Chapter 5. Aggregate Planning

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1 Chaper 5 Aggregae Planning

2 Supply Chain Planning Marix procuremen producion disribuion sales longerm Sraegic Nework Planning miderm shorerm Maerial Requiremens Planning Maser Planning Producion Planning Scheduling Disribuion Planning Transpor Planning Demand Planning Demand Fulfilmen & ATP Producion Managemen 44

3 Supply Chain Planning Marix procuremen producion disribuion sales longerm maerials program plan locaion physical disribuion produc program supplier selecion producion sysem srucure sraegic sales cooperaions planning miderm personnel planning maerial requ. planning conracs maser producion scheduling capaciy planning disribuion planning mid-erm sales planning shorerm personnel planning ordering maerials lo-sizing machine scheduling shop floor conrol warehouse replenishemen ranspor planning shor-erm sales planning flow of goods informaion flows Producion Managemen 45

4 Aggregae Planning Example: one produc (plasic case) wo injecion molding machines, 550 pars/hour one worker, 55 pars/hour seady sales cases/monh 4 weeks/monh, 5 days/week, 8h/day how many workers? in real life consan demand is rare change demand produce a consan rae anyway vary producion Producion Managemen 46

5 Aggregae Planning Influencing demand do no saisfy demand shif demand from peak periods o nonpeak periods produce several producs wih peak demand in differen period Planning Producion Producion plan: how much and when o make each produc rolling planning horizon long range plan inermediae-range plan unis of measuremens are aggregaes produc family plan deparmen changes in workforce, addiional machines, subconracing, overime,... Shor-erm plan Producion Managemen 47

6 Aggregae Planning Aspecs of Aggregae Planning Capaciy: how much a producion sysem can make Aggregae Unis: producs, workers,... Coss producion coss (economic coss!) invenory coss(holding and shorage) capaciy change coss Producion Managemen 48

7 Aggregae Planning Spreadshee Mehods Zero Invenory Plan Precision Transfer, Inc. Produces more han 300 differen precision gears ( he aggregaion uni is a gear!). Las year (=260 working days) Precision made gears of various kinds wih an average of 40 workers gears per year 40 x 260 worker-days/year = 3,98 -> 4 gears/ worker-day Aggregae demand forecas for precision gear: Monh January February March April May June Toal Demand Producion Managemen 49

8 Aggregae Planning holding coss: $5 per gear per monh backlog coss: $15 per gear per monh hiring coss: $450 per worker lay-off coss: $600 per worker wages: $15 per hour ( all workers are paid for 8 hours per day) here are currenly 35 workers a Precision currenly no invenory Producion plan? Producion Managemen 50

9 Aggregae Planning Zero Invenory Plan produce exacly amoun needed per period adap workforce Producion Managemen 51

10 Aggregae Planning Number of Workers (hired / laid off) Change in Workforce January February March April May June Monh Producion Managemen 52

11 Aggregae Planning Level Work Force Plan backorders allowed consan numbers of workers demand over he planning horizon gears a worker can produce over he horizon 19670/(4x129)=38,12 -> 39 workers are always needed Producion Managemen 53

12 Aggregae Planning Invenory: January: = 516 February: March: = -66! -Backorders: 66 x $15 = $ number of unis (invenory / back-orders) ne invenory -400 January February March April May June Monh Producion Managemen 54

13 Aggregae Planning no backorders are allowed workers= cumulaive demand/(cumulaive days x unis/workers/day) January: 2760/(21 x 4) = 32,86 -> 33 workers February: ( )/[(21+20) x 4] = 37,07 -> 38 workers. March: /(64 x 4) =>40 workers April: /(85 x 4) => 40 workers May: /(107 x 4) => 40 workers June: 19670/(129 x 4) => 39 workers Producion Managemen 55

14 Aggregae Planning Example Mixed Plan The number of workers used is an educaed guess based on he zero invenory and level work force plans! Producion Managemen 56

15 Spreadshee Mehods Summary Zero-Inv. Level/BO Level/No BO Mixed Hiring cos Lay-off cos Labor cos Holding cos BO cos Toal cos Workers Producion Managemen 57

16 Aggregae Planning Linear Programming Approaches o Aggregae Planning Producion Managemen 58

17 Aggregae Planning Producion Managemen 59

18 Aggregae Planning Decision Variables: P Knumber of unis produced in period W Knumber of workers available in period H Knumber of workers hired in period L Knumber of workers laid off in period I Knumber of unis held in invenory in period B Knumber of unis backordered in period Producion Managemen 60

19 Aggregae Planning Producion Managemen 61

20 Aggregae Planning Example: Precision Transfer Planning horizon: 6 monhs T= 6 Coss do no vary over ime C P =0 d : days in monh C W = $120d C H = $450 C L = $600 C I =$5 We assume ha no backorders are allowed! no producion coss and no backorder coss are included! Demand January February March April May June Toal Producion Managemen 62

21 Linear Program Model for Precision Transfer Producion Managemen 63

22 Aggregae Planning LP soluion (oal cos = $ ,60) Producion Invenory Hired Laid off Workers January 2940,00 180,00 0,00 0,00 35,00 February 3232,86 92,86 5,41 0,00 40,41 March 3877,14 0,00 1,73 0,00 42,14 April 3540,00 0,00 0,00 0,00 42,14 May 3180,00 0,00 0,00 6,01 36,14 June 2900,00 0,00 0,00 3,18 32,95 Producion Managemen 64

23 Aggregae Planning Rounding LP soluion January February March April May June Toal Days Unis/Worker Demand Workers Capaciy Capaciy - Demand Cumulaive Difference Produced Ne invenory Hired Laid Off Coss Producion Managemen 65

24 Aggregae Planning Pracical Issues variables and consrains LP/MIP Solvers: CPLEX, XPRESS-MP,... Exensions Bounds I I L I U I I U L 0.05W Training W = W + H L 1 1 Producion Managemen 66

25 Aggregae Planning Transporaion Models supply poins: periods, iniial invenory demand poins: periods, excess demand, final invenory nw = capaciy during period D = forecased number of unis demanded in period C C P I = he cos o produce one uni in period = he cos o hold one uni in invenory in period Producion Managemen 67

26 Aggregae Planning iniial invenory: 50 final invenory: 75 Producion Managemen 68

27 Aggregae Planning Ending invenory Excess capaciy Available capaciy Beginning invenory Period 1 Period 2 Period Demand Producion Managemen 69

28 Aggregae Planning Exension: capaciy n W demand producion coss holding coss overime: overime capaciy is 90, 90 and 75 in period 1, 2 and 3; overime coss are $16, $18 and $ 20 for he hree periods respecively; backorders:unis can be backordered a a cos of $5 per uni-monh; producion in period 2 can be used o saisfy demand in period 1 Producion Managemen 70

29 Aggregae Planning Beginning invenory Period 1 Period 2 Period 3 Demand Regular ime Overime Regular ime Overime Regular ime Overime Ending invenory Excess capaciy Available capaciy Producion Managemen 71

30 Aggregae Planning Disaggregaing Plans aggregae unis are no acually produced, so he plan should consider individual producs disaggregaion maser producion schedule Quesions: In which order should individual producs be produced? e.g.: shores run-ou ime How much of each produc should be produced? e.g.: balance run-ou ime R = I / D i i i Producion Managemen 72

31 Aggregae Planning Advanced Producion Planning Models Muliple Producs same noaion as before add subscrip i for produc i Objecive funcion min T N W H L C W + C H + C L + = 1 i= 1 C P i P i + C I i I i Producion Managemen 73

32 Aggregae Planning subjec o N i=1 1 ni Pi W = 1, 2,..., T W = W + H L 1 i i 1 i i =1,2,...,T I = I + P D =1,2,...,T; i=1,2,...,n P W, H, L, I 0 =1,2,...,T; i=1,2,...,n i, i Producion Managemen 74

33 Aggregae Planning Compuaional Effor: 10 producs, 12 periods: 276 variables, 144 consrains 100 producs, 12 periods: 2436 variables, 1224 consains Producion Managemen 75

34 Aggregae Planning Example: Carolina Hardwood Produc Mix Carolina Hardwood produces 3 ypes of dining ables; There are currenly 50 workers employed who can be hired and laid off a any ime; Iniial invenory is 100 unis for able1, 120 unis for able 2 and 80 unis for able 3; Producion Managemen 76

35 Aggregae Planning The number of unis ha can be made by one worker per period: Forecased demand, uni cos and holding cos per uni are: Producion Managemen 77

36 Aggregae Planning Producion Managemen 78

37 Aggregae Planning Muliple Producs and Processes Producion Managemen 79

38 Aggregae Planning Producion Managemen 80

39 Aggregae Planning Example: Cacus Cycles process plan CC produces 2 ypes of bicycles, sree and road; Esimaed demand and curren invenory: available capaciy(hours) and holding coss per bike: Capaciy(hours) Holding Machine Worker Sree Road Producion Managemen 81

40 Aggregae Planning process coss ( process1, process2) and resource requiremen per uni: Producion Managemen 82

41 Aggregae Planning Producion Managemen 83

42 Aggregae Planning soluion: Objecive Funcion value = $368, Producion Managemen 84

43 Aggregae Planning - Exensions Hopp/Spearman, S Noaion:...amoun of X i c Kcapaciy of produc i r K ne profi from one uni of i S i a ij j Kamoun of Kime required on worksaion worksaion producedin period produc i produc i sold in period j o produce one uni of produc i jin period in unis (consisen wih a ij ) Producion Managemen 85

44 Aggregae Planning - Exensions Backorders max d I I i i X i a i, S S I I X + i i, i i 1 I i + i m i= 1 subjec o m i= 1 = = ij = 1 c + I d, I r S X i i i i j i i S 0 h I i i + i π I i for all i, for all j, for all i, for all i, for all i, Producion Managemen 86

45 Aggregae Planning - Exensions Overime l j O m i= 1 X j a i, = overime a worksaion j in period in hours S cos of max subjec o = ij m n + (ri Si hi Ii π iii ) = 1 i= 1 j= 1 X i, I i + i, I c i one hour of j,o + O j j 0 overime a worksaion j for all i, for all i, l O j Producion Managemen 87

46 Aggregae Planning - Exensions Yield loss 1 α 1 β 1 γ α β γ α, β, γ Kfracion of y ij Kcumulaive yield from saion j onward (including saion j) for produc i we mus release d y ij oupu ha is los unis of i ino saion j Producion Managemen 88

47 Aggregae Planning - Exensions Basic model + Yield loss exension (no backorders) max subjec o d I i X i m i= 1 i, a = ij y S S X ij I = 1 i= 1 i i, i i 1 I c i m (r S d j i i + X 0 i i h I S i i i ) for all i, for all j, for all i, for all i, Producion Managemen 89

48 Aggregae Planning - WorkforcePlanning Single produc, workforce resizing, overime allocaion Noaion b = number of man - hours required o produce one uni of produc l = cos of regular ime in dollars/man - hour l = cos of overime in dollars/man - hour e = cos o increase workforce by one man - hour per period e = cos o decrease workforce by one man - hour per period W = workforce in period in man - hours of regular ime H = increase in workforce from period -1o in man - hours F O = decrease in workforce from period -1o in man - hours = overime in period in hours Producion Managemen 90

49 Aggregae Planning - WorkforcePlanning LP formulaion: maximize ne profi, including labor, overime, holding, and hiring/firing coss subjec o consrains on sales, capaciy,... max subjec o d a I j W bx X X, = = W S S I W, = 1 1 I { rs h I lw l O eh e F } c 1 j + d X + H + O S, O W F,, F, H, for all for all j, for all for all for all 0 for all Producion Managemen 91

50 AP-WP Example Revenue: 1000$ worker capaciy: 168h/monh iniially 15 workers no iniial invenory holding coss: 10$/uni/monh regular labor coss: 35$/hour overime: 150% of regular hiring coss: 2500$ (2500/168 ~ 15$ per man-hour) lay-off coss: 1500$ (1500/168 ~ 9$ per man-hour) no backordering demands over 12 monhs: 200, 220, 230, 300, 400, 450, 320, 180, 170,170, 160, 180 demands mus be me! (S=D) Producion Managemen 92

51 AP-WP Example(con.) Deermine over a 12 monh horizon: Number of workers: W Oupu: X Overime use: O Invenory: I (H, F are addiional choice variables in he model) Producion Managemen 93

52 Aggregae Planning - WorkforcePlanning Producion Managemen 94

53 Aggregae Planning - WorkforcePlanning Producion Managemen 95

54 Aggregae Planning - WorkforcePlanning Producion Managemen 96

55 Aggregae Planning-Summary The following scenarios have been discussed: single produc, single resource, single process find: workforce, oupu, invenory (w. or w/o backorders) muliple producs, single resource, single process find: workforce, all oupus, all invenories (w. or w/o backorders) muliple producs, muliple resources, muliple processes (workforce given) find: all oupus, all invenories, use of processes Producion Managemen 97

56 Aggregae Planning-Summary The following scenarios have been discussed: muliple producs, muliple worksaions (worksaion capciies given) find: all sales, all oupus, all invenories (w. or w/o backorders) muliple producs, muliple worksaions find: all sales, all oupus, all invenories (w. or w/o backorders), OT single produc, muliple worksaions, one resource find: workforce, all sales, all oupus, all invenories (w. or w/o backorders), OT Producion Managemen 98

57 Aggregae Planning Work o do: Examples: 5.7, 5.8abcdef, 5.9abcd, 5.10abcd, 5.16abcd, 5.21, 5.22, 5.29, 5.30 Replace capaciy columns of able in problem 5.29 wih Monh Machine Worker Minicase BF SWING II Producion Managemen 99

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