lead times are considered for items, not for status on floor Bom Explosion. Netting and lot sizing is done for each sub item.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.10/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p Example: Period 1 2 3 Net Requirements 10 15 10

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ 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.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ 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.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p Example: Period 1 2 3 Net Requirements 10 15 10 Quantity 1 setup cost Part-Periods Inventory cost 10 30 0 0 25 30

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p Example: Period 1 2 3 Net Requirements 10 15 10 Quantity 1 setup cost Part-Periods Inventory cost 10 30 0 0 25 30 15

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p Example: Period 1 2 3 Net Requirements 10 15 10 Quantity 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.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p Example: Period 1 2 3 Net Requirements 10 15 10 Quantity 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.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p Example: Period 1 2 3 Net Requirements 10 15 10 Quantity 1 10 25 35 setup cost Part-Periods Inventory cost 30 0 0 30 15 15 30

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p Example: Period 1 2 3 Net Requirements 10 15 10 Quantity 1 10 25 35 setup cost 30 30 30 Part-Periods Inventory cost 0 0 15 15 35

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.11/31

Part Period Balancing
Number of items n Number of Periods p the item is carried in the inventory. Part Period cost is n ∗ p Example: Period 1 2 3 Net Requirements 10 15 10 Quantity 1 10 25 35 setup cost 30 30 30 Part-Periods 0 15 35 Inventory cost 0 15 35

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.11/31

Issues with MRP

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.12/31

Issues with MRP
Assume constant lead times. To take care of variation Safety Stock and Safety Lead time is used.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.12/31

Issues with MRP
Assume constant lead times. To take care of variation Safety Stock and Safety Lead time is used. Capacity Infeasibility, there is no capacity check.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.12/31

Issues with MRP
Assume constant lead times. To take care of variation Safety Stock and Safety Lead time is used. Capacity Infeasibility, there is no capacity check. Long Planned Lead time due to variation in delivery time.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.12/31

Issues with MRP
Assume constant lead times. To take care of variation Safety Stock and Safety Lead time is used. Capacity Infeasibility, there is no capacity check. Long Planned Lead time due to variation in delivery time. System Nervousness. Plans that are feasible can become infeasible.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.12/31

Questians or comments to MRP
Are there any questians or comments ?

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.13/31

Manufacturing Resource Planning

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.14/31

Manufacturing Resource Planning
Address deficiencies in MRP

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.14/31

Manufacturing Resource Planning
Address deficiencies in MRP Brings in new functionalities including:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.14/31

Manufacturing Resource Planning
Address deficiencies in MRP Brings in new functionalities including:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.14/31

Long-Range Planning

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.15/31

Long-Range Planning
Forecasting seeks to predict demands of the future.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.15/31

Long-Range Planning
Forecasting seeks to predict demands of the future. Resource Planning. Determines long time capacity need. Is used to decide is knew facilities must be build or old facilities must be expanded.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.15/31

Long-Range Planning
Forecasting seeks to predict demands of the future. Resource Planning. Determines long time capacity need. 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.15/31

Intermidiate Planning

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.16/31

Intermidiate Planning
Demand management Converts long-term forecast into actual customer orders and forecast of anticipated orders.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.16/31

Intermidiate Planning
Demand management Converts long-term forecast into actual customer orders and forecast of anticipated orders. Available to promise Secures that an order can be meet at a given due date. This can be done by using forward loading.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.16/31

Intermidiate Planning
Demand management Converts long-term forecast into actual customer orders and forecast of anticipated orders. Available to promise Secures that an order can be meet at a given due date. This can be done by using forward loading. Master Production Schedule Generates an anticipated production schedule.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.16/31

Intermidiate Planning
Demand management Converts long-term forecast into actual customer orders and forecast of anticipated orders. Available to promise Secures that an order can be meet at a given due date. This can be done by using forward loading. Master Production Schedule Generates an anticipated production schedule. Rough-cut Planning Provides a schedule where the capacity on critical resources is meet.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.16/31

Intermidiate Planning
Demand management Converts long-term forecast into actual customer orders and forecast of anticipated orders. Available to promise Secures that an order can be meet at a given due date. This can be done by using forward loading. Master Production Schedule Generates an anticipated production schedule. Rough-cut Planning Provides a schedule where the capacity on critical resources is meet. Capacity Requirements Planning Does not preform actual capacity check. CRP assumes infinite capacity on resources. Basically it just calculates finish dates based on fixed lead times.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.16/31

Short-term control

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.17/31

Short-term control
Job release Converts jobs to scheduled receipts. Resolves conflicts if several high-level items uses same low-level item.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.17/31

Short-term control
Job release Converts jobs to scheduled receipts. Resolves conflicts if several high-level items uses same low-level item. Job dispatching Maintains queue in front of each workstation and try to maintain due date.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.17/31

Short-term control
Job release Converts jobs to scheduled receipts. Resolves conflicts if several high-level items uses same low-level item. Job dispatching Maintains queue in front of each workstation and try to maintain due date. Shortest process time Chooses the shortest job

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.17/31

Short-term control
Job release Converts jobs to scheduled receipts. Resolves conflicts if several high-level items uses same low-level item. Job dispatching Maintains queue in front of each workstation and try to maintain due date. Shortest process time Chooses the shortest job Earliest due date dispatches job with nearest due date

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.17/31

Short-term control
Job release Converts jobs to scheduled receipts. Resolves conflicts if several high-level items uses same low-level item. Job dispatching Maintains queue in front of each workstation and try to maintain due date. Shortest process time Chooses the shortest job Earliest due date dispatches job with nearest due date Least slack Choose job where, the due date minus remaining process time is lowest.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.17/31

Short-term control
Job release Converts jobs to scheduled receipts. Resolves conflicts if several high-level items uses same low-level item. Job dispatching Maintains queue in front of each workstation and try to maintain due date. Shortest process time Chooses the shortest job Earliest due date dispatches job with nearest due date Least slack Choose job where, the due date minus remaining process time is lowest. Least slack per remaining operation Divide slack with number of operation remaining on routing.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.17/31

Questians or comments to MRP II
Are there any questians or comments ?

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.18/31

Rough-Cut Capacity Planning(RCCP)

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.19/31

Rough-Cut Capacity Planning(RCCP)
Considers aggregated work

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.19/31

Rough-Cut Capacity Planning(RCCP)
Considers aggregated work Allocates work in time buckets

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.19/31

Rough-Cut Capacity Planning(RCCP)
Considers aggregated work Allocates work in time buckets Determines resources in order to reach due dates

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.19/31

Rough-Cut Capacity Planning(RCCP)
Considers aggregated work Allocates work in time buckets Determines resources in order to reach due dates Both regular and nonregular (outsourcing over time etc.) is considered

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.19/31

Rough-Cut Capacity Planning(RCCP)
Considers aggregated work Allocates work in time buckets Determines resources in order to reach due dates Both regular and nonregular (outsourcing over time etc.) is considered Time driven RCCP is when project dates must be meet.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.19/31

Rough-Cut Capacity Planning(RCCP)
Considers aggregated work Allocates work in time buckets Determines resources in order to reach due dates Both regular and nonregular (outsourcing over time etc.) is considered Time driven RCCP is when project dates must be meet. In resource-driven RCCP only regular capacity can be used

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.19/31

Rough-Cut Capacity Planning(RCCP)
Considers aggregated work Allocates work in time buckets Determines resources in order to reach due dates Both regular and nonregular (outsourcing over time etc.) is considered Time driven RCCP is when project dates must be meet. In resource-driven RCCP only regular capacity can be used This session will consider the time driven

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.19/31

Some notation

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn k resources R1 , · · · , Rn

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn k resources R1 , · · · , Rn T time buckets

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn k resources R1 , · · · , Rn T time buckets Qkt is the regular capacity for resource k in period t

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn k resources R1 , · · · , Rn T time buckets Qkt is the regular capacity for resource k in period t

Job Jj requires qjk units of resource k

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn k resources R1 , · · · , Rn T time buckets Qkt is the regular capacity for resource k in period t

Job Jj requires qjk units of resource k xkt denotes the fraction of job Jj performed in period t

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn k resources R1 , · · · , Rn T time buckets Qkt is the regular capacity for resource k in period t

Job Jj requires qjk units of resource k xkt denotes the fraction of job Jj performed in period t Jj must be performed in time window [rj , dj ]

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn k resources R1 , · · · , Rn T time buckets Qkt is the regular capacity for resource k in period t

Job Jj requires qjk units of resource k xkt denotes the fraction of job Jj performed in period t Jj must be performed in time window [rj , dj ] pj is the minimum number of periods job Jj can use.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Some notation n jobs J1 , J2 , · · · , Jn k resources R1 , · · · , Rn T time buckets Qkt is the regular capacity for resource k in period t

Job Jj requires qjk units of resource k xkt denotes the fraction of job Jj performed in period t Jj must be performed in time window [rj , dj ] pj is the minimum number of periods job Jj can use.

is the maximum fraction of a job that can be completed in a week.

1 pj

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.20/31

Precedence constraints
If job Ji must finish before Jj there is a precedence relation. For a period τ this can be modelled as:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.21/31

Precedence constraints
If job Ji must finish before Jj there is a precedence relation. For a period τ this can be modelled as: τ −1

xjτ > 0 → t=dt xit = 1

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.21/31

Precedence constraints
If job Ji must finish before Jj there is a precedence relation. For a period τ this can be modelled as: τ −1

xjτ > 0 → t=dt xit = 1

There will be dj − rj constraints per precedence relation.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.21/31

Precedence constraints
If job Ji must finish before Jj there is a precedence relation. For a period τ this can be modelled as: τ −1

xjτ > 0 → t=dt xit = 1

There will be dj − 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.21/31

Nonregular capacity
Let Qkt denote the nonregular capacity for resource k in period t. Then for each resource and time period:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.22/31

Nonregular capacity
Let Qkt denote the nonregular capacity for resource k in period t. Then for each resource and time period: n Ukt = max{0, j=1 qjk xjt − Qkt

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.22/31

Nonregular capacity
Let Qkt denote the nonregular capacity for resource k in period t. Then for each resource and time period: n Ukt = max{0, j=1 qjk xjt − Qkt

The cost of using nonregular capacity for resource k in time period t is ckt

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.22/31

Nonregular capacity
Let Qkt denote the nonregular capacity for resource k in period t. Then for each resource and time period: n Ukt = max{0, j=1 qjk xjt − Qkt

The cost of using nonregular capacity for resource k in 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.22/31

Mathematical Model min subject
T t=1 K k=1 ckt Ukt

to dj t=rj

xjt

xjt n j=1 qjk xjt

=1 1 ≤ pj − Ukt ≤ 0

1≤j≤n 1 ≤ j ≤ n, 1 ≤ t ≤ T 1 ≤ j ≤ n, 1 ≤ t ≤ T 1 ≤ j ≤ n, 1 ≤ t ≤ T

xjt , Ukt ≥ 0

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.23/31

Controlling feasibility
Allowed To Work window for job Jj is defined as [Sj , Cj ].

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.24/31

Controlling feasibility
Allowed To Work window for job Jj is defined as [Sj , Cj ]. Job Jj cannot start before Sj or after Cj

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.24/31

Controlling feasibility
Allowed To Work window for job Jj is defined as [Sj , Cj ]. Job Jj cannot start before Sj or after Cj A ATW for job Jj is feasible if:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.24/31

Controlling feasibility
Allowed To Work window for job Jj is defined as [Sj , Cj ]. Job Jj cannot start before Sj or after Cj A ATW for job Jj is feasible if: 1. Sj ≥ rj and Cj ≤ dj 2. Cj − Sj ≥ pj − 1

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.24/31

Controlling feasibility
Allowed To Work window for job Jj is defined as [Sj , Cj ]. Job Jj cannot start before Sj or after Cj A ATW for job Jj is feasible if: 1. Sj ≥ rj and Cj ≤ dj 2. Cj − Sj ≥ pj − 1 A set S of ATW windows is feasible if:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.24/31

Controlling feasibility
Allowed To Work window for job Jj is defined as [Sj , Cj ]. Job Jj cannot start before Sj or after Cj A ATW for job Jj is feasible if: 1. Sj ≥ rj and Cj ≤ dj 2. Cj − Sj ≥ pj − 1 A set S of ATW windows is feasible if: 1. Every ATW window is feasible 2. Sj > Cj if Ji → Jj

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.24/31

Mathematical Model ATW windows sjt = 1 Sj ≤ t ≤ Cj 0 otherwise

(PS ) min subjectto

T t=1 dj t=rj

K k=1 ckt Ukt

xjt

xjt n j=1 qjk xjt

=1 s ≤ pj j − Ukt ≤ 0

1≤j≤n 1 ≤ j ≤ n, 1 ≤ t ≤ T 1 ≤ j ≤ n, 1 ≤ t ≤ T 1 ≤ j ≤ n, 1 ≤ t ≤ T

xjt , Ukt ≥ 0

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.25/31

Constructive heuristics (HBASIC )
Construct a feasible set S of ATW windows.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.26/31

Constructive heuristics (HBASIC )
Construct a feasible set S of ATW windows. Solve problem PS

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.26/31

Constructive heuristics (HBASIC )
Construct a feasible set S of ATW windows. Solve problem PS To obtain a feasible set of ATW windows construct them as follows:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.26/31

Constructive heuristics (HBASIC )
Construct a feasible set S of ATW windows. Solve problem PS To obtain a feasible set of ATW windows construct them as follows: Set Sj = rj

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.26/31

Constructive heuristics (HBASIC )
Construct a feasible set S of ATW windows. Solve problem PS To obtain a feasible set of ATW windows construct them as follows: Set Sj = rj Set Cj = min{dj , mink|ji →Jk rk − 1}

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.26/31

Constructive heuristics (HBASIC )
Construct a feasible set S of ATW windows. Solve problem PS To obtain a feasible set of ATW windows construct them as follows: Set Sj = rj Set Cj = min{dj , mink|ji →Jk rk − 1} Have I forgotten an important assumption ?

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.26/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )
{Ji1 , Ji2 , ·, Jik } is a ordered set if:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )
{Ji1 , Ji2 , ·, Jik } is a ordered set if: Ji1 → Ji2 , Ji3 → Ji4 , ·, Jik−1 → Jik

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )
{Ji1 , Ji2 , ·, Jik } is a ordered set if: Ji1 → Ji2 , Ji3 → Ji4 , ·, Jik−1 → Jik

A critical path is a path where:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )
{Ji1 , Ji2 , ·, Jik } is a ordered set if: Ji1 → Ji2 , Ji3 → Ji4 , ·, Jik−1 → Jik

A critical path is a path where:
Lj1 = Lj2 = · = min1≤n Lj

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )
{Ji1 , Ji2 , ·, Jik } is a ordered set if: Ji1 → Ji2 , Ji3 → Ji4 , ·, Jik−1 → Jik

A critical path is a path where:
Lj1 = Lj2 = · = min1≤n Lj Sji = Sji−1 + pi−1 for2 ≤ i ≤ R

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )
{Ji1 , Ji2 , ·, Jik } is a ordered set if: Ji1 → Ji2 , Ji3 → Ji4 , ·, Jik−1 → Jik

A critical path is a path where:
Lj1 = Lj2 = · = min1≤n Lj Sji = Sji−1 + pi−1 for2 ≤ i ≤ R Cji = Cji+1 − pji+1 for1 ≤ i ≤ R

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )
{Ji1 , Ji2 , ·, Jik } is a ordered set if: Ji1 → Ji2 , Ji3 → Ji4 , ·, Jik−1 → Jik

A critical path is a path where:
Lj1 = Lj2 = · = min1≤n Lj Sji = Sji−1 + pi−1 for2 ≤ i ≤ R Cji = Cji+1 − pji+1 for1 ≤ i ≤ R

A critical path is maximal if for all Jl :

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

Constructive heuristics (HCP M )
Define the slack of job Jj as Lj = Cj − (Sj + pj )
{Ji1 , Ji2 , ·, Jik } is a ordered set if: Ji1 → Ji2 , Ji3 → Ji4 , ·, Jik−1 → Jik

A critical path is a path where:
Lj1 = Lj2 = · = min1≤n Lj Sji = Sji−1 + pi−1 for2 ≤ i ≤ R Cji = Cji+1 − pji+1 for1 ≤ i ≤ R

A critical path is maximal if for all Jl :
{Ji1 , Ji2 , · · · , Jik , Jil } is critical {Jil , Ji1 , Ji2 , · · · , Jik } is critical

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.27/31

(HCP M ) continued
Initialize Sj = rj and Cj = dj for all Jj

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.28/31

(HCP M ) continued
Initialize Sj = rj and Cj = dj for all Jj Compute the slack for all jobs

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.28/31

(HCP M ) continued
Initialize Sj = rj and Cj = dj for all Jj Compute the slack for all jobs Find a maximal critical path {Ji1 , Ji2 , ·, Jik }

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.28/31

(HCP M ) continued
Initialize Sj = rj and Cj = dj for all Jj Compute the slack for all jobs Find a maximal critical path {Ji1 , Ji2 , ·, Jik }
¯ Compute the total slack L = CjR − (Sj1 +
R i=1 pji

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.28/31

(HCP M ) continued
Initialize Sj = rj and Cj = dj for all Jj Compute the slack for all jobs Find a maximal critical path {Ji1 , Ji2 , ·, Jik }
¯ Compute the total slack L = CjR − (Sj1 +
R i=1 pji R k=1 pik | i−1 k=1 pik

Set Sji = Sj1 +

¯ + |L

i−1 k=1 pik /

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.28/31

(HCP M ) continued
Initialize Sj = rj and Cj = dj for all Jj Compute the slack for all jobs Find a maximal critical path {Ji1 , Ji2 , ·, Jik }
¯ Compute the total slack L = CjR − (Sj1 +
R i=1 pji R k=1 pik | i−1 k=1 pik

Set Sji = Sj1 +

¯ + |L

i−1 k=1 pik /

Change to Cik = Sik+1 − 1

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.28/31

HCP M example
1 S 0 C 10 p 5 2 5 15 5 3 15 25 10 4 20 30 5

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.29/31

HCP M example
1 S 0 C 10 p 5 2 5 15 5 3 15 25 10 4 20 30 5

¯ L = C4 − (0 + 20) = 5

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.29/31

HCP M example
1 S 0 C 10 p 5 2 5 15 5 3 15 25 10 4 20 30 5 i−1 k=1 pjk

¯ L = C4 − (0 + 20) = 5 ˆ Recall Sji = Sji + ¯ + |L i−1 k=1 / R k=1 pjk |

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.29/31

HCP M example
1 S 0 C 10 p 5 2 5 15 5 3 15 25 10 4 20 30 5 i−1 k=1 pjk

¯ L = C4 − (0 + 20) = 5 ˆ Recall Sji = Sji + S2 = 0 + 5 +
5∗5 25

¯ + |L

i−1 k=1 /

R k=1 pjk |

=6

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.29/31

HCP M example
1 S 0 C 10 p 5 2 5 15 5 3 15 25 10 4 20 30 5 i−1 k=1 pjk

¯ L = C4 − (0 + 20) = 5 ˆ Recall Sji = Sji + S2 = 0 + 5 + S3 = 0 + 10
5∗5 25 = 6 + 10∗5 = 25

¯ + |L

i−1 k=1 /

R k=1 pjk |

12

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.29/31

HCP M example
1 S 0 C 10 p 5 2 5 15 5 3 15 25 10 4 20 30 5 i−1 k=1 pjk

¯ L = C4 − (0 + 20) = 5 ˆ Recall Sji = Sji + S2 = 0 + 5 + S3 = 0 + 10 S4 = 0 + 20
5∗5 25 = 6 + 10∗5 = 25 + 20∗5 = 25

¯ + |L

i−1 k=1 /

R k=1 pjk |

12 24

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.29/31

HCP M example
1 S 0 C 10 p 5 2 5 15 5 3 15 25 10 4 20 30 5 i−1 k=1 pjk

¯ L = C4 − (0 + 20) = 5 ˆ Recall Sji = Sji + S2 = 0 + 5 + S3 = 0 + 10 S4 = 0 + 20
5∗5 25 = 6 + 10∗5 = 25 + 20∗5 = 25

¯ + |L

i−1 k=1 /

R k=1 pjk |

12 24

C1 = S2 − 1 = 5, C2 = 11, C3 = 23

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.29/31

Neighbourhoods

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.30/31

Neighbourhoods
For job Jj increase Sj or decrease Cj

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.30/31

Neighbourhoods
For job Jj increase Sj or decrease Cj Decrease Sj implies Sj > rj , Ck = Sj − 1 for any preceding job Jk and Ck − Sk ≥ pk

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.30/31

Neighbourhoods
For job Jj increase Sj or decrease Cj Decrease Sj implies Sj > rj , Ck = Sj − 1 for any preceding job Jk and Ck − Sk ≥ pk Neighbourhood can be ordered after the greedy choice or the steepest edge rule.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.30/31

Exercises
Ex 1 Suggest some improvements for 2-3 of the modules in the MRP II model. You should describe what additional data the system and need and what value it would add for the users.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.31/31

Exercises
Ex 1 Suggest some improvements for 2-3 of the modules in the MRP II model. You should describe what additional data the system and need and what value it would add for the users. Ex 2 For RCCP we have focused on the time driven case in this exercise we consider the resource driven case:

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.31/31

Exercises
Ex 1 Suggest some improvements for 2-3 of the modules in the MRP II model. You should describe what additional data the system and need and what value it would add for the users. Ex 2 For RCCP we have focused on the time driven case in this exercise we consider the resource driven case: Ex 2.1 Give a mathematical model for the Resource driven RCCP without precedence constraints.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.31/31

Exercises
Ex 1 Suggest some improvements for 2-3 of the modules in the MRP II model. You should describe what additional data the system and need and what value it would add for the users. Ex 2 For RCCP we have focused on the time driven case in this exercise we consider the resource driven case: Ex 2.1 Give a mathematical model for the Resource driven RCCP without precedence constraints. Ex 2.2 If we use HBASIC to solve the resource driven RCCP will it result in a feasible solution ? Justify you answer

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.31/31

Exercises
Ex 1 Suggest some improvements for 2-3 of the modules in the MRP II model. You should describe what additional data the system and need and what value it would add for the users. Ex 2 For RCCP we have focused on the time driven case in this exercise we consider the resource driven case: Ex 2.1 Give a mathematical model for the Resource driven RCCP without precedence constraints. Ex 2.2 If we use HBASIC to solve the resource driven RCCP will it result in a feasible solution ? Justify you answer Ex 2.3 Describe a heuristic for the resource driven RCCP. The heuristic should include a constructive heuristic and a improvement heuristic.

Production Planning Solution Techniques Part 1 MRP, MRP-II – p.31/31