Aggregate Planning - univie.ac.at

1 Chapter 5 Aggregate PlanningProduction Management44 Supply Chain Planning Matrixproduction distributionsales procurementStrategic Network PlanningMaster PlanningDistribution PlanningTransport PlanningProduction PlanningDemand PlanningDemand Fulfilment & AT PSchedulingMaterial Requirements Planninglong-termmid-termshort-termProdu ction Management45 Supply Chain Planning Matrixproduction distributionsales procurement materials program plant location physical distribution product program supplier selection production systemstructure strategic sales cooperationsplanning personnel Planning material contracts mid-term salesplanninglong-termmid-termshort-term master productionscheduling capacity Planning distributionplanning personnel Planning ordering materials short-term salesplanning lot-sizing machine scheduling shop floor control warehousereplenishement transport planninginformation flowsflow of goodsProduction Management46 Aggregate PlanningaExample:`one product (plastic case)`two injection molding machines, 550 parts/hour`one worker, 55 parts/hour`steady sales cases/month `4 weeks/month, 5 days/week, 8h/day`how many workers?

2 Ain real life constant demand is rare`change demand `produce a constant rate anyway`vary productionProduction Management47 Aggregate PlanningaInfluencing demand `do not satisfy demand `shift demand from peak periods to nonpeak periods`produce several products with peak demand in different periodaPlanning Production`Production plan: how much and when to make each product`rolling Planning horizon`long range plan`intermediate-range plan units of measurements are aggregates product family plant department changes in workforce, additional machines, subcontracting, overtime,..`Short-term planProduction Management48 Aggregate PlanningaAspects of Aggregate Planning `Capacity: how much a production system can make` Aggregate Units: products, workers,..`Costs production costs (economic costs!) inventory costs(holding and shortage) capacity change costsProduction Management49 Aggregate PlanningaSpreadsheet MethodsaZero Inventory Plan`Precision Transfer, Inc.

3 Produces more than 300 different precision gears ( the aggregation unit is a gear!). `Last year (=260 working days) Precision made gears of various kinds with an average of 40 workers.` gears per year`40 x 260 worker-days/year = 3,98 -> 4 gears/ worker-day` Aggregate demand forecast for precision Management50 Aggregate Planning `holding costs: $5 per gear per month`backlog costs: $15 per gear per month`hiring costs: $450 per worker`lay-off costs: $600 per worker`wages: $15 per hour ( all workers are paid for 8 hours per day)`there are currently 35 workers at Precision`currently no inventory`Production plan?Production Management51 Aggregate PlanningaZero Inventory Plan`produce exactly amount needed per period`adapt workforceProduction Management52 Aggregate Planning -292-1-6-4-8-6-4-20246810 January FebruaryMarchAprilMayJuneMonthNumber of Workers (hired / laid off)Change in WorkforceProduction Management53 Aggregate PlanningaLevel Work Force Plan`backorders allowed`constant numbers of workers` demand over the Planning horizon`gears a worker can produce over the horizon`19670/(4x129)=38,12 -> 39 workers are always neededProduction Management54 Aggregate Planning `Inventory: January: 3276 - 2760 = 516`February: 516 + 3120 3320`March: 316 + 3588 3670 = -66!

4 -Backorders: 66 x $15 = $990516316-66-330-780358-400-300-200-100 0100200300400500600 JanuaryFebr uar yMarchAprilMayJuneMonthnumber of units (inventory / back-orders)net inventoryProduction Management55 Aggregate Planningano backorders are allowed`workers= cumulative demand /(cumulative days x units/workers/day)`January: 2760/(21 x 4) = 32,86 -> 33 workers`February: (2760+3320)/[(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 workersProduction Management56 Aggregate PlanningaExample Mixed Plan`The number of workers used is an educated guess based on the zeroinventory and level work force plans!Production Management57 Spreadsheet Methods Level/No BOMixedHiring cost4950180022503150 Lay-off cost7800004200 Labor cost59856603720619200593520 Holding cost0416063503890BO cost071100990 Total cost611310616790627800605180 Workers33394035 Production Management58 Aggregate PlanningaLinear Programming Approaches to Aggregate PlanningProduction Management59 Aggregate PlanningProduction Management60 Aggregate PlanningDecision Variables:number of units produced in period tnumber of workers available in period tnumber of workers hired in period tnumber of workers laid off in period tnumber of units hetttttPWHLIKKKKKld in inventory in period tnumber of units backordered in period ttBKProduction Management61 Aggregate PlanningProduction Management62 Aggregate PlanningaExample: Precision Transfer` Planning horizon.

5 6 months T= 6`Costs do not vary over time CtP=0`dt: days in month t`CtW= $120dt`CtH= $450`CtL= $600`CtI=$5`We assume that no backorders are allowed!`no production costs and no backorder costs are included!` demand JanuaryFebruary MarchAprilMayJuneTotal Production Management63 Linear Program Model for Precision TransferProduction Management64 Aggregate PlanningaLP solution (total cost = $600 191,60)ProductionInventory HiredLaid off WorkersJanuary2940,00 180,000,000,0035,00 February3232,8692,865,410,0040,41 Mar ch3877,140,001,730,0042,14 Apr il3540,000,000,000,0042,14 May3180,000,000,006,0136,14 June2900,000,000,003,1832,95 Production Management65 Aggregate PlanningaRounding LP solutionJanuaryFebruary MarchAprilMayJuneTotalDays21202321222212 9 Units/W orker848092848888516 Demand27603320397035403180290019670 Workers35 4142423633229 Capacity29403280386435283168290419684 Capacity - Demand180-40-106-12-12414 Cumulative Difference18014034221014400 Produced29303280386435283168290019670 Net inventory170130241200336 Hired0 610007 Laid Off0 000639 Costs89050101750116490105900986408892060 0750 Production Management66 Aggregate PlanningaPractical Issues` variables and constraints`LP/MIP Solvers: CPLEX, XPRESS-MP.

6 AExtensions` tIIWWW H L =+ Production Management67 Aggregate PlanningaTransportation Models`supply points: periods, initial inventory` demand points: periods, excess demand , final inventoryPtItcapacity during period tforecasted number of units demanded in period tCthe cost to produce one unit in period tCthe cost to hold one unit in inventory in period ttttnWD====Production Management68 Aggregate Planninginitial inventory: 50final inventory: 75 Production Management69 Aggregate PlanningAvailablecapacity024605050101214 160350150507575-111315 0300300--12140350350 Demand1050 Excess capacityEnding inventory123 Beginning inventoryPeriod 1 Period 2 Period 37520030040075 Production Management70 Aggregate Planning `Extension: overtime: overtime capacity is 90, 90and 75in period 1, 2 and 3; overtime costs are $16, $18and $ 20for the three periods respectively; backorders:units can be backordered at a cost of $5per unit-month.

7 Production in period 2 can be used to satisfy demand in period 1t123capacity ntWt350350300demand 400300400production costs101112holding costs222 Production Management71 Aggregate PlanningAvailablecapacity024602525101214 1603501618202205040161113150275752318202 2090221712140300302520220751305 DemandExcess capacityEnding inventory12313040030040075 Beginning inventoryPeriod 1 Regular tim eOvertim eRegular tim eOvertim ePeriod 3 Regular tim eOvertim ePeriod 290350507530090350 Production Management72 Aggregate PlanningaDisaggregating Plans` Aggregate units are not actually produced, so the plan should consider individual products`disaggregation`master production scheduleaQuestions:`In which order should individual products be produced? : shortest run-out time`How much of each product should be produced? : balance run-out timeiiiDIR/=Production Management73 Aggregate PlanningaAdvanced Production Planning Models`Multiple Products`same notation as before`add subscript i for product i`Objective function == ++++TtNiitIititPittLttHttWtICPCLCHCWC11m inProduction Management74 Aggregate PlanningN i=11it1it,subject to11, 2.

8 , t=1,2,..,TI t=1,2,..,T; i=1,2,..,NP,, ,0 t=1,2,..,T; i=1,2,..,Nittittt ttititittttitPWtTnWW H LIPDWH LI = =+ =+ Production Management75 Aggregate PlanningaComputational Effort:`10 products, 12 periods: 276 variables, 144 constraints`100 products, 12 periods: 2436 variables, 1224 constaintsProduction Management76 Aggregate Planning `Example: Carolina Hardwood Product Mix Carolina Hardwood produces 3 types of dining tables; There are currently 50 workers employed who can be hired and laid off at any time; Initial inventory is 100 units for table1, 120 units for table 2 and 80 units for table 3;Production Management77 Aggregate Planning The number of units that can be made by one worker per period: Forecasted demand , unit cost and holding cost per unit are:Production Management78 Aggregate PlanningProduction Management79 Aggregate PlanningaMultiple Products and ProcessesProduction Management80 Aggregate PlanningProduction Management81 Aggregate Planning `Example: Cactus Cycles process plan`CC produces 2 types of bicycles, street and road.

9 `Estimated demand and current inventory:`available capacity(hours) and holding costs per bike:t Machine Worker StreetRoad186001700056285001660067388001 720057 Capacity(hours)HoldingProduction Management82 Aggregate Planning `process costs ( process1, process2) and resource requirement per unit:Production Management83 Aggregate PlanningProduction Management84 Aggregate Planningasolution: Objective Function value = $368, Management85 Aggregate Planning - ExtensionsaHopp/Spearman, S. 522-540aNotation: tperiodin produced iproduct ofamount ..Xit)a t with(consisten units in t period in j on workstatiofcapacity ciproduct ofunit one produce toj on workstation required timea tperiod in sold iproduct ofamount product ofunit one fromprofit net rijjtijiKKKKitSiProduction Management86 Aggregate Planning - ExtensionsaBackordersi,tIISXi,tIIIi,tSXI Ij,tcXi,tdSdIIhSitititititititititititjt itititittiitiitmi allfor 0, allfor allfor allfor a allfor subject tor max,,1m1iijt1ti1 = += + + = =+= Production Management87 Aggregate Planning - ExtensionsaOvertimei,tIISXi,tcXlIIhSliti tititjtitnjitiitiitj allfor 0O,, allfor Oasubject toO)

10 (r maxhoursin t periodin jtion at worksta overtime Ojtion at worksta overtime ofhour one ofcost jt,,m1ijtijt1t1jtim1ijt + == +=== += Production Management88 Aggregate Planning - ExtensionsaYield loss jstation into i of units yd releasemust weiproduct for j)station (including onward jstation from yield cumulativelost ist output tha offraction ,,ijKKijy 1 1 1 Production Management89 Aggregate Planning - ExtensionsaBasic model + Yield loss extension (no backorders)i,tISXi,tSXIIj,tci,tdSdIhSiti titititititjtyXititititiitijit allfor 0 allfor allfor allfor subject to)r( max,,1m1iat1tim1iij += === Production Management90 Aggregate Planning - WorkforcePlanningaSingle product, workforce resizing, overtime allocationaNotationhoursin t periodin overtimeOhours-manin t to1- tperiod from cein workfor decreaseFhours-manin t to1- tperiod from cein workfor increaseHmeregular ti of hours-manin t periodin workforceWperiodper hour -man oneby workforcedecrease cost toeperiodper hour -man oneby workforceincrease cost toehour -ndollars/main overtime ofcost hour-ndollars/main meregular ti ofcost lproduct ofunit one produce torequired hours-man ofnumber btttt===== == ==lProduction Management91 Aggregate Planning - WorkforcePlanningaLP formulation: maximize net profit, including labor, overtime, holding, and hiring/firing costsasubject to constraints on sales, capacity.)