Chapter 5. Aggregate Planning

Chaper 5 Aggregae Planning

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

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

Aggregae Planning Example: one produc (plasic case) wo injecion molding machines, 550 pars/hour one worker, 55 pars/hour seady sales 80.000 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

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

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

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 41.383 gears of various kinds wih an average of 40 workers. 41.383 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 2760 3320 3970 3540 3180 2900 19.670 Producion Managemen 49

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

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

Aggregae Planning 10 8 9 Number of Workers (hired / laid off) 6 4 2 0-2 -4-2 2-1 -4 Change in Workforce -6-6 -8 January February March April May June Monh Producion Managemen 52

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

Aggregae Planning Invenory: January: 3276-2760 = 516 February: 516 + 3120 3320 March: 316 + 3588 3670 = -66! -Backorders: 66 x $15 = $990 600 number of unis (invenory / back-orders) 500 400 300 200 100 0-100 -200-300 516 316-66 -330-78 0 358 ne invenory -400 January February March April May June Monh Producion Managemen 54

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: (2760+3320)/[(21+20) x 4] = 37,07 -> 38 workers. March: 10.050/(64 x 4) =>40 workers April: 13.590/(85 x 4) => 40 workers May: 16.770/(107 x 4) => 40 workers June: 19670/(129 x 4) => 39 workers Producion Managemen 55

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

Spreadshee Mehods Summary Zero-Inv. Level/BO Level/No BO Mixed Hiring cos 4950 1800 2250 3150 Lay-off cos 7800 0 0 4200 Labor cos 59856 603720 619200 593520 Holding cos 0 4160 6350 3890 BO cos 0 7110 0 990 Toal cos 611310 616790 627800 605180 Workers 33 39 40 35 Producion Managemen 57

Aggregae Planning Linear Programming Approaches o Aggregae Planning Producion Managemen 58

Aggregae Planning Producion Managemen 59

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

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 2760 3320 3970 3540 3180 2900 19.670 Producion Managemen 62

Linear Program Model for Precision Transfer Producion Managemen 63

Aggregae Planning LP soluion (oal cos = $600 191,60) 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

Aggregae Planning Rounding LP soluion January February March April May June Toal Days 21 20 23 21 22 22 129 Unis/Worker 84 80 92 84 88 88 516 Demand 2760 3320 3970 3540 3180 2900 19670 Workers 35 41 42 42 36 33 229 Capaciy 2940 3280 3864 3528 3168 2904 19684 Capaciy - Demand 180-40 -106-12 -12 4 14 Cumulaive Difference 180 140 34 22 10 14 400 Produced 2930 3280 3864 3528 3168 2900 19670 Ne invenory 170 130 24 12 0 0 336 Hired 0 6 1 0 0 0 7 Laid Off 0 0 0 0 6 3 9 Coss 89050 101750 116490 105900 98640 88920 600750 Producion Managemen 65

Aggregae Planning Pracical Issues 100.000 variables and 40.000 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

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

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

Aggregae Planning 1 2 3 Ending invenory Excess capaciy Available capaciy Beginning 0 2 4 6 0 50 invenory Period 1 Period 2 Period 3 50 10 12 14 16 0 350 150 50 75 75-11 13 15 0 300 300 - - 12 14 0 350 350 Demand 200 300 400 75 75 1050 Producion Managemen 69

Aggregae Planning Exension: 1 2 3 capaciy n W 350 350 300 demand 400 300 400 producion coss 10 11 12 holding coss 2 2 2 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

Aggregae Planning Beginning invenory Period 1 Period 2 Period 3 Demand Regular ime Overime Regular ime Overime Regular ime Overime 1 2 3 Ending invenory Excess capaciy 0 2 4 6 0 25 25 10 12 14 16 0 350 16 18 20 22 0 50 40 16 11 13 15 0 275 75 23 18 20 22 0 90 22 17 12 14 0 300 30 25 20 22 0 75 400 300 400 75 130 Available capaciy 50 350 90 350 90 300 75 1305 Producion Managemen 71

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

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

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

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

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

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

Aggregae Planning Muliple Producs and Processes Producion Managemen 79

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 1 8600 17000 5 6 2 8500 16600 6 7 3 8800 17200 5 7 Producion Managemen 81

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

Aggregae Planning soluion: Objecive Funcion value = $368,756.25 Producion Managemen 84

Aggregae Planning - Exensions Hopp/Spearman, S. 522-540 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

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

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

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

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

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

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

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

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

Aggregae Planning - WorkforcePlanning Producion Managemen 94

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

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

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 1 1350 19000 2 1270 19000 3 1350 19500 Minicase BF SWING II Producion Managemen 99