2OVERVIEW Definition of the Quasi-Unit Strategies Computer Applications ObjectivesDefinition of the Quasi-UnitStrategiesComputer ApplicationsMaster Production Schedule
3Aggregate Planning Definition The overall employment of the firm’s facilities andother resources over the next 3 to 18 months so asto satisfy customer demand for all goods and servicesat minimum cost, as well as certain corporate policiessuch as “no layoffs” and “no overtime pay”.
4Corporate Policy Requirements EXAMPLES A stable work force100% in-house productionSufficient inventories to reduce thelikelihood of stockouts to =< 5%Overtime labor hours not to exceed10% of all regular labor hours
5The Quasi-Unit A unit of product that is representative of all the firm’s goods and services.Examples are appliances and vehicles in manufacturing.Examples are airline passenger miles flown and restaurant meals in the service sector.
6The Meal Quasi-Unit x ounces of meat RESTAURANTx ounces of meatx ounces of fishx ounces of poultryx gallons of water forcooking / cleaningx amount of gas andelectricity for cookingx amount of labor time and cost for cookingx amount of labor time and cost for servingx ounces of vegetables of various typesAnd much more!
7The Quasi - Unit Not individual brands, bottles, kegs, cans, varieties MANUFACTURINGGallons of BeerNot individual brands, bottles, kegs, cans, varietiesTons of SteelNot ingots or beams of varying tensile strength
8The Quasi - Unit Transcends the number of hours of classroom SERVICE SECTORFaculty-to-Student Contact HoursTranscends the number of hours of classroominstruction, student advising, directed studies,internships, and so on.Airline Passenger Miles FlownTranscends the number of flights by specificaircraft over specific routes.
9The Pseudo / Composite Unit ALTERNATE NAMES FOR THE QUASI - UNITSometimes, the unit does not exist at all!It is a collection of square feet of sheet metal,several dozen screws or bolts, a variety ofcomponents, assemblies, ounces of glue,paint, fabric, and so on.STRICTLY USED FORPLANNING PURPOSES
10The New Quasi - Unit Definition A SINGLE PRODUCT representinga family of individual products that:are processed on the same machinesare processed by the same workersshare the same general machine setuphave similar cost structures, carrycosts, and output ratesshare more / less the same parts andassemblies as well as physical charac-teristics
11Quasi-Unit Interpretations OtherMid-sized Product in a line of similar products ( autos, refrigerators )Only Product made in a particular manufacturing plantBasic Product with minor differences between modelsHybrid Product or “cross” between several types of products produced in one or more plants
12Basic Product with Minor Differences UNITED STATESMEXICO
13Basic Product with Minor Differences 2013 Ford Fusion2013 Lincoln MKZ
14Basic Product with Minor Differences 2013 Ford Fusion2013 Lincoln MKZ
15Overview of the Process AGGREGATE PLANNINGA quasi-unit demand forecast is developed for 3 to 18 months into the future.The firm then manipulates production rates, inventory levels, and work force levels to generate a series of aggregate plans that meet the forecasted demand.
16Overview of the Process AGGREGATE PLANNINGCost estimates are developed and the lowestcost aggregate plan is adopted.Plan is then decomposed or disaggregatedinto a series of master production schedulesthat specify the exact number of products andservices to be generated on a daily, weekly, ormonthly basis. ( by make, model, color, and options )
18The Aggregate Plan Specified production rate for each time period. MINIMUM DATA REQUIREMENTSSpecified production rate for each time period.Specified level of inventory for each time period.Specified labor force size for each time period.** ( USUALLY 1 MONTH OR 1 QUARTER )
19The Three Principal Strategies AGGREGATE PLANNINGInventory Cushion or Level Work ForceSkeleton Force or CadreChase or Matching
20Inventory Cushion Strategy Labor force size is fixed.Production rate is fixed.Inventories rise during slow demand periods.Inventories shrink during high demand periods.Inventory stockout costs are reduced.Overtime pay, hiring, firing, subcontracting, and production rate change costs are eliminated.
21The Inventory Cushion DURING HIGH DEMAND DURING LOW DEMAND DECREASES INCREASESTHE INVENTORY CUSHION INSULATES THE FACTORY FROM DEMAND FLUCTUATIONS
22Skeleton Force or Cadre Strategy The permanent labor force size is usually set forthe lowest monthly or quarterly forecasted quasi-unit demand.Higher demand must then be met by schedulingovertime, hiring temporary workers, subcontract-ing, and so on.Lower demand, if any, is tolerated as paid idle time.
23SKELETON FORCE STRATEGY U.S. ARMY$100,000.TO PAYANDEQUIPEACHSOLDIERPERMANENT WORK FORCE$25,000.TO PAYANDEQUIPEACHSOLDIERPART-TIMEWORK FORCE*ACTIVE DUTY480,00046%RESERVE / NATIONAL GUARD563,00054%RETIRED AND STANDBY RESERVES ACTIVATED ONLY IF ABSOLUTELY NECESSARY - 12,000,000 TROOPS
24SKELETON FORCE STRATEGY HIGHEREDUCATIONIn 1984, full-time faculty were 80% of all facultyIn 1987, full-time faculty were 67% of all facultyIn 2001, full-time faculty were 55% of all facultyIn 2003, full-time faculty were 50% of all facultyBETWEEN 1995 – 1997, 67% OF ALL NEW PROFESSORSWERE HIRED AS ADJUNCTS, IN ORDER TO SAVE $$$
25Chase or Matching Strategy Calls for monthly / quarterly adjustment of thelabor force size as necessary to match produc-tion to demand.Eliminates or reduces inventory carry costs and stockout costs.It generates substantial hiring, training, and termination costs and risks the degradation of employee morale and loyalty.
26Two Types of Costs Those that WILL change from one developed plan to the nextThose that WILL NOT change from one developed planto the nextRELEVANTNON-RELEVANT
27NOT ASSIST THE PLANNER IN IDENTIFYING THE MOST COST- EFFECTIVE PLAN. NON-RELEVANT COSTS ARE OMITTED FROM THE AGGREGATE PLANNING ANALYSIS SINCE THEY DONOT ASSIST THE PLANNER IN IDENTIFYING THEMOST COST- EFFECTIVE PLAN.THEIR INCLUSION WOULD NOT DIFFERENTIATE ONE PLAN FROM ANOTHER
28Possible Plan Costs Regular Hourly Labor Rate AGGREGATE PLANNINGRegular Hourly Labor RateOvertime Hourly Labor RateDirect Labor Unit CostDirect Materials Unit CostOverhead Unit CostLabor Severance Cost per UnitSubcontracting Unit CostInventory Unit Carry CostInventory Unit Stockout CostProduction Rate Change CostsLabor Hire/Train Cost per Unit
29Possible Data Input Productivity per worker per day AGGREGATE PLANNINGProductivity per worker per dayNumber of production days in the planAccurate monthly or quarterly demand forecastsExisting plant capacityRequired labor hours per unitRequired direct materials per unitCorporate policy regarding overtime,subcontracting,backordering, etc.Machine processing hours per unit
30Possible Decision Variables AGGREGATE PLANNINGProduction Rate ChangesProduction SubcontractingOvertime Labor HoursEquipment RentalBackorderingTemporary EmployeesPart-time EmployeesUSEFUL FOR DEVELOPINGALTERNATIVE PLANSUNDER VARIOUS STRATEGIES
31The Selected Aggregate Plan ALMOST ALWAYS IT IS A MIXED STRATEGY CHARACTERIZED BY :MODERATE INVENTORY LEVELSMODERATE STOCKOUT COSTSA SMALL NUMBER OF PRODUCTIONRATE CHANGES WITH RELATIVELYSMALL MAGNITUDESThe“ 4th “Strategy
33Product Demand Pattern PRE - STABILIZATIONTHE DEMAND RATE MAY VARY DRAMATICALLYFROM THE NORMAL PRODUCTION RATE,MAKING AGGREGATE PLANNING DIFFICULTAND LESS COST EFFECTIVE( units )Normal Production OutputVariable Product Demand( time )
34Product Demand Pattern STABILIZATIONTHE LEVELING OF DEMAND TO APPROACHTHE NORMAL PRODUCTION RATE MAKESAGGREGATE PLANNING MUCH EASIERAND MORE COST EFFECTIVENormal Production Output( units )Variable Product Demand( time )
35Some Demand Leveling Tactics Heavy advertising, price discounts, coupons,and contests during periods of low demand.Little or no advertising and price increasesduring periods of high demand.Production of countercyclic, similar products.Reservation systems.
43Inventory Cushion Strategy EXAMPLEOBJECTIVETO MAINTAIN A CONSTANT-SIZE WORK FORCE AND UNIFORM PRODUCTIONRATE OVER THE SPECIFIED PLANNING PERIOD.ASSUMPTIONSDEMAND FORECAST OF 6,200 QUASI-UNITS OVER THE NEXT SIX MONTHSONE-HUNDRED-TWENTY- FOUR AVAILABLE PRODUCTION DAYSQUASI-UNIT INVENTORY CARRY COST IS $5.00 PER MONTHEACH WORKER PRODUCES FIVE QUASI-UNITS PER DAYEACH WORKER IS PAID $ PER DAY
44∑ Inventory Cushion Strategy JAN 1100 900 +200 200 FEB 700 400 MAR FIRM MUST PRODUCE 50 UNITS DAILY IN ORDER TOMEET THE SIX-MONTH DEMAND ( 6,200 / 124 DAYS )CALENDARMONTHACTUALPRODUCTIONQUASI-UNITFORECASTCUSHION NET CHANGEENDING INVENTORYJAN1100900+200200FEB700400MAR1050800+250650APR1200- 150500MAY1500- 400100JUN1000- 1006200units1850 units22 DAYSAVAILABLEX50 UNITSDAILY18 DAYSAVAILABLEX50 UNITSDAILY21 DAYSAVAILABLEX50 UNITSDAILY∑
451.6 hours of labor per quasi-unit $15.00 / hour average labor rate InventoryCarry CostperMonthQuasi-UnitDemandForecastsPlannedMonthlyProduction1.6 hours of labor per quasi-unitX$15.00 / hour average labor rate
46Inventory Cushion Strategy EXAMPLETOTAL COSTS: $158,050.00INVENTORY CARRY COSTS…………...….$9, ( 1,850 units x $5.00/unit )OVERTIME, HIRE/FIRE, SUBCONTRACTING $0.00 ( fixed work force )PRODUCTION RATE CHANGE COSTS………$0.00 ( uniform production rate )LABOR COSTS..$148,800.00…..( 50/5 = 10 workers x $120.00/day x 124 days)
48Quasi-Unit Production Regular TimeQuasi-Unit ProductionQuasi-Unit Demand
49( peaks at mid-term of plan ) The Inventory Cushion( peaks at mid-term of plan )
50Skeleton Force Strategy EXAMPLEOBJECTIVETO BUILD A PERMANENT LABOR FORCE AROUND A SPECIFIC LEVEL OFDEMAND, TOLERATING PAID IDLE TIME DURING LOWER DEMANDPERIODS AND INCURRING COSTS OF OVERTIME LABOR ORSUBCONTRACTING DURING HIGHER DEMAND PERIODS.THE SPECIFIC LEVEL OF DEMAND IS USUALLYTHE LOWEST LEVEL OF DEMAND
51Skeleton Force Strategy EXAMPLEASSUMPTIONSA PERMANENT LABOR FORCE BUILT AROUND THE LOWEST DEMAND PERIODIN ORDER TO SAVE ON RETIREMENT BENEFITS, HEALTH INSURANCE , PAIDVACATIONS, LEAVE, ETC.FEBRUARY HAS THE LOWEST FORECASTED QUASI-UNIT DEMAND (700 units)FEBRUARY HAS EIGHTEEN (18) AVAILABLE PRODUCTION DAYSFIRM WANTS TO SUBCONTRACT PRODUCTION TO AN OUTSIDE COMPANYWHENEVER QUASI-UNIT DEMAND EXCEEDS THE PERMANENT LABOR FORCECAPABILITYSUBCONTRACTED QUASI-UNITS COST THE FIRM $10.00 EACH
52Skeleton Force Strategy EXAMPLECALCULATIONSDAILY FEBRUARY PRODUCTION… /18 days = 39 units dailyIN-HOUSE PRODUCTION…..39 units/day x 124 days = 4,836 unitsSUBCONTRACTED PRODUCTION…….6,200 – 4,836 = 1,364 unitsREQUIRED WORKERS……..…39/5 units per worker per day = 7.8
53which resulted in overproduction of 2 quasi-units Over Production in Regular TimeQuasi-UnitSubcontractCostIn February, in-house production was 39 units per day for 18 days = 702 quasi-unitswhich resulted in overproduction of 2 quasi-unitsIn March, in-house production was 39 units per day for 21 days = 819 quasi-unitswhich resulted in overproduction of 19 quasi-unitsIn April, in-house production was 39 units per day for 21 days = 819 units.The shortfall seems to be ( ) = 381 units, but it was reduced to360 quasi-units, due to the 21 quasi-unit surplus generatedin February and March
54Skeleton Force Strategy EXAMPLECOSTS: $129,704.00LABOR COST...$116, ( 7.8 workers x $ per day x 124 days)SUBCONTRACT COST………..$13, (1,364 units x $10.00 per unit)OVERTIME, HIRE/FIRE, TRAINING COSTS……..$0.00 (rejected options)INVENTORY CARRY COST……..$0.00 (all demand satisfied exactly viahouse production or subcontracting)
58Chase or Matching Strategy EXAMPLEOBJECTIVETO HIRE OR TERMINATE PERSONNEL AS NEEDED IN ORDERTO MATCH PRODUCTION TO DEMAND, PERIOD-BY-PERIOD,RESULTING IN THE ELIMINATION OR DRASTIC REDUCTION OFBOTH INVENTORY CARRY AND STOCKOUT COSTS.
59Chase or Matching Strategy EXAMPLEASSUMPTIONSEACH QUASI-UNIT REQUIRES 1.6 HOURS OF DIRECT LABORPERSONNEL TERMINATION COST IS PRORATED AT $15.00PER MANUFACTURED QUASI-UNIT CANCELLEDPERSONNEL RECRUITING AND TRAINING COST IS PRORATEDAT $10.00 PER MANUFACTURED QUASI-UNIT ADDEDEACH WORKER EARNS $15.00 PER HOUR ON AVERAGE.
60PRORATED TERMINATION COST PRORATED HIRE/TRAIN COST EXAMPLE: If sales were forecasted to be 100 units lower in thenext period, then the prorated employee terminationcosts would be ( 100 x $15.00 ) $If sales were forecasted to be 100 units higher in thenext period, then the prorated employee hiring andtraining costs would be ( 100 x $10.00 ) $
61The Chase Strategy ∑ JAN 900 FEB 700 MAR 800 APR 1200 MAY 1500 JUN TOTAL MONTHLY COST = PRODUCTION + HIRE( FIRE ) COSTSMONTHDEMAND FORECASTPRODUCTIONCOSTSFORECAST CHANGEHIRE/FIRETOTAL COSTSJAN900$21,600.FEB700$16,800.(200)x$15$3,000.$19,800.MAR800$19,200.100 x $10$1,000.$20,200.APR1200$28,800.400 x $10$4,000.$32,800.MAY1500$36,000.300 x $10$39,000.JUN1100$26,400.(400)x$15$6,000.$32,400.∑$148,800.$8,000.$9,000.$165,800.900 UNITSx1.6 HOURS$15.00=$21,600.00700 UNITSX1.6 HOURS$15.00=$16,800.00
62Chase or Matching Strategy EXAMPLECOSTS : $165,800.00REGULAR TIME LABOR COST……………………………..$148,800.HIRE / TERMINATION COSTS………………………………..$17,000INVENTORY CARRY AND STOCKOUT COSTS………………... $ 0.6200 UNITS x 1.6 HOURS/UNIT = 9,920 HOURS x $15.00/HOUR$8, HIRE COSTS + $9, TERMINATION COSTSPRODUCTION MATCHES DEMAND EXACTLY PERIOD-BY-PERIOD
65PRODUCTION EQUALS CUMULATIVE DEMAND ( ONE IN THE SAME LINE )
66Aggregate Plan Examples POSTSCRIPTIf only three strategies or plans were generated andevaluated, the firm would select the skeleton forcesince it has the lowest projected total costs.Direct material cost, direct machine hour cost, andapplied overhead per quasi-unit were identical underall three plans. Hence, they are non-relevant costsand routinely omitted from the analysis.
67The Relevant Range of Activity PRODUCTION OF 6200 QUASI-UNITSFALLS JUST WITHIN THE RELEVANTCOST RANGE OF UNITS.THEREFORE, UNIT DIRECT LABOR,DIRECT MATERIALS, AND OVERHEADREMAIN THE SAMEVARIABLE COSTSSEMI-VARIABLECOSTSCOSTRelevant Range 2Relevant Range 3Relevant Range 1FIXED COSTS6200XCUMULATIVE PRODUCTION ( IN UNITS )
68Aggregate Plan Examples POSTSCRIPTThe mix of resources—labor force size, productionrate, and inventory level as well as subcontracting----and their timing allowed the development of 3unique aggregate plan proposals and associatedcosts.In the skeleton force strategy, the firm elected toaugment the capacity of its small permanent laborforce by subcontracting exclusively. Variations ofthis strategy could, and usually are generated us-ing overtime hours, temporary labor hours, andsubcontracting exclusively or in combination.
69Aggregate Plan Examples POSTSCRIPTCorporate policies may impose limitations on theuse of subcontracting, overtime hours, inventorylevels, production rates, machines, available daysfor production, and so on.
77The number of quasi-units Beginning Inventory ( from May ) that can besubcontracted outeach monthPer Unit Labor CostsBeginning Inventory ( from May )50 Quasi-Units can beproduced on overtimeeach monthForecastedQuasi-UnitDemand700 Quasi-Units can beproduced onregular timeeach monthInventory Carry Costsper Quasi-Unitper Month
78June demand of 800 is met by 50 units of beginning inventory, 700 units of June regular production, and 50 units of June subcontracted production.July demand of 1000 is met by 50 units of beginning inventory, 50 units of June overtime production,700 units of July regular production, 50 units of July overtime production, and 150 units of subcontractedJuly production.August demand of 750 is met by 700 units of August regular production, and 50 units of August overtimeproduction.
79For each month that a quasi-unit remains in inventory, an additional $2.00 carry (holding) cost is added to its original costThis shows the costs and headingsto be inserted in each cell for thenormal transportation tableau,if there had been one.Note that cells that are notallowed to be filled, havea prohibitive cost of$9, !Also note that the dummy columnfor unused capacity in eachmonth is missing in the originaltransportation tableau !
80Total quasi-unit production over the 3-month aggregate plan Shows the total number of quasi-unitsthat should be made underregular-time, overtime, andsubcontracting over the life of the3-month aggregate plan.The only carry costs were for theinitial inventory of 100 quasi-units
81Here, we are using the regular transportation algorithm module to solve the sameaggregate planning problem
85For each month that aquasi-unit is kept ininventory, a $2.00carry cost will beadded to itsoriginal productioncost
86June demand of 800 was met by 100 units of beginning inventory (from May) and 700 units of regular time production in June itself.July demand of 1,000 was met by 50 units made overtime in June, 50 units subcontracted inJune, 700 units of regular time production in July itself, 50 units made overtime in July, and150 units subcontracted in July.August demand of 750 was met by 700 units of regular time production in August and 50units made overtime in August.
87The 1st feasible solution The 2nd feasible solution
101The Simplex Method An alternative to the transportation method of linear programming.Must be employed where non-linear costs areinvolved, such as hiring and layoff.Minimum and maximum constraints can be puton the desired amounts of regular labor, overtimelabor, subcontracting, backordering, and manyother factors on a monthly, bi-monthly, quarterly,or semi-annual basis.
102The Simplex Method Constraint formulation is quite complex. The optimal solution virtually always must beobtained via computer.Dozens or hundreds of variables are involved.
103The Simplex MethodEXAMPLEA production manager must develop an aggregate plan for the nexttwo quarters of the year. The plant produces computer terminals.700 terminals need to be shipped to customers in the 1st quarter and3,200 in the 2nd quarter. It is the firm’s policy to ship orders in thequarter in which they are ordered.It takes 5 hrs labor to produce each terminal, and only 9,000 hoursof straight-time labor is available in each of the two quarters.Overtime can be used, but the firm limits overtime in each quarterto 10% of straight-time labor available. Labor costs $12.00 per hourat the straight-time rate and $18.00 per hour at the overtime rate.
104The Simplex MethodIf a terminal is produced in one quarter and shipped in the nextquarter, a carrying cost of $50.00 is incurred.Requirement:How many terminals should be produced on straight-time andovertime in each of the two quarters to minimize straight-timelabor, overtime labor, and carrying costs?The market requirements, straight-time labor availability, andovertime policy must be adhered to.
105The Simplex Method Defining the Decision Variables X1 = terminals made on straight-time in 1st quarter and shipped in 1st quarter.X2 = terminals made on overtime in 1st quarter and shipped in the 1st quarter.X3 = terminals made on straight-time in 1st quarter and shipped in the 2nd quarter.X4 = terminals made on overtime in 1st quarter and shipped in the 2nd quarter.X5 = terminals made on straight-time in 2nd quarter and shipped in the 2nd quarter.X6 = terminals made on overtime in 2nd quarter and shipped in the 2nd quarter.Q1 = 1st quarter , Q2 = 2nd quarter, Z = total cost of the plan
106The Simplex Method The Model Minimize Z = 60X1 + 90X X X4 + 60X5 + 90X6Subject to:X1 + X => Q1 demandX3 + X4 + X5 + X6 => 3,200 Q2 demand5X X =< 9,000 Q1 straight-time labor5X =< 9,000 Q2 straight-time labor5X X =< Q1 overtime labor5X6 =< Q2 overtime labor
107Aggregate Planning with QM for Windows SimplexLinearProgramming
114X1 = 580 units made and shipped on straight- time in 1st QtrX2 = 120 units made on overtime and shippedin 1st QtrX3 = 1,220 units made on straight-time in 1stQtr and shipped during 2nd QtrX5 = 1,800 units made and shipped on straight-time in 2nd QtrX6 = 180 units made on overtime in 2nd Qtr andshipped in 2nd Qtr