Chapter 7. Production, Capacity and Material Planning

Transcription

1 Chapter 7 Production, Capacity and Material Planning

2 Production, Capacity and Material Planning Production plan quantities of final product, subassemblies, parts needed at distinct points in time To generate the Production plan we need: end-product demand forecasts Master production schedule Master production schedule (MPS) delivery plan for the manufacturing organization exact amounts and delivery timings for each end product accounts for manufacturing constraints and final goods inventory Production Management 0

3 Production, Capacity and Material Planning Based on the MPS: rough-cut capacity planning Material requirements planning determines material requirements and timings for each phase of production detailed capacity planning Production Management 02

4 Production, Capacity and Material Planning Updates Rough-Cut Capacity Detailed Capacity Planning End-Item Demand Estimate Master Production Schedule (MPS) Material Requirements Planning (MRP) Material Plan Shop Orders Purchasing Plan Shop Floor Control Updates Production Management 03

5 Master Production Scheduling Aggregate plan demand estimates for individual end-items demand estimates vs. MPS inventory capacity constraints availability of material production lead time... Market environments make-to-stock (MTS) make-to-order (MTO) assemble-to-order (ATO) Production Management 04

6 Master Production Scheduling MTS produces in batches minimizes customer delivery times at the expense of holding finishedgoods inventory MPS is performed at the end-item level production starts before demand is known precisely small number of end-items, large number of raw-material items MTO no finished-goods inventory customer orders are backlogged MPS is order driven, consisits of firm delivery dates Production Management 05

7 Master Production Scheduling ATO large number of end-items are assembled from a relatively small set of standard subassemblies, or modules automobile industry MPS governs production of modules (forecast driven) Final Assembly Schedule (FAS) at the end-item level (order driven) 2 lead times, for consumer orders only FAS lead time relevant Production Management 06

8 Master Production Scheduling MPS- SIBUL manufactures phones three desktop models A, B, C one wall telephone D MPS is equal to the demand forecast for each model WEEKLY MPS Jan Feb (= FORECAST) Product Week Week Model A Model B Model C Model D weekly total monthly total Production Management 07

9 Master Production Scheduling MPS Planning - Example MPS plan for model A of the previous example: Make-to-stock environment No safety-stock for end-items I t = I t- + Q t max{f t,o t } I t = end-item inventory at the end of week t Q t = manufactured quantity to be completed in week t F t = forecast for week t O t = customer orders to be delivered in week t INITIAL DATA Model A Jan Feb Current Inventory = Week Week forecast Ft orders Ot Production Management 08

10 Master Production Scheduling Batch production: batch size = 2500 I t = max{0, I t- } max{f t, O t } Q t 0, if It > 0 = 2500, otherwise I = max{0, 600} max{000, 200} = 400 >0 I 2 = max{0, 400} max{000, 800} = -600 <0 => Q2 = 2500 I 2 = max{000, 800} = 900, etc. MPS Jan Feb Current Inventory = 600 Week Week forecast Ft orders Ot Inventory It MPS Qt ATP Production Management 09

11 Master Production Scheduling Available to Promise (ATP) ATP = = 400 ATP 2 = 2500 ( ) = 400, etc. Whenever a new order comes in, ATP must be updated Lot-for-Lot production MPS Jan Feb Current Inventory = 600 Week Week forecast Ft orders Ot Inventory It MPS Qt ATP Production Management 0

12 Master Production Scheduling MPS Modeling differs between MTS-ATO and MTO find final assembly lot sizes additional complexity because of joint capacity constraints cannot be solved for each product independently Production Management

13 Master Production Scheduling Make-To-Stock-Modeling Q it = production quantity of product i in period t I it = Inventory of product i at end of period t Dit = demand (requirements) for product i in time period t ai = production hours per unit of product i hi = inventory holding cost per unit of product i per time period Ai = set-up cost for product i G = production hours available in period t t y =,if set-up for product i occurs in period t (Q > 0) it it Production Management 2

14 Master Production Scheduling Make-To-Stock-Modeling min i= t= ( Ay + hi ) i,- t it it it n i= Q it it i n T i it i it I + Q I = D for all (i,t) a Q G for all t y it T it k = t Q 0; I 0; y {0,} it D ik 0 for all (i,t) it Production Management 3

15 Master Production Scheduling Assemble-To-Order Modeling two master schedules MPS: forecast-driven FAS: order driven overage costs holding costs for modules and assembled products shortage costs final product assemply based on available modules no explicit but implicit shortage costs for modules final products: lost sales, backorders Production Management 4

16 Master Production Scheduling m module types and n product types Q kt = quantity of module k produced in period t g kj = number of modules of type k required to assemble order j Decision Variables: I kt = inventory of module k at the end of period t y jt =, if order j is assembled and delivered in period t; 0, otherwise h k = holding cost π jt = penalty costs, if order j is satisfied in period t and order j is due in period t (t <t); holding costs if t > t Production Management 5

17 Master Production Scheduling Assemble-To-Order Modeling min subject to I j= t= I kt n L kt = a y k kt k = t= j= t= j jt m I k, t y jt L = for all j 0; y h + Q G jt t I kt + n n j= g L kj π y jt jt y jt for all (k, t) for all t { 0,} for all (j,k, t) Production Management 6

18 Master Production Scheduling Capacity Planning Bottleneck in production facilities Rough-Cut Capacity Planning (RCCP) at MPS level feasibility detailed capacity planning (CRP) at MRP level both RCCP and CRP are only providing information Production Management 7

19 Master Production Scheduling MPS: January Week Product A B C D Bill of capacity (min) Assembly Inspection A 20 2 B C 22 2 D Capacity requires (hr) Week weekly capacity requirements? Assembly: 000* * *25 = min = 33,33 hr Inspection: 000* * *2,4 = 6440 min = 07,33 hr etc. available capacity per week is 200 hr for the assembly work center and 0 hours for the inspection station; Available capacity per week Assembly !! Inspection !! 83 0 Production Management 8

20 Master Production Scheduling Infinite capacity planning (information providing) finding a feasible cost optimal solution is a NP-hard problem if no detailed bill of capacity is available: capacity planning using overall factors (globale Belastungsfaktoren) required input: MPS standard hours of machines or direct labor required historical data on individual shop workloads (%) Example from Günther/Tempelmeier C33.3: overall factors Production Management 9

21 Master Production Scheduling capacity planning using overall factors week product A B work on work on Total product critical machine non-critical machine A 2 3 B historic capacity requirements on critical machines: 40% on machine a 60% on machine b Production Management 20

22 Master Production Scheduling in total 500 working units are available per week, 80 on machine a and 20 on machine b; Solution: overall factor = time per unit x historic capacity needs product A: machine a: x 0,4 = 0,4 machine b: x 0,6 = 0,6 product B: machine a: 4 x 0,4 =,6 machine b: 4 x 0,6 = 2,4 Production Management 2

23 Master Production Scheduling capacity requirements: product A machine week a b other capacity requirements: product B machine week a b other Production Management 22

24 Master Production Scheduling total capacity requirements machine week a b other Production Management 23

25 Master Production Scheduling capacity requirements week a (max 80) b (max 20) other (max 300) Production Management 24

26 Master Production Scheduling Capacity Modeling heuristic approach for finite-capacity-planning based on input/output analysis relationship between capacity and lead time G= work center capacity R t = work released to the center in period t Q t = production (output) from the work center in period t W t = work in process in period t U t = queue at the work center measured at the beginning of period t, prior to the release of work L t = lead time at the work center in period t Production Management 25

27 Production Management 26 Master Production Scheduling Lead time is not constant assumptions: constant production rate any order released in this period is completed in this period G W L Q U R U W Q R U U R G U Q t t t t t t t t t t t t t t = + = + = + = + = }, min{

28 Master Production Scheduling Example Period G (hr/week) R t (hours) Q t (hours) U t (hours) W t (hours) L t (weeks) 0,83 0,83,67,22,33,44 Production Management 27

29 Material Requirements Planning Inputs master production schedule inventory status record bill of material (BOM) Outputs planned order releases purchase orders(supply lead time) workorders(manufacturing lead time) Production Management 28

30 Material Requirements Planning Level 0 End-Item Level S/A 2 Legend: S/A = subassembly PP = purchased part Level 2 PP 5 4 S/A 6 2 MP = manufactured part RM = raw material Level 3 MP 9 2 PP 0 part # quantity Level 4 RM 2 RM Production Management 29

31 Material Requirements Planning MRP Process goal is to find net requirements (trigger purchase and work orders) explosion Example: MPS, 00 end items yields gross requirements netting Net requirements = Gross requirements - on hand inventory - quantity on order done at each level prior to further explosion offsetting the timing of order release is determined lotsizing batch size is determined Production Management 30

32 Material Requirements Planning Example 7-6 Telephone Microphone S/A Receiver S/A 2 Upper Cover 3 Hand Set Assembly Lower Cover Tapping Screw 2 4 Housing S/A 5 2 Base Assembly Key Key Pad Pad Cord Production Management 3 Board Pack S/A Rubber Pad 23 3 Hand Set Cord 4 Tapping Screw

33 Material Requirements Planning PART (gross requirements given) net requirements? Planned order release? Net requ.(week 2) = 600 ( ) = -700 =>Net requ.(week2) = 0 Net requ.(week 3) = 000 ( ) = -900 =>Net requ.(week3) = 0 Net requ.(week 4) = = 00 etc. week current gross requirements scheduled receipts projected inventory balance net requirements planned receipts planned order release Production Management 32

34 Material Requirements Planning Assumptions: lot size: 3000 lead time: 2 weeks week current gross requirements scheduled receipts projected inventory balance net requirements planned receipts planned order release Production Management 33

35 Material Requirements Planning Multilevel explosion part number description Qty 2 base assembly 2 housing S/A 23 rubber pad 4 2 key pad lead time is one week lot for lot for parts 2, 23, 2 part 2: fixed lot size of 3000 Production Management 34

36 Part 2 current gross requirements scheduled receipts projected inventory balance net requirements planned receipts planned order release x x x Part 2 current gross requirements scheduled receipts x4 x4 x4 projected inventory balance net requirements planned receipts planned order release Part 23 current gross requirements scheduled receipts 0000 projected inventory balance net requirements planned receipts planned order release Part 2 current gross requirements scheduled receipts 500 projected inventory balance net requirements planned receipts planned order release x x Production Management 35 x

37 Material Requirements Planning MRP Updating Methods MRP systems operate in a dynamic environment regeneration method: the entire plan is recalculated net change method: recalculates requirements only for those items affected by change February Updated MPS for February Week Week Product A B C D Net Change for February Week Product A B C -200 D Production Management 36

38 Material Requirements Planning Additional Netting procedures implosion: opposite of explosion finds common item combining requirements: process of obtaining the gross requirements of a common item pegging: identify the item s end product useful when item shortages occur Production Management 37

39 Material Requirements Planning Lot Sizing in MRP minimize set-up and holding costs can be formulated as MIP a variety of heuristic approaches are available simplest approach: use independent demand procedures (e.g. EOQ) at every level Production Management 38

40 Material Requirements Planning MIP Formulation Indices: i =...P t =...T m =...M Parameters: Γ(i) Γ -( i) s i c ij h i a mi b mi L mt oc m G D it label of each item in BOM (assumed that all labels are sorted with respect to the production level starting from the end-items) period t resource m set of immediate successors of item i set of immediate predeccessors of item i setup cost for item i quantity of itme i required to produce item j holding cost for one unit of item i capacity needed on resource m for one unit of item i capacity needed on resource m for the setup process of item i available capacity of resource m in period t overtime cost of resource m large number, but as small as possible (e.g. sum of demands) external demand of item i in period t Production Management 39

41 Material Requirements Planning I P i= i, t Decision variables: x it I it O mt Equations: = I i, t + xi, t cij j Γ ( i) mi it mi deliverd quantity of item i in period t inventory level of item i at the end of period t overtime hours required for machine m in period t y it binary variable indicating if item i is produced in period t (=) or not (=0) it P T min ( s y + h ( a x + b y ) L + O mt i it i it i= t= t= m= x jt D mt it i,t m,t I T M ) + oc m O x it Gy x it it mt 0 i,t, I, O 0, y {0,} it mt it i, m, t Production Management 40

42 Material Requirements Planning Multi-Echelon Systems Multi-echelon inventory each level is referred as an echelon total inventory in the system varies with the number of stocking points Modell (Freeland 985): demand is insensitive to the number of stocking points demand is normally distributed and divided evenly among the stocking points, demands at the stocking points are independent of one another a (Q,R) inventory policy is used β-service level (fill rate) is applied Q is determined from the EOQ formula Production Management 4

43 Material Requirements Planning Reorder point in (Q,R) policies: i: total annual inventory costs (%) c: unit costs A: ordering costs τ σ τ :lead time : variance of demand in lead time β z(β ) given a fill rate choose such that: L( z) φ = z ( y z) φ( y) dy : density of N(0,) distribution; L(z): standard loss function = ( β ) Q σ τ Production Management 42

44 Unit Normal Linear Loss Integral L(Z) Z Production Management

45 Material Requirements Planning Safety stock: s = z σ τ Reorder point: R = D + z τ σ τ Order quantity: Q Average inventory: = EOQ = Q I () = + s 2 I ( n ) = average 2 A ic inventory D for n stocking points I () = 2 2A D ic + zσ τ Production Management 44

46 Material Requirements Planning for two stocking points : demand at each point : D/2 variance of 2 lead - time demand : σ standard deviation is : σ τ / 2 τ / 2 average inventory at each stocking point is : 2 2AD/2 ic zσ + τ 2 = 2 ( Q / 2 + s) Production Management 45

47 Material Requirements Planning the average inventory for two stocking point is : I (2) = I ( n) 2 = n I () ( Q / 2 + s) = 2 2 ( Q / 2 + s) = 2 I () for each level the safety stock is :s/ the total safety stock is n s n Production Management 46

48 Material Requirements Planning Example: At the packaging department of a sugar refinery: A very-high-grade powdered sugar: Level 0 Boxed Sugar Level Sugar Cartons Sugar-refining lead time is five days; Production lead time (filling time) is negligible; Annual demand: D = 800 tons and σ= 2,5 Lead-time demand is normally distributed with Dτ = 6 tons and στ = 3,54 tons Fill rate = 95% A = $50, c = $4000, i = 20% Production Management 47

49 Material Requirements Planning Inventory at level 0 and? Safety stock? 2 AD 2 x 50 x800 Q = = = 0 tons ic 800 ß = 0,95 => z = 0,7 s = zστ = 0,7x3,54 = 2,5 tons Suppose we keep inventory in level 0 only, i.e., n = : Q 0 I ( ) = + s = + 2,5 = 7, 5tons 2 2 Suppose inventory is maintained at both level 0 and level, i.e., n = 2: I ( 2) = 2I () = 0, 62 tons The safety stock in each level is going to be: s 2 2,5 = 2 =,77tons Production Management 48

50 Material Requirements Planning MRP as Multi-Echelon Inventory Control continuous-review type policy (Q,R) hierarchy of stocking points (installation) installation stock policy echelon stock (policy): installation inventory position plus all downstream stock MRP: rolling horizon level by level approach bases ordering decisions on projected future installation inventory level Production Management 49

51 Material Requirements Planning All demands and orders occur at the beginning of the time period orders are initiated immediately after the demands, first for the final items and then successively for the components all demands and orders are for an integer number of units T= planning horizon τ i = lead time for item i s i = safety stock for item I R i = reorder point for item I Q i =Fixed order quantity of item i D it = external requirements of item i in period t Production Management 50

52 Material Requirements Planning Installation stock policies (Q,R i ) for MRP: a production order is triggered if the installation stock minus safety stock is insufficient to cover the requirements over the next τ i periods an order may consist of more than one order quantity Q if lead time τ i = 0, the MRP is equal to an installation stock policy. safety stock = reorder point Production Management 5

53 Material Requirements Planning Echelon stock policies (Q,R e ) for MRP: Consider a serial assembly system Installation is the downstream installation (final product) the output of installation i is the input when producing one unit of item i- at the immediate downstream installation w i = installation inventory position at installation i I i = echelon inventory position at installation i (at the same moment) I i = w i + w i w a multi-echelon (Q,R) policy is denoted by (Q i,r ie ) R i e gives the reorder point for echelon inventory at i Production Management 52

54 Material Requirements Planning R e = s +Dτ R ie = s i +Dτ i +R i- e +Q i- Example: Two-level system, 6 periods 0 0 e e I = 8, I 2 = 38, R = 20, R 2 = 34, Q = 0, Q 2 = D = 2 (Item ), τ =, τ 2 = 2 30 Production Management 53

55 Material Requirements Planning Item Item 2 Period Demand Level w Production Level w Production Suppose now that five units were demanded in period 2: Period Demand Item Item 2 Level w Level w Production Production Production Management 54

56 Material Requirements Planning Lot Size and Lead Time lead time is affected by capacity constraints lot size affects lead time batching effect an increase in lot size should increase lead time saturation effect when lot size decreases, and set-up is not reduced, lead time will increase expected lead time can be calculated using models from queueing theory (M/G/) Production Management 55

57 Material Requirements Planning L = lead time L = 2 2 ( λ / μ) + λ σ 2λ( λ / μ) 2 + μ λ = mean arrival rate μ = mean service rate σ 2 = service time variance Production Management 56

58 Production Management 57 Material Requirements Planning n j j j j j ) ( ) ( : variance time - service : time service mean : batches of rate arrival mean j product for lotsize Q j product for time up - set S j product for time production - unit t j product for period per demand + = + = = = = = = = = = = = = = μ λ λ σ μ λ λ λ λ n j j n j j j j j j j j n j j n j n j j j j j Q t S Q t S Q D D

59 Material Requirements Planning Production Management 58

60 Material Planning Work to do: 7.7ab, 7.8, 7.0, 7., 7.4 (additional information: available hours: 225 (Paint), 30 (Mast), 00 (Rope)), 7.5, 7.6, 7.7, Production Management 59