Production Planning Solution Techniques Part 1 MRP, MRP-II

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1 Production Planning Solution Techniques Part 1 MRP, MRP-II Mads Kehlet Jepsen Production Planning Solution Techniques Part 1 MRP, MRP-II p.1/31

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

3 Overview Material Requirement Planning(MRP) Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/31

4 Overview Material Requirement Planning(MRP) MRP Procedure Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/31

5 Overview Material Requirement Planning(MRP) MRP Procedure Issues with MRP Production Planning Solution Techniques Part 1 MRP, MRP-II p.2/31

6 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

7 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

8 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

9 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

10 Material Requirement Planning(MRP) Production Planning Solution Techniques Part 1 MRP, MRP-II p.3/31

11 Material Requirement Planning(MRP) Originally system was based on reorder point. Production Planning Solution Techniques Part 1 MRP, MRP-II p.3/31

12 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

13 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

14 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

15 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

16 Overview of MRP Production Planning Solution Techniques Part 1 MRP, MRP-II p.4/31

17 Overview of MRP External orders is called Purchase orders. Production Planning Solution Techniques Part 1 MRP, MRP-II p.4/31

18 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

19 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

20 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

21 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

22 Schematic of MRP Production Planning Solution Techniques Part 1 MRP, MRP-II p.5/31

23 MRP Inputs and Outputs Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/31

24 MRP Inputs and Outputs Master Production Schedule: Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/31

25 MRP Inputs and Outputs Master Production Schedule: Item, Quantity and due dates. Production Planning Solution Techniques Part 1 MRP, MRP-II p.6/31

26 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

27 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

28 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

29 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

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

31 MRP Procedure T is the number of time periods. Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/31

32 MRP Procedure T is the number of time periods. D t gross requirements (demand) for period t Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/31

33 MRP Procedure T is the number of time periods. D t gross requirements (demand) for period t S t quantity currently scheduled to complete in period t Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/31

34 MRP Procedure T is the number of time periods. D t gross requirements (demand) for period t S t quantity currently scheduled to complete in period t I t Projected on-hand inventory in period t Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/31

35 MRP Procedure T is the number of time periods. D t gross requirements (demand) for period t S t quantity currently scheduled to complete in period t I t Projected on-hand inventory in period t N t net requirements for period t Production Planning Solution Techniques Part 1 MRP, MRP-II p.7/31

36 MRP Procedure: Netting Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/31

37 MRP Procedure: Netting 1. Compute I t = I t 1 D t t Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/31

38 MRP Procedure: Netting 1. Compute I t = I t 1 D t t 2. Find t m = {min 1 t T : I t < 0} Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/31

39 MRP Procedure: Netting 1. Compute I t = I t 1 D t t 2. Find t m = {min 1 t T : I t < 0} 3. If the first SR has t > t m. Generate Change Notice and adjust SR and S t. Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/31

40 MRP Procedure: Netting 1. Compute I t = I t 1 D t t 2. Find t m = {min 1 t T : I t < 0} 3. If the first SR has t > t m. Generate Change Notice and adjust SR and S t. Continue until I m > 0 or no more SRs. Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/31

41 MRP Procedure: Netting 1. Compute I t = I t 1 D t t 2. Find t m = {min 1 t T : I t < 0} 3. If the first SR has t > t m. Generate Change Notice and adjust SR and S t. Continue until I m > 0 or no more SRs. 4. Adjust projected on-hand inventory to I t = I t + S t Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/31

42 MRP Procedure: Netting 1. Compute I t = I t 1 D t t 2. Find t m = {min 1 t T : I t < 0} 3. If the first SR has t > t m. Generate Change Notice and adjust SR and S t. Continue until I m > 0 or no more SRs. 4. Adjust projected on-hand inventory to I t = I t + S t 5. Find t = {t I t < 0} Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/31

43 MRP Procedure: Netting 1. Compute I t = I t 1 D t t 2. Find t m = {min 1 t T : I t < 0} 3. If the first SR has t > t m. Generate Change Notice and adjust SR and S t. Continue until I m > 0 or no more SRs. 4. Adjust projected on-hand inventory to I t = I t + S t 5. Find t = {t I t < 0} Net requirement follows as: N t = 0 t < t I t t = t t > t D t Production Planning Solution Techniques Part 1 MRP, MRP-II p.8/31

44 Netting example Gross requierments Scheduled receipts Adjusted SRs Projected on-hand 20 Net requirements Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/31

45 Netting example Gross requierments Scheduled receipts Adjusted SRs Projected on-hand 20 5 Net requirements I 1 = D 1 I 0 = 5 Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/31

46 Netting example Gross requierments Scheduled receipts Adjusted SRs 20 Projected on-hand 20 5 Net requirements I 1 = D 1 I 0 = 5 I 1 > 0 Adjust S 1. S 2 = S 2 + S 1 = 20 Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/31

47 Netting example Gross requierments Scheduled receipts Adjusted SRs 20 Projected on-hand Net requirements I 1 = D 1 I 0 = 5 I 1 > 0 Adjust S 1. S 2 = S 2 + S 1 = 20 I 2 = I 1 D 2 = 5 20 < 0 I 2 = I 2 + S 2 = = 5 Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/31

48 Netting example Gross requierments Scheduled receipts Adjusted SRs 20 Projected on-hand Net requirements I 1 = D 1 I 0 = 5 I 1 > 0 Adjust S 1. S 2 = S 2 + S 1 = 20 I 2 = I 1 D 2 = 5 20 < 0 I 2 = I 2 + S 2 = = 5 I 3 = I 2 D 3 = 45 Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/31

49 Netting example Gross requierments Scheduled receipts Adjusted SRs 20 Projected on-hand Net requirements 45 I 1 = D 1 I 0 = 5 I 1 > 0 Adjust S 1. S 2 = S 2 + S 1 = 20 I 2 = I 1 D 2 = 5 20 < 0 I 2 = I 2 + S 2 = = 5 I 3 = I 2 D 3 = 45 N 3 = I 3 = 45 Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/31

50 Netting example Gross requierments Scheduled receipts Adjusted SRs 20 Projected on-hand Net requirements I 1 = D 1 I 0 = 5 I 1 > 0 Adjust S 1. S 2 = S 2 + S 1 = 20 I 2 = I 1 D 2 = 5 20 < 0 I 2 = I 2 + S 2 = = 5 I 3 = I 2 D 3 = 45 N 3 = I 3 = 45 N 4 = D 4 = 50 Production Planning Solution Techniques Part 1 MRP, MRP-II p.9/31

51 MRP Procedure continued Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/31

52 MRP Procedure continued Lot sizing: Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/31

53 MRP Procedure continued Lot sizing: Wagner Whitin Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/31

54 MRP Procedure continued Lot sizing: Wagner Whitin lot for lot Production Planning Solution Techniques Part 1 MRP, MRP-II p.10/31

55 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

56 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

57 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

58 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

59 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

60 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

61 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 Net Requirements Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

62 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

63 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

64 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

65 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

66 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

67 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

68 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

69 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

70 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 Net Requirements Quantity 1 setup cost Part-Periods Inventory cost Production Planning Solution Techniques Part 1 MRP, MRP-II p.11/31

71 Issues with MRP Production Planning Solution Techniques Part 1 MRP, MRP-II p.12/31

72 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

73 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

74 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

75 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

76 Questians or comments to MRP Are there any questians or comments? Production Planning Solution Techniques Part 1 MRP, MRP-II p.13/31

77 Manufacturing Resource Planning Production Planning Solution Techniques Part 1 MRP, MRP-II p.14/31

78 Manufacturing Resource Planning Address deficiencies in MRP Production Planning Solution Techniques Part 1 MRP, MRP-II p.14/31

79 Manufacturing Resource Planning Address deficiencies in MRP Brings in new functionalities including: Production Planning Solution Techniques Part 1 MRP, MRP-II p.14/31

80 Manufacturing Resource Planning Address deficiencies in MRP Brings in new functionalities including: Production Planning Solution Techniques Part 1 MRP, MRP-II p.14/31

81 Long-Range Planning Production Planning Solution Techniques Part 1 MRP, MRP-II p.15/31

82 Long-Range Planning Forecasting seeks to predict demands of the future. Production Planning Solution Techniques Part 1 MRP, MRP-II p.15/31

83 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

84 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

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

86 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

87 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

88 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

89 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

90 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

91 Short-term control Production Planning Solution Techniques Part 1 MRP, MRP-II p.17/31

92 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

93 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

94 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

95 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

96 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

97 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

98 Questians or comments to MRP II Are there any questians or comments? Production Planning Solution Techniques Part 1 MRP, MRP-II p.18/31

99 Rough-Cut Capacity Planning(RCCP) Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/31

100 Rough-Cut Capacity Planning(RCCP) Considers aggregated work Production Planning Solution Techniques Part 1 MRP, MRP-II p.19/31

101 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

102 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

103 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

104 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

105 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

106 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

107 Some notation Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

108 Some notation n jobs J 1,J 2,,J n Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

109 Some notation n jobs J 1,J 2,,J n k resources R 1,,R n Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

110 Some notation n jobs J 1,J 2,,J n k resources R 1,,R n T time buckets Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

111 Some notation n jobs J 1,J 2,,J n k resources R 1,,R n T time buckets Q kt is the regular capacity for resource k in period t Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

112 Some notation n jobs J 1,J 2,,J n k resources R 1,,R n T time buckets Q kt is the regular capacity for resource k in period t Job J j requires q jk units of resource k Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

113 Some notation n jobs J 1,J 2,,J n k resources R 1,,R n T time buckets Q kt is the regular capacity for resource k in period t Job J j requires q jk units of resource k x kt denotes the fraction of job J j performed in period t Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

114 Some notation n jobs J 1,J 2,,J n k resources R 1,,R n T time buckets Q kt is the regular capacity for resource k in period t Job J j requires q jk units of resource k x kt denotes the fraction of job J j performed in period t J j must be performed in time window [r j,d j ] Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

115 Some notation n jobs J 1,J 2,,J n k resources R 1,,R n T time buckets Q kt is the regular capacity for resource k in period t Job J j requires q jk units of resource k x kt denotes the fraction of job J j performed in period t J j must be performed in time window [r j,d j ] p j is the minimum number of periods job J j can use. Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

116 Some notation n jobs J 1,J 2,,J n k resources R 1,,R n T time buckets Q kt is the regular capacity for resource k in period t Job J j requires q jk units of resource k x kt denotes the fraction of job J j performed in period t J j must be performed in time window [r j,d j ] p j is the minimum number of periods job J j can use. 1 p j is the maximum fraction of a job that can be completed in a week. Production Planning Solution Techniques Part 1 MRP, MRP-II p.20/31

117 Precedence constraints If job J i must finish before J j 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

118 Precedence constraints If job J i must finish before J j there is a precedence relation. For a period τ this can be modelled as: x jτ > 0 τ 1 t=d t x it = 1 Production Planning Solution Techniques Part 1 MRP, MRP-II p.21/31

119 Precedence constraints If job J i must finish before J j there is a precedence relation. For a period τ this can be modelled as: x jτ > 0 τ 1 t=d t x it = 1 There will be d j r j constraints per precedence relation. Production Planning Solution Techniques Part 1 MRP, MRP-II p.21/31

120 Precedence constraints If job J i must finish before J j there is a precedence relation. For a period τ this can be modelled as: x jτ > 0 τ 1 t=d t x it = 1 There will be d j r j 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

121 Nonregular capacity Let Q kt 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

122 Nonregular capacity Let Q kt denote the nonregular capacity for resource k in period t. Then for each resource and time period: U kt = max{0, n j=1 q jk x jt Q kt Production Planning Solution Techniques Part 1 MRP, MRP-II p.22/31

123 Nonregular capacity Let Q kt denote the nonregular capacity for resource k in period t. Then for each resource and time period: U kt = max{0, n j=1 q jk x jt Q kt The cost of using nonregular capacity for resource k in time period t is c kt Production Planning Solution Techniques Part 1 MRP, MRP-II p.22/31

124 Nonregular capacity Let Q kt denote the nonregular capacity for resource k in period t. Then for each resource and time period: U kt = max{0, n j=1 q jk x jt Q kt The cost of using nonregular capacity for resource k in time period t is c kt It is assumed that there is no limit on the nonregular resources. Production Planning Solution Techniques Part 1 MRP, MRP-II p.22/31

125 Mathematical Model min T t=1 K k=1 c ktu kt subject to dj t=r j x jt = 1 1 j n x jt 1 p j 1 j n, 1 t T n j=1 q jkx jt U kt 0 1 j n, 1 t T x jt,u kt 0 1 j n, 1 t T Production Planning Solution Techniques Part 1 MRP, MRP-II p.23/31

126 Controlling feasibility Allowed To Work window for job J j is defined as [S j,c j ]. Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/31

127 Controlling feasibility Allowed To Work window for job J j is defined as [S j,c j ]. Job J j cannot start before S j or after C j Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/31

128 Controlling feasibility Allowed To Work window for job J j is defined as [S j,c j ]. Job J j cannot start before S j or after C j A ATW for job J j is feasible if: Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/31

129 Controlling feasibility Allowed To Work window for job J j is defined as [S j,c j ]. Job J j cannot start before S j or after C j A ATW for job J j is feasible if: 1. S j r j and C j d j 2. C j S j p j 1 Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/31

130 Controlling feasibility Allowed To Work window for job J j is defined as [S j,c j ]. Job J j cannot start before S j or after C j A ATW for job J j is feasible if: 1. S j r j and C j d j 2. C j S j p j 1 A set S of ATW windows is feasible if: Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/31

131 Controlling feasibility Allowed To Work window for job J j is defined as [S j,c j ]. Job J j cannot start before S j or after C j A ATW for job J j is feasible if: 1. S j r j and C j d j 2. C j S j p j 1 A set S of ATW windows is feasible if: 1. Every ATW window is feasible 2. S j > C j if J i J j Production Planning Solution Techniques Part 1 MRP, MRP-II p.24/31

132 Mathematical Model ATW windows s jt = { 1 S j t C j 0 otherwise (P S ) min T t=1 K k=1 c ktu kt subjectto dj t=r j x jt = 1 1 j n x jt s j p j 1 j n, 1 t T n j=1 q jkx jt U kt 0 1 j n, 1 t T x jt,u kt 0 1 j n, 1 t T Production Planning Solution Techniques Part 1 MRP, MRP-II p.25/31

133 Constructive heuristics (H BASIC ) Construct a feasible set S of ATW windows. Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/31

134 Constructive heuristics (H BASIC ) Construct a feasible set S of ATW windows. Solve problem P S Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/31

135 Constructive heuristics (H BASIC ) Construct a feasible set S of ATW windows. Solve problem P S To obtain a feasible set of ATW windows construct them as follows: Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/31

136 Constructive heuristics (H BASIC ) Construct a feasible set S of ATW windows. Solve problem P S To obtain a feasible set of ATW windows construct them as follows: Set S j = r j Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/31

137 Constructive heuristics (H BASIC ) Construct a feasible set S of ATW windows. Solve problem P S To obtain a feasible set of ATW windows construct them as follows: Set S j = r j Set C j = min{d j, min k ji J k r k 1} Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/31

138 Constructive heuristics (H BASIC ) Construct a feasible set S of ATW windows. Solve problem P S To obtain a feasible set of ATW windows construct them as follows: Set S j = r j Set C j = min{d j, min k ji J k r k 1} Have I forgotten an important assumption? Production Planning Solution Techniques Part 1 MRP, MRP-II p.26/31

139 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

140 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) {J i1,j i2,,j ik } is a ordered set if: Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

141 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) {J i1,j i2,,j ik } is a ordered set if: J i1 J i2,j i3 J i4,,j ik 1 J ik Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

142 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) {J i1,j i2,,j ik } is a ordered set if: J i1 J i2,j i3 J i4,,j ik 1 J ik A critical path is a path where: Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

143 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) {J i1,j i2,,j ik } is a ordered set if: J i1 J i2,j i3 J i4,,j ik 1 J ik A critical path is a path where: L j1 = L j2 = = min 1 n L j Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

144 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) {J i1,j i2,,j ik } is a ordered set if: J i1 J i2,j i3 J i4,,j ik 1 J ik A critical path is a path where: L j1 = L j2 = = min 1 n L j S ji = S ji 1 + p i 1 for2 i R Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

145 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) {J i1,j i2,,j ik } is a ordered set if: J i1 J i2,j i3 J i4,,j ik 1 J ik A critical path is a path where: L j1 = L j2 = = min 1 n L j S ji = S ji 1 + p i 1 for2 i R C ji = C ji+1 p ji+1 for1 i R Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

146 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) {J i1,j i2,,j ik } is a ordered set if: J i1 J i2,j i3 J i4,,j ik 1 J ik A critical path is a path where: L j1 = L j2 = = min 1 n L j S ji = S ji 1 + p i 1 for2 i R C ji = C ji+1 p ji+1 for1 i R A critical path is maximal if for all J l : Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

147 Constructive heuristics (H CPM ) Define the slack of job J j as L j = C j (S j + p j ) {J i1,j i2,,j ik } is a ordered set if: J i1 J i2,j i3 J i4,,j ik 1 J ik A critical path is a path where: L j1 = L j2 = = min 1 n L j S ji = S ji 1 + p i 1 for2 i R C ji = C ji+1 p ji+1 for1 i R A critical path is maximal if for all J l : {J i1,j i2,,j ik,j il } is critical {J il,j i1,j i2,,j ik } is critical Production Planning Solution Techniques Part 1 MRP, MRP-II p.27/31

148 (H CPM ) continued Initialize S j = r j and C j = d j for all J j Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/31

149 (H CPM ) continued Initialize S j = r j and C j = d j for all J j Compute the slack for all jobs Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/31

150 (H CPM ) continued Initialize S j = r j and C j = d j for all J j Compute the slack for all jobs Find a maximal critical path {J i1,j i2,,j ik } Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/31

151 (H CPM ) continued Initialize S j = r j and C j = d j for all J j Compute the slack for all jobs Find a maximal critical path {J i1,j i2,,j ik } Compute the total slack L = C jr (S j1 + R i=1 p j i Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/31

152 (H CPM ) continued Initialize S j = r j and C j = d j for all J j Compute the slack for all jobs Find a maximal critical path {J i1,j i2,,j ik } Compute the total slack L = C jr (S j1 + R i=1 p j i Set S ji = S j1 + i 1 k=1 p i k + L i 1 k=1 p i k / R k=1 p i k Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/31

153 (H CPM ) continued Initialize S j = r j and C j = d j for all J j Compute the slack for all jobs Find a maximal critical path {J i1,j i2,,j ik } Compute the total slack L = C jr (S j1 + R i=1 p j i Set S ji = S j1 + i 1 k=1 p i k + L i 1 k=1 p i k / R k=1 p i k Change to C ik = S ik+1 1 Production Planning Solution Techniques Part 1 MRP, MRP-II p.28/31

154 H CPM example S C p Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/31

155 H CPM example S C p L = C 4 (0 + 20) = 5 Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/31

156 H CPM example S C p L = C 4 (0 + 20) = 5 Recall ˆ Sji = S ji + i 1 k=1 p j k + L i 1 k=1 / R k=1 p jk Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/31

157 H CPM example S C p L = C 4 (0 + 20) = 5 Recall ˆ Sji = S ji + i 1 k=1 p j k + L i 1 k=1 / R k=1 p jk S 2 = = 6 Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/31

158 H CPM example S C p L = C 4 (0 + 20) = 5 Recall ˆ Sji = S ji + i 1 k=1 p j k + L i 1 k=1 / R k=1 p jk S 2 = = 6 S 3 = = 12 Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/31

159 H CPM example S C p L = C 4 (0 + 20) = 5 Recall ˆ Sji = S ji + i 1 k=1 p j k + L i 1 k=1 / R k=1 p jk S 2 = = 6 S 3 = = 12 S 4 = = 24 Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/31

160 H CPM example S C p L = C 4 (0 + 20) = 5 Recall ˆ Sji = S ji + i 1 k=1 p j k + L i 1 k=1 / R k=1 p jk S 2 = = 6 S 3 = = 12 S 4 = = 24 C 1 = S 2 1 = 5, C 2 = 11, C 3 = 23 Production Planning Solution Techniques Part 1 MRP, MRP-II p.29/31

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

162 Neighbourhoods For job J j increase S j or decrease C j Production Planning Solution Techniques Part 1 MRP, MRP-II p.30/31

163 Neighbourhoods For job J j increase S j or decrease C j Decrease S j implies S j > r j, C k = S j 1 for any preceding job J k and C k S k p k Production Planning Solution Techniques Part 1 MRP, MRP-II p.30/31

164 Neighbourhoods For job J j increase S j or decrease C j Decrease S j implies S j > r j, C k = S j 1 for any preceding job J k and C k S k p k 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

165 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

166 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

167 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

168 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 H BASIC 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

169 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 H BASIC 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

OR topics in MRP-II. Mads Jepsens. OR topics in MRP-II p.1/25

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