Aggregate Planning Planning the overall use of the organizations assets Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall,

Aggregate PlanningAggregate Planning

Planning the overall use of the Planning the overall use of the organization’s assetsorganization’s assets

Applied Management Science for Decision Making, 1e Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD© 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD

OVERVIEWOVERVIEW

ObjectivesObjectives

Definition of the Definition of the Quasi-UnitQuasi-Unit

StrategiesStrategies

Computer ApplicationsComputer Applications

Master Production ScheduleMaster Production Schedule

Aggregate Planning Aggregate Planning DefinitionDefinition

The overall employment of the firm’s facilities and other resources over the next 3 to 18 months so as to satisfy customer demand for all goods and services at minimum cost, as well as certain corporate policies such as “no layoffs” and “no overtime pay”.

Corporate PolicyCorporate Policy Requirements Requirements EXAMPLESEXAMPLES

A stable work force 100% in-house production Sufficient inventories to reduce the

likelihood of stockouts to =< 5% Overtime labor hours not to exceed

10% of all regular labor hours

The The Quasi-UnitQuasi-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.

The Meal Quasi-UnitThe Meal Quasi-Unit

x ounces of meat x ounces of fish x ounces of poultry x gallons of water for

cooking / cleaning x amount of gas and

electricity for cooking

x amount of labor time and cost for cooking

x amount of labor time and cost for serving

x ounces of vegetables of various types

And much more!

RESTAURANT

The Quasi - UnitThe Quasi - Unit

Gallons of Beer

Not individual brands, bottles, kegs, cans, varieties

Tons of Steel Not ingots or beams of varying tensile strength

MANUFACTURING

The Quasi - UnitThe Quasi - Unit

Faculty-to-Student Contact Hours

Transcends the number of hours of classroom

instruction, student advising, directed studies,

internships, and so on.

Airline Passenger Miles Flown

Transcends the number of flights by specific

aircraft over specific routes.

SERVICE SECTOR SERVICE SECTOR

The Pseudo / Composite UnitThe Pseudo / Composite UnitALTERNATE NAMES FOR THE QUASI - UNIT

Sometimes, 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

The The NewNew Quasi - Unit Definition Quasi - Unit Definition

A SINGLE PRODUCTSINGLE PRODUCT representing a family of individual products that:

are processed on the same machines are processed by the same workers share the same general machine setup have similar cost structures, carry costs, and output rates share more / less the same parts and assemblies as well as physical charac- teristics

Quasi-Unit InterpretationsQuasi-Unit Interpretations

Mid-sized ProductMid-sized Product in a line of similar products ( autos, refrigerators )

Only ProductOnly Product made in a particular manufacturing plant

Basic ProductBasic Product with minor differences between models

Hybrid ProductHybrid Product or “cross” between several types of products produced in one or more plants

Other

Basic Product with Minor Differences

UNITED STATESUNITED STATES

MEXICOMEXICO


2013 Ford Fusion

2013 Lincoln MKZ


2013 Ford Fusion

2013 Lincoln MKZ

Overview of the ProcessOverview of the Process

A 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.

AGGREGATE PLANNINGAGGREGATE PLANNING

Overview of the ProcessOverview of the ProcessAGGREGATE PLANNINGAGGREGATE PLANNING

Cost estimates are developed and the lowest cost aggregate plan is adopted.

Plan is then decomposed or disaggregated into a series of master production schedules that specify the exact number of products and services to be generated on a daily, weekly, or monthly basis. ( by make, model, color, and options )

The Aggregate PlanThe Aggregate Plan

I. Specified production rate for each time period.

II. Specified level of inventory for each time period.

III. Specified labor force size for each time period.

* ( USUALLY 1 MONTH OR 1 QUARTER )

*

MINIMUM DATA REQUIREMENTSMINIMUM DATA REQUIREMENTS

The Three Principal Strategies

Inventory Cushion or Level Work Force

Skeleton Force or Cadre

Chase or Matching

AGGREGATE PLANNING

Inventory Cushion StrategyInventory Cushion Strategy

Labor force size is fixed. Production rate is fixed. Inventories riserise during slowslow demand periods. Inventories shrinkshrink during highhigh demand periods. Inventory stockout costs are reduced. Overtime pay, hiring, firing, subcontracting, and

production rate change costs are eliminated.

The Inventory CushionThe Inventory Cushion

DURINGHIGH

DEMANDDECREASESDECREASES

DURINGLOW

DEMANDINCREASESINCREASES

THE INVENTORY CUSHION INSULATES THE FACTORY FROM DEMAND FLUCTUATIONS

Skeleton Force or Cadre Skeleton Force or Cadre StrategyStrategy

The permanent labor force size is usually set for the lowest monthly or quarterly forecasted quasi- unit demand.

Higher demand must then be met by scheduling overtime, hiring temporary workers, subcontracting, and so on.

Lower demand, if any, is tolerated as paid idle time.

SKELETON FORCE SKELETON FORCE STRATEGYSTRATEGY U.S. ARMYU.S. ARMY

ACTIVE DUTY480,000

46%

RESERVE / NATIONAL GUARD563,000

54%

$100,000.TO PAY

AND EQUIPEACH

SOLDIERPERMANENT

WORK FORCE

$25,000.TO PAY

AND EQUIPEACH

SOLDIERPART-TIME

WORK FORCE

*

RETIRED AND STANDBY RESERVES ACTIVATED ONLY IF ABSOLUTELY NECESSARY - 12,000,000 TROOPS

SKELETON FORCE SKELETON FORCE STRATEGYSTRATEGY HIGHER HIGHER

EDUCATIONEDUCATION

In 1984, full-time faculty were 80% of all faculty




BETWEEN 1995 – 1997, 67% OF ALL NEW PROFESSORSWERE HIRED AS ADJUNCTS, IN ORDER TO SAVE $$$

Chase Chase oror Matching Strategy Matching Strategy

Calls for monthly / quarterly adjustment of the

labor 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.

Two Types of Two Types of CostsCosts

Those that Those that WILLWILL change from one change from one

developed plan developed plan

to the nextto the next

Those that Those that WILL NOTWILL NOT change from one change from one developed plandeveloped plan

to the nextto the next

NON-RELEVANTNON-RELEVANTRELEVANTRELEVANT

THEIR INCLUSION WOULD NOT DIFFERENTIATE ONE PLAN FROM ANOTHERTHEIR INCLUSION WOULD NOT DIFFERENTIATE ONE PLAN FROM ANOTHER

NON-RELEVANT COSTS ARE OMITTED FROM THE AGGREGATE PLANNING ANALYSIS SINCE THEY DO

NOT ASSIST THE PLANNER IN IDENTIFYING THE MOST COST- EFFECTIVE PLAN.

Possible Plan CostsPossible Plan Costs

Regular Hourly Labor Rate

Overtime Hourly Labor Rate

Direct Labor Unit Cost Direct Materials Unit

Cost Overhead Unit Cost Labor Severance Cost

per Unit

Subcontracting Unit Cost

Inventory Unit Carry Cost

Inventory Unit Stockout Cost

Production Rate Change Costs

Labor Hire/Train Cost per Unit

AGGREGATE PLANNINGAGGREGATE PLANNING

Possible Data InputPossible Data Input

Productivity per worker per day

Number of production days in the plan

Accurate monthly or quarterly demand forecasts

Existing plant capacity

Required labor hours per unit

Required direct materials per unit

Corporate policy regarding overtime,

subcontracting,

backordering, etc. Machine processing

hours per unit

AGGREGATE PLANNING

Possible Possible Decision VariablesDecision VariablesAGGREGATE PLANNINGAGGREGATE PLANNING

Production Rate Changes Production Subcontracting Overtime Labor Hours Equipment Rental Backordering Temporary Employees Part-time Employees

USEFUL FOR DEVELOPINGUSEFUL FOR DEVELOPINGALTERNATIVE PLANSALTERNATIVE PLANS

UNDER VARIOUSUNDER VARIOUSSTRATEGIESSTRATEGIES

The Selected Aggregate PlanThe Selected Aggregate Plan

MODERATE INVENTORY LEVELS MODERATE STOCKOUT COSTS A SMALL NUMBER OF PRODUCTION

RATE CHANGES WITH RELATIVELY

SMALL MAGNITUDES

ALMOST ALWAYS IT IS A MIXED STRATEGY CHARACTERIZED BY :

The The “ “ 44thth “ “

StrategyStrategy

Aggregate PlanningAggregate PlanningTWO STARTING ASSUMPTIONSTWO STARTING ASSUMPTIONS

PASSIVEPASSIVE

ASSUMES THE PRODUCTDEMANDPATTERN

CANNOT BEALTERED

AGGRESSIVEAGGRESSIVE

ASSUMES THEPRODUCTDEMANDPATTERNCAN BE

ALTEREDIF NECESSARY

Product Demand PatternProduct Demand Pattern PRE - STABILIZATIONPRE - STABILIZATION

THE DEMAND RATE MAY VARY DRAMATICALLYFROM THE NORMAL PRODUCTION RATE,

MAKING AGGREGATE PLANNING DIFFICULTAND LESS COST EFFECTIVE

( time )

( u

nit

s )

Normal Production Output

Variable Product Demand

Product Demand PatternProduct Demand Pattern

Normal Production Output

( u

nit

s )

( time )

Variable Product Demand

STABILIZATIONSTABILIZATION

THE LEVELING OF DEMAND TO APPROACHTHE NORMAL PRODUCTION RATE MAKESAGGREGATE PLANNING MUCH EASIER

AND MORE COST EFFECTIVE

Some Some Demand Demand Leveling Leveling TacticsTactics

Heavy advertising, price discounts, coupons, and contests during periods of low demand.

Little or no advertising and price increases during periods of high demand.

Production of countercyclic, similar products.

Reservation systems.

Aggregate Planning withQM for Windows

We Select Aggregate Planning

From The Menu

WE SELECTAGGREGATE

PLANNINGFROM THE MENU

WE DESIRE TOSET UP A

NEW PROGRAM To

We Select The1st

Menu

WE SELECT THEFIRST OPTION

THE DIALOGUEBOX APPEARS

WE SELECT SIX PERIODSFOR THE AGGREGATE PLAN

AND LABEL THEM“JANUARY” THROUGH

“JUNE”

IF DEMAND EXCEEDSPRODUCT SUPPLY IN

ANY MONTHLY PERIOD,IT IS ASSUMED THOSE

SALES ARE LOST FOREVER

THE DATA TABLE APPEARS

Inventory Cushion StrategyInventory Cushion StrategyEXAMPLEEXAMPLE

OBJECTIVE

TO MAINTAIN A CONSTANT-SIZE WORK FORCE AND UNIFORM PRODUCTIONRATE OVER THE SPECIFIED PLANNING PERIOD.

ASSUMPTIONS

DEMAND FORECAST OF 6,200 QUASI-UNITS OVER THE NEXT SIX MONTHS ONE-HUNDRED-TWENTY- FOUR AVAILABLE PRODUCTION DAYS QUASI-UNIT INVENTORY CARRY COST IS $5.00 PER MONTH EACH WORKER PRODUCES FIVE QUASI-UNITS PER DAY EACH WORKER IS PAID $120.00 PER DAY

CALENDAR

MONTH

ACTUAL

PRODUCTION

QUASI-UNIT

FORECAST

CUSHION NET CHANGE

ENDINGINVENTORY

JAN 1100 900 +200 200

FEB 900 700 +200 400

MAR 1050 800 +250 650

APR 1050 1200 - 150 500

MAY 1100 1500 - 400 100

JUN 1000 1100 - 100 0

6200units

6200units

1850 units

22 DAYSAVAILABLE

X 50 UNITS

DAILY

18 DAYSAVAILABLE

X50 UNITS

DAILY

FIRM MUST PRODUCE 50 UNITS DAILY IN ORDER TOMEET THE SIX-MONTH DEMAND ( 6,200 / 124 DAYS )

∑21 DAYS

AVAILABLEX

50 UNITSDAILY

Inventory Cushion StrategyInventory Cushion Strategy

1.6 hours of labor per quasi-unit1.6 hours of labor per quasi-unitXX

$15.00 / hour average labor rate$15.00 / hour average labor rate

Quasi-UnitQuasi-UnitDemandDemand

ForecastsForecasts

Quasi-UnitQuasi-UnitInventoryInventory

Carry CostCarry Costperper

MonthMonthPlannedPlannedMonthlyMonthly

ProductionProduction

Inventory Inventory Cushion StrategyCushion StrategyEXAMPLE

TOTAL COSTS: $158,050.00

INVENTORY CARRY COSTS…………...….$9,250.00 ( 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)

Strategy Total CostStrategy Total Cost Total Labor CostTotal Labor Cost Total Inventory Carry CostsTotal Inventory Carry Costs

Quasi-Unit DemandQuasi-Unit DemandRegular TimeRegular Time

Quasi-Unit ProductionQuasi-Unit Production

The Inventory CushionThe Inventory Cushion( peaks at mid-term of plan )( peaks at mid-term of plan )

Skeleton Force StrategySkeleton Force StrategyEXAMPLE

OBJECTIVE

TO BUILD A PERMANENT LABOR FORCE AROUND A SPECIFIC LEVEL OF DEMAND, TOLERATING PAID IDLE TIME DURING LOWER DEMAND

PERIODS AND INCURRING COSTS OF OVERTIME LABOR OR SUBCONTRACTING DURING HIGHER DEMAND PERIODS.

THE SPECIFIC LEVEL OF DEMAND IS USUALLY THE LOWEST LEVEL OF DEMAND

Skeleton Force StrategySkeleton Force StrategyEXAMPLEEXAMPLE

ASSUMPTIONS

A PERMANENT LABOR FORCE BUILT AROUND THE LOWEST DEMAND PERIOD IN ORDER TO SAVE ON RETIREMENT BENEFITS, HEALTH INSURANCE , PAID VACATIONS, LEAVE, ETC.

FEBRUARY HAS THE LOWEST FORECASTED QUASI-UNIT DEMAND (700 units)

FEBRUARY HAS EIGHTEEN (18) AVAILABLE PRODUCTION DAYS

FIRM WANTS TO SUBCONTRACT PRODUCTION TO AN OUTSIDE COMPANY WHENEVER QUASI-UNIT DEMAND EXCEEDS THE PERMANENT LABOR FORCE CAPABILITY

SUBCONTRACTED QUASI-UNITS COST THE FIRM $10.00 EACH


CALCULATIONS

DAILY FEBRUARY PRODUCTION…....700/18 days = 39 units daily

IN-HOUSE PRODUCTION…..39 units/day x 124 days = 4,836 units

SUBCONTRACTED PRODUCTION…….6,200 – 4,836 = 1,364 units

REQUIRED WORKERS……..…39/5 units per worker per day = 7.8

Quasi-UnitQuasi-UnitSubcontractSubcontract

CostCost

In February, in-house production was 39 units per day for 18 days = 702 quasi-unitswhich resulted in overproduction of 2 quasi-units

In March, in-house production was 39 units per day for 21 days = 819 quasi-unitswhich resulted in overproduction of 19 quasi-units

In April, in-house production was 39 units per day for 21 days = 819 units.The shortfall seems to be ( 1200 - 819 ) = 381 units, but it was reduced to

360 quasi-units, due to the 21 quasi-unit surplus generated in February and March

Over Production in Regular TimeOver Production in Regular Time


COSTS: $129,704.00

LABOR COST...$116,064.00 ( 7.8 workers x $120.00 per day x 124 days)

SUBCONTRACT COST………..$13,640.00 (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 via house production or subcontracting)

RT - Regular Time Production

Sub - Subcontracted Production

SubcontractingSubcontracting

Over ProductionOver ProductionInIn

Regular TimeRegular Time

In-House ProductionIn-House ProductionShortfallShortfall

( Subcontracted )( Subcontracted )

Chase or Matching StrategyChase or Matching StrategyEXAMPLE

OBJECTIVE

TO HIRE OR TERMINATE PERSONNEL AS NEEDED IN ORDER TO MATCH PRODUCTION TO DEMAND, PERIOD-BY-PERIOD, RESULTING IN THE ELIMINATION OR DRASTIC REDUCTION OF BOTH INVENTORY CARRY AND STOCKOUT COSTS.


ASSUMPTIONS

EACH QUASI-UNIT REQUIRES 1.6 HOURS OF DIRECT LABOR

PERSONNEL TERMINATION COST IS PRORATED AT $15.00 PER MANUFACTURED QUASI-UNIT CANCELLED

PERSONNEL RECRUITING AND TRAINING COST IS PRORATED AT $10.00 PER MANUFACTURED QUASI-UNIT ADDED

EACH WORKER EARNS $15.00 PER HOUR ON AVERAGE.

EXAMPLE: If sales were forecasted to be 100 units lower in the next period, then the prorated employee termination costs would be ( 100 x $15.00 ) $1500.00 If sales were forecasted to be 100 units higher in the next period, then the prorated employee hiring and training costs would be ( 100 x $10.00 ) $1000.00

PRORATED TERMINATION COSTPRORATED TERMINATION COST

PRORATED HIRE/TRAIN COSTPRORATED HIRE/TRAIN COST

MONTH DEMANDFORECAST

PRODUCTION

COSTS

FORECASTCHANGE

HIRE/FIREFIRE

COSTS

TOTALCOSTS

JANJAN 900900 $21,600.$21,600. $21,600.$21,600.

FEBFEB 700700 $16,800.$16,800. (200)x$15 $3,000. $19,800.$19,800.

MARMAR 800800 $19,200.$19,200. 100 x $10100 x $10 $1,000.$1,000. $20,200.$20,200.

APRAPR 12001200 $28,800.$28,800. 400 x $10400 x $10 $4,000.$4,000. $32,800.$32,800.

MAYMAY 15001500 $36,000.$36,000. 300 x $10300 x $10 $3,000.$3,000. $39,000.$39,000.

JUNJUN 11001100 $26,400.$26,400. (400)x$15 $6,000. $32,400.$32,400.

∑∑ $148,800.$148,800. $8,000. $8,000.

$9,000.$9,000.

$165,800.$165,800.

900 UNITS x

1.6 HOURS x

$15.00 =

$21,600.00

700 UNITSX

1.6 HOURSX

$15.00=

$16,800.00

TOTAL MONTHLY COST = PRODUCTION + HIRE( TOTAL MONTHLY COST = PRODUCTION + HIRE( FIRE FIRE ) COSTS) COSTS

The Chase StrategyThe Chase Strategy


COSTS : $165,800.00

REGULAR TIME LABOR COST……………………………..$148,800.

HIRE / TERMINATION COSTS………………………………..$17,000

INVENTORY CARRY AND STOCKOUT COSTS………………... $ 0.

6200 UNITS x 1.6 HOURS/UNIT = 9,920 HOURS x $15.00/HOUR

$8,000.00 HIRE COSTS + $9,000.00 TERMINATION COSTS

PRODUCTION MATCHES DEMAND EXACTLY PERIOD-BY-PERIOD

$17,000.00 totalbroken downinto hire/fire

andtermination

Period Demand = Period Production

CUMULATIVE PRODUCTION

EQUALSCUMULATIVE

DEMAND( ONE IN THE SAME LINE )

Aggregate Plan ExamplesAggregate Plan ExamplesPOSTSCRIPT

I. If only three strategies or plans were generated and

evaluated, the firm would select the skeleton forceskeleton force since it has the lowest projected total costs.

II. Direct material cost, direct machine hour cost, and applied overhead per quasi-unit were identical under all three plans. Hence, they are non-relevant costs and routinely omitted from the analysis.

The Relevant Range of ActivityThe Relevant Range of Activity

0 1000 2000 3000 4000 5000 6000 7000 80000 1000 2000 3000 4000 5000 6000 7000 8000

CUMULATIVE PRODUCTION ( CUMULATIVE PRODUCTION ( IN UNITS )IN UNITS )

CCOOSSTTSS

SEMI-VARIABLE COSTS

VARIABLE COSTS

Relevant Range 1

Relevant Range 2

Relevant Range 3

X6200

FIXED COSTS

PRODUCTION OF 6200 QUASI-UNITSFALLS JUST WITHIN THE RELEVANTCOST RANGE OF 6000-8500 UNITS.THEREFORE, UNIT DIRECT LABOR,

DIRECT MATERIALS, AND OVERHEADREMAIN THE SAME

6000 8500


III. The mix of resources—labor force size, production rate, and inventory level as well as subcontracting ----and their timing allowed the development of 3 unique aggregate plan proposals and associated costs.

IV. In the skeleton force strategy, the firm elected to augment the capacity of its small permanent labor force by subcontracting exclusively. Variations of this strategy could, and usually are generated using overtime hours, temporary labor hours, and subcontracting exclusively or in combination.


V. Corporate policies may impose limitations on the use of subcontracting, overtime hours, inventory levels, production rates, machines, available days for production, and so on.


TransportationAlgorithm

Transportation Algorithm Transportation Algorithm Approach to Aggregate PlanningApproach to Aggregate Planning

When aggregate planning is viewed as an allocation of capacity to meet forecasted demand.

Produces an optimal plan for minimizing costs !

Can specify regular, overtime, and subcontracting production in each time period.

Can specify inventory carryover from period to period.

Will not handle non-linear costs such as hiring and layoff.


ForecastedQuasi-UnitDemand

700 Quasi-Units can beproduced onregular timeeach month

50 Quasi-Units can beproduced on overtime

each month

The number of quasi-unitsthat can be

subcontracted outeach month

Beginning Inventory ( from May )

Per Unit Labor Costs

Inventory Carry Costsper Quasi-Unit

per Month

June 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.

This shows the costs and headings to be inserted in each cell for the

normal transportation tableau,if there had been one.

Note that cells that are notallowed to be filled, have

a prohibitive cost of $9,999.00 !

Also note that the dummy columnfor unused capacity in each

month is missing in the originaltransportation tableau !

For each month that a quasi-unit remains in inventory, an additional$2.00 carry (holding) cost is added to its original cost

Shows the total number of quasi-unitsthat should be made underregular-time, overtime, and

subcontracting over the life of the3-month aggregate plan.

Total quasi-unit productionover the 3-month

aggregate plan

The only carry costs were for theinitial inventory of 100 quasi-units

Here, we are using the regulartransportation algorithm module to solve the same

aggregate planning problem

For each month that a quasi-unit is kept in inventory, a $2.00 carry cost will be

added to itsoriginal production

cost

June 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 in June, 700 units of regular time production in July itself, 50 units made overtime in July, and 150 units subcontracted in July.

August demand of 750 was met by 700 units of regular time production in August and 50 units made overtime in August.

The 1st feasible solution

The 2nd feasible solution

The 3rd feasible and

optimal solution


Sample Data +

Basic Template

The Simplex MethodThe Simplex Method

An alternative to the transportation method of linear programming.

Must be employed where non-linear costs are involved, such as hiring and layoff.

Minimum and maximum constraints can be put on the desired amounts of regular labor, overtime labor, subcontracting, backordering, and many other factors on a monthly, bi-monthly, quarterly, or semi-annual basis.


Constraint formulation is quite complex.

The optimal solution virtually always must be obtained via computer.

Dozens or hundreds of variables are involved.


A 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 hours of 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.

EXAMPLE


If 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.


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

Defining the Decision Variables


Minimize Z = 60X1 + 90X2 + 110X3 + 140X4 + 60X5 + 90X6

Subject to:

X1 + X2 => 700 Q1 demand

X3 + X4 + X5 + X6 => 3,200 Q2 demand

5X1 + 5X3 =< 9,000 Q1 straight-time labor

5X5 =< 9,000 Q2 straight-time labor

5X2 + 5X4 =< 900 Q1 overtime labor

5X6 =< 900 Q2 overtime labor

The Model


SimplexLinear

Programming

X1 = 580 units made and shipped on straight- time in 1st QtrX2 = 120 units made on overtime and shipped in 1st QtrX3 = 1,220 units made on straight-time in 1st Qtr 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 and shipped in 2nd Qtr



Documents

Aggregate Planning Planning the overall use of the organizations assets Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall,