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CATEDRA 8
PLANIFICACION DE LA CAPACIDAD, UBICACION Y LAYOUT
Capacidad (Capacity)Capacidad (Capacity)
● Diseño de la capacidad. (Design and Effective Diseño de la capacidad. (Design and Effective Capacity). Capacity).
● Estrategia y capacidad (Capacity and Estrategia y capacidad (Capacity and Strategy). Strategy).
● Planificación (Planificación (CapacityCapacity Planning).Planning).● Analisis de equilibrio (Breakeven Analysis for Analisis de equilibrio (Breakeven Analysis for
Single-Product & Multiproduct).Single-Product & Multiproduct).● Arboles de decision (Decision Trees to Arboles de decision (Decision Trees to
Capacity Decisions).Capacity Decisions).
Definición
The throughput, or the number of units a facility can hold, receive, store, or produce in a period of time
Determines fixed costs
Determines if demand will be satisfied
Three time horizons
Modify capacityModify capacity Use capacityUse capacity
Horizontes de planeación
Intermediate-Intermediate-range range planningplanningMPMP
Subcontract Add personnelAdd equipment Build or use inventory Add shifts
Short-range Short-range planningplanningCPCP
Schedule jobsSchedule personnel Allocate machinery
Long-range Long-range planningplanningLPLP
Add facilitiesAdd long lead time equipment
Figure S7.1Figure S7.1
Design and Effective Capacity
Design capacity is the maximum theoretical output of a systemNormally expressed as a rate
Effective capacity is the capacity a firm expects to achieve given current operating constraintsOften lower than design capacity
Utilization and Efficiency
Utilization is the percent of design capacity achieved
Efficiency is the percent of effective capacity achieved
Utilization = Actual Output/Design Capacity
Efficiency = Actual Output/Effective Capacity
Ejemplo (Bakery)
Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 - 8 hour shifts
Design capacity Design capacity = (7 x 3 x 8) x (1,200) = 201,600= (7 x 3 x 8) x (1,200) = 201,600 rolls rolls
Ejemplo (Bakery)
Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 - 8 hour shifts
Design capacity Design capacity = (7 x 3 x 8) x (1,200) = 201,600= (7 x 3 x 8) x (1,200) = 201,600 rolls rolls
Utilization Utilization = 148,000/201,600 = 73.4%= 148,000/201,600 = 73.4%
Ejemplo (Bakery)
Actual production last week = Actual production last week = 148,000148,000 rolls rollsEffective capacity = Effective capacity = 175,000175,000 rolls rollsDesign capacity = Design capacity = 1,2001,200 rolls per hour rolls per hourBakery operates Bakery operates 77 days/week, days/week, 3 -3 - 88 hour shifts hour shifts
Design capacity Design capacity = (7 x 3 x 8) x (1,200) = 201,600= (7 x 3 x 8) x (1,200) = 201,600 rolls rolls
Utilization Utilization = 148,000/201,600 = 73.4%= 148,000/201,600 = 73.4%
Efficiency Efficiency = 148,000/175,000 = 84.6%= 148,000/175,000 = 84.6%
Ejemplo (Bakery)
Actual production last week = Actual production last week = 148,000148,000 rolls rollsEffective capacity = Effective capacity = 175,000175,000 rolls rollsDesign capacity = Design capacity = 1,2001,200 rolls per hour rolls per hourBakery operates Bakery operates 77 days/week, days/week, 3 -3 - 88 hour shifts hour shiftsEfficiency Efficiency = 84.6%= 84.6%Efficiency of new line Efficiency of new line = 75%= 75%
Expected Output = Expected Output = ((Effective CapacityEffective Capacity)()(EfficiencyEfficiency))
= (175,000)(.75) = 131,250= (175,000)(.75) = 131,250 rolls rolls
Capacity and Strategy
Capacity decisions impact all 10 decisions of operations management as well as other functional areas of the organization
Capacity decisions must be integrated into the organization’s mission and strategy
Managing DemandManaging Demand
Demand exceeds capacityDemand exceeds capacity Curtail demand by raising prices, scheduling Curtail demand by raising prices, scheduling
longer lead timelonger lead time
Long term solution is to increase capacityLong term solution is to increase capacity
Capacity exceeds demandCapacity exceeds demand Stimulate marketStimulate market
Product changesProduct changes
Adjusting to seasonal demandsAdjusting to seasonal demands Produce products with complimentary demand Produce products with complimentary demand
patternspatterns
Economies and Diseconomies of Scale
Economies Economies of scaleof scale
Diseconomies Diseconomies of scaleof scale
25 - Room 25 - Room Roadside MotelRoadside Motel 50 - Room 50 - Room
Roadside MotelRoadside Motel
75 - Room 75 - Room Roadside MotelRoadside Motel
Number of RoomsNumber of Rooms2525 5050 7575
Av
era
ge
un
it c
ost
Av
era
ge
un
it c
ost
(do
llars
pe
r ro
om
per
nig
ht)
(do
llars
pe
r ro
om
per
nig
ht)
Figure S7.2Figure S7.2
Capacity ConsiderationsCapacity Considerations
Forecast demand accuratelyForecast demand accurately
Understanding the technology and Understanding the technology and capacity incrementscapacity increments
Find the optimal operating level Find the optimal operating level (volume)(volume)
Build for changeBuild for change
Tactics for Matching Capacity to Demand
1.1. Making staffing changesMaking staffing changes
2.2. Adjusting equipment and processesAdjusting equipment and processes Purchasing additional machineryPurchasing additional machinery
Selling or leasing out existing equipmentSelling or leasing out existing equipment
3.3. Improving methods to increase Improving methods to increase throughputthroughput
4.4. Redesigning the product to facilitate more Redesigning the product to facilitate more throughputthroughput
Complementary Demand Patterns
4,000 4,000 –
3,000 3,000 –
2,000 2,000 –
1,000 1,000 –
J F M A M J J A S O N D J F M A M J J A S O N D JJ F M A M J J A S O N D J F M A M J J A S O N D J
Sal
es in
un
its
Sal
es in
un
its
Time (months)Time (months)
By combining By combining both, the both, the
variation is variation is reducedreduced
Snowmobile Snowmobile salessales
Jet ski Jet ski salessales
Figure S7.3Figure S7.3
Approaches to Capacity Expansion
(a)(a) Leading demand with Leading demand with incremental expansionincremental expansion
Dem
and
Dem
and
Expected Expected demanddemand
New New capacitycapacity
(b)(b) Leading demand with Leading demand with one-step expansionone-step expansion
Dem
and
Dem
and
New New capacitycapacity
Expected Expected demanddemand
(d)(d) Attempts to have an average Attempts to have an average capacity with incremental capacity with incremental expansionexpansion
Dem
and
Dem
and
New New capacitycapacity Expected Expected
demanddemand
(c)(c) Capacity lags demand with Capacity lags demand with incremental expansionincremental expansion
Dem
and
Dem
and
New New capacitycapacity
Expected Expected demanddemand
Figure S7.4Figure S7.4
Approaches to Capacity Expansion
(a)(a) Leading demand with incremental Leading demand with incremental expansionexpansion
Expected Expected demanddemand
Figure S7.4Figure S7.4
New New capacitycapacity
Dem
and
Dem
and
Time (years)Time (years)11 22 33
Approaches to Capacity Expansion
(b)(b) Leading demand with one-step Leading demand with one-step expansionexpansion
New New capacitycapacity
Expected Expected demanddemand
Figure S7.4Figure S7.4
Dem
and
Dem
and
Time (years)Time (years)11 22 33
Approaches to Capacity Expansion
(c)(c) Capacity lags demand with incremental Capacity lags demand with incremental expansionexpansion
Expected Expected demanddemand
Figure S7.4Figure S7.4
Dem
and
Dem
and
Time (years)Time (years)11 22 33
New New capacitycapacity
Approaches to Capacity Expansion
(d)(d) Attempts to have an average capacity with Attempts to have an average capacity with incremental expansionincremental expansion
Expected Expected demanddemand
Figure S7.4Figure S7.4
New New capacitycapacity
Dem
and
Dem
and
Time (years)Time (years)11 22 33
Break-Even Analysis Technique for evaluating process and equipment alternatives
Objective is to find the point in dollars and units at which cost equals revenue
Requires estimation of fixed costs, variable costs, and revenue.
Fixed costs are costs that continue even if no units are produced
•Depreciation, taxes, debt, mortgage payments
Variable costs are costs that vary with the volume of units produced
•Labor, materials, portion of utilities
•Contribution is the difference between selling price and variable cost
Break-Even Analysis
Costs and revenue are linear functionsGenerally not the case in the real world
We actually know these costsVery difficult to accomplish
There is no time value of money
Assumptions
Break-Even AnalysisTotal revenue lineTotal revenue line
Total cost lineTotal cost line
Variable costVariable cost
Fixed costFixed cost
Break-even pointBreak-even pointTotal cost = Total revenueTotal cost = Total revenue
–
900 900 –
800 800 –
700 700 –
600 600 –
500 500 –
400 400 –
300 300 –
200 200 –
100 100 –
–
| | | | | | | | | | | |
00 100100 200200 300300 400400 500500 600600 700700 800800 900900 10001000 11001100
Co
st in
do
llars
Co
st in
do
llars
Volume (units per period)Volume (units per period)Figure S7.5Figure S7.5
Break-Even Analysis
BEPBEPxx == Break-even Break-even point in unitspoint in unitsBEPBEP$$ == Break-even Break-even point in dollarspoint in dollarsPP == Price per Price per unit (after all discounts)unit (after all discounts)
xx == Number of units Number of units producedproducedTRTR == Total Total revenue = Pxrevenue = PxFF== Fixed costsFixed costsVV == Variable Variable costscostsTCTC == Total Total costs = F + Vxcosts = F + Vx
TR = TCTR = TCoror
Px = F + VxPx = F + Vx
Break-even point Break-even point occurs whenoccurs when
BEPBEPxx = =FF
P - VP - V
Break-Even Analysis
BEPBEPxx == Break-even Break-even point in unitspoint in unitsBEPBEP$$ == Break-even Break-even point in dollarspoint in dollarsPP == Price per Price per unit (after all discounts)unit (after all discounts)
xx == Number of units Number of units producedproducedTRTR == Total Total revenue = Pxrevenue = PxFF== Fixed costsFixed costsVV == Variable Variable costscostsTCTC == Total Total costs = F + Vxcosts = F + VxBEPBEP$$ = BEP= BEPx x PP
= P= P
==
= =
FF((P - VP - V))/P/P
FFP - VP - V
FF1 -1 - V/P V/P
ProfitProfit = TR - TC= TR - TC
= Px - = Px - ((F + VxF + Vx))
= Px - F - Vx= Px - F - Vx
= = ((P - VP - V))x - Fx - F
Break-Even Example
Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit
BEPBEP$$ = == =FF
1 - (1 - (V/PV/P))$10,000$10,000
1 - [(1.50 + .75)/(4.00)]1 - [(1.50 + .75)/(4.00)]
$10,000$10,0004.00 - (1.50 + .75)4.00 - (1.50 + .75)
Break-Even Example
Fixed costs Fixed costs = $10,000= $10,000 Material Material = $.75= $.75/unit/unitDirect labor Direct labor = $1.50= $1.50/unit/unit Selling price Selling price = $4.00= $4.00 per unit per unit
BEPBEP$$ = == =FF
1 - (1 - (V/PV/P))$10,000$10,000
1 - [(1.50 + .75)/(4.00)]1 - [(1.50 + .75)/(4.00)]
= = $22,857.14= = $22,857.14$10,000$10,000
.4375.4375
BEPBEPxx = = = 5,714= = = 5,714FF
P - VP - V
Break-Even Example
50,000 50,000 –
40,000 40,000 –
30,000 30,000 –
20,000 20,000 –
10,000 10,000 –
–
| | | | | |
00 2,0002,000 4,0004,000 6,0006,000 8,0008,000 10,00010,000
Do
llars
Do
llars
UnitsUnits
Fixed costsFixed costs
Total Total costscosts
RevenueRevenue
Break-even Break-even pointpoint
Break-Even Example
BEPBEP$$ ==FF
∑∑ 1 - x (1 - x (WWii))VVii
PPii
Multiproduct Case
wherewhere VV = variable cost per unit= variable cost per unitPP = price per unit= price per unitFF = fixed costs= fixed costs
WW = percent each product is of total dollar sales= percent each product is of total dollar salesii = each product= each product
Multiproduct Example
Annual ForecastedAnnual ForecastedItemItem PricePrice CostCost Sales UnitsSales Units
SandwichSandwich $2.95$2.95 $1.25$1.25 7,0007,000Soft drinkSoft drink .80.80 .30.30 7,0007,000Baked potatoBaked potato 1.551.55 .47.47 5,0005,000TeaTea .75.75 .25.25 5,0005,000Salad barSalad bar 2.852.85 1.001.00 3,0003,000
Fixed costs Fixed costs = $3,500= $3,500 per month per month
Multiproduct Example
Annual ForecastedAnnual ForecastedItemItem PricePrice CostCost Sales UnitsSales Units
SandwichSandwich $2.95$2.95 $1.25$1.25 7,0007,000Soft drinkSoft drink .80.80 .30.30 7,0007,000Baked potatoBaked potato 1.551.55 .47.47 5,0005,000TeaTea .75.75 .25.25 5,0005,000Salad barSalad bar 2.852.85 1.001.00 3,0003,000
Sandwich $2.95 $1.25 .42 .58 $20,650 .446 .259Soft drink .80 .30 .38 .62 5,600 .121 .075Baked 1.55 .47 .30 .70 7,750 .167 .117 potatoTea .75 .25 .33 .67 3,750 .081 .054Salad bar 2.85 1.00 .35 .65 8,550 .185 .120
$46,300 1.000 .625
Annual WeightedSelling Variable Forecasted % of Contribution
Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $ Sales (col 5 x col 7)
Fixed costs Fixed costs = $3,500= $3,500 per month per month
Multiproduct Example
BEP$ =F
∑ 1 - x (Wi)Vi
Pi
= = $67,200$3,500 x 12
.625
Daily sales = = $215.38
$67,200312 days
.446 x $215.38$2.95 = 32.6 ≈ 33
sandwichesper day
Decision Trees and Capacity Decision
-$14,000
$13,000
$18,000
-$90,000-$90,000Market unfavorable (.6)Market unfavorable (.6)
Market favorable (.4)Market favorable (.4)$100,000$100,000
Large plant
Large plant
Market favorable (.4)Market favorable (.4)
Market unfavorable (.6)Market unfavorable (.6)
$60,000$60,000
-$10,000-$10,000
Medium plantMedium plant
Market favorable (.4)Market favorable (.4)
Market unfavorable (.6)Market unfavorable (.6)
$40,000$40,000
-$5,000-$5,000
$0$0
Do nothing
Do nothing
Localizacion (Location)
Factors That Affect Location DecisionsFactors That Affect Location Decisions Labor ProductivityLabor Productivity
Exchange Rates and Currency RisksExchange Rates and Currency Risks
CostsCosts
AttitudesAttitudes
Proximity to MarketsProximity to Markets
Proximity to SuppliersProximity to Suppliers
Proximity to Competitors (Clustering)Proximity to Competitors (Clustering)
Localizacion (Location)
Methods Of Evaluating Location Methods Of Evaluating Location AlternativesAlternatives The Factor-Rating MethodThe Factor-Rating Method Locational Break-Even AnalysisLocational Break-Even Analysis Center-of-Gravity MethodCenter-of-Gravity Method The Transportation MethodThe Transportation Method
Localizacion decision estrategica (Location Strategy)
One of the most important decisions a One of the most important decisions a firm makesfirm makes
Increasingly global in natureIncreasingly global in nature
Long term impact and decisions are Long term impact and decisions are difficult to changedifficult to change
The objective is to maximize the benefit The objective is to maximize the benefit of location to the firmof location to the firm
Localizacion decision estrategica
Long-term decisions Long-term decisions
Decisions made infrequentlyDecisions made infrequently
Decision greatly affects both fixed and Decision greatly affects both fixed and variable costs variable costs
Once committed to a location, many Once committed to a location, many resource and cost issues are difficult resource and cost issues are difficult to changeto change
Location DecisionsCountry DecisionCountry Decision Critical Success FactorsCritical Success Factors
1.1. Political risks, government Political risks, government rules, attitudes, incentivesrules, attitudes, incentives
2.2. Cultural and economic Cultural and economic issuesissues
3.3. Location of marketsLocation of markets
4.4. Labor availability, attitudes, Labor availability, attitudes, productivity, costsproductivity, costs
5.5. Availability of supplies, Availability of supplies, communications, energycommunications, energy
6.6. Exchange rates and Exchange rates and currency riskscurrency risks
Location DecisionsRegion/ Region/
Community Community DecisionDecision
Critical Success FactorsCritical Success Factors
1.1. Corporate desiresCorporate desires
2.2. Attractiveness of region Attractiveness of region
3.3. Labor availability, costs, Labor availability, costs, attitudes towards unionsattitudes towards unions
4.4. Costs and availability of utilitiesCosts and availability of utilities
5.5. Environmental regulationsEnvironmental regulations
6.6. Government incentives and Government incentives and fiscal policiesfiscal policies
7.7. Proximity to raw materials and Proximity to raw materials and customerscustomers
8.8. Land/construction costsLand/construction costs
MN
WI
MI
IL INOH
Figure 8.1Figure 8.1
Location DecisionsSite DecisionSite Decision Critical Success FactorsCritical Success Factors
1.1. Site size and costSite size and cost
2.2. Air, rail, highway, and Air, rail, highway, and waterway systemswaterway systems
3.3. Zoning restrictionsZoning restrictions
4.4. Nearness of services/ Nearness of services/ supplies neededsupplies needed
5.5. Environmental impact Environmental impact issuesissues
Figure 8.1Figure 8.1
Factors That Affect Location Decisions
Labor productivityLabor productivity Wage rates are not the only costWage rates are not the only cost
Lower productivity may increase total costLower productivity may increase total cost
Labor cost per dayLabor cost per day
Productivity (units per day)Productivity (units per day)= cost per unit= cost per unit
ConnecticutConnecticut
= $1.17= $1.17 per unit per unit$70$70
6060 units units
JuarezJuarez
= $1.25= $1.25 per unit per unit$25$25
2020 units units
Factors That Affect Location Decisions
Exchange rates and currency risksExchange rates and currency risks Can have a significant impact on cost Can have a significant impact on cost
structurestructure
Rates change over timeRates change over time
CostsCosts Tangible - easily measured costs such as Tangible - easily measured costs such as
utilities, labor, materials, taxesutilities, labor, materials, taxes
Intangible - less easy to quantify and include Intangible - less easy to quantify and include education, public transportation, community, education, public transportation, community, quality-of-lifequality-of-life
Factors That Affect Location Decisions
AttitudesAttitudes National, state, local governments toward National, state, local governments toward
private and intellectual property, zoning, private and intellectual property, zoning, pollution, employment stabilitypollution, employment stability
Worker attitudes towards turnover, unions, Worker attitudes towards turnover, unions, absenteeismabsenteeism
Globally cultures have different attitudes Globally cultures have different attitudes towards punctuality, legal, and ethical issuestowards punctuality, legal, and ethical issues
Factors That Affect Location Decisions
Proximity to marketsProximity to markets Very important to servicesVery important to services
JIT systems or high transportation costs may JIT systems or high transportation costs may make it important to manufacturersmake it important to manufacturers
Proximity to suppliersProximity to suppliers Perishable goods, high transportation costs, Perishable goods, high transportation costs,
bulky productsbulky products
Factors That Affect Location Decisions
Proximity to competitorsProximity to competitors Called clusteringCalled clustering
Often driven by resources such as natural, Often driven by resources such as natural, information, capital, talentinformation, capital, talent
Found in both manufacturing and service Found in both manufacturing and service industriesindustries
Factor-Rating Method Popular because a wide variety of factors can Popular because a wide variety of factors can
be included in the analysisbe included in the analysis Six steps in the methodSix steps in the method
1.1. Develop a list of relevant factors called critical Develop a list of relevant factors called critical success factorssuccess factors
2.2. Assign a weight to each factorAssign a weight to each factor
3.3. Develop a scale for each factorDevelop a scale for each factor
4.4. Score each location for each factorScore each location for each factor
5.5. Multiply score by weights for each factor for each Multiply score by weights for each factor for each locationlocation
6.6. Recommend the location with the highest point Recommend the location with the highest point scorescore
Factor-Rating Example
CriticalCritical ScoresScoresSuccessSuccess (out of 100)(out of 100) Weighted ScoresWeighted ScoresFactorFactor WeightWeight FranceFrance DenmarkDenmark FranceFrance DenmarkDenmark
Labor Labor availability availability and attitude and attitude .25.25 7070 6060 (.25)(70) = 17.5(.25)(70) = 17.5 (.25)(60) = 15.0(.25)(60) = 15.0People-toPeople-to car ratiocar ratio .05.05 5050 6060 (.05)(50) = 2.5(.05)(50) = 2.5 (.05)(60) = 3.0(.05)(60) = 3.0Per capitaPer capita incomeincome .10.10 8585 8080 (.10)(85) = 8.5(.10)(85) = 8.5 (.10)(80) = 8.0(.10)(80) = 8.0Tax structureTax structure .39.39 7575 7070 (.39)(75) = 29.3(.39)(75) = 29.3 (.39)(70) = 27.3(.39)(70) = 27.3EducationEducation and healthand health .21.21 6060 7070 (.21)(60) = 12.6(.21)(60) = 12.6 (.21)(70) = 14.7(.21)(70) = 14.7TotalsTotals 1.001.00 70.470.4 68.068.0
Locational Break-Even Analysis
Method of cost-volume analysis used for Method of cost-volume analysis used for industrial locationsindustrial locations
Three steps in the methodThree steps in the method
1.1. Determine fixed and variable costs for each Determine fixed and variable costs for each locationlocation
2.2. Plot the cost for each location Plot the cost for each location
3.3. Select location with lowest total cost for Select location with lowest total cost for expected production volumeexpected production volume
Locational Break-Even Analysis Example
Three locations:Three locations:
AkronAkron $30,000$30,000 $75$75 $180,000$180,000
Bowling GreenBowling Green $60,000$60,000 $45$45 $150,000$150,000
ChicagoChicago $110,000$110,000 $25$25 $160,000$160,000
Selling price Selling price = $120= $120
Expected volumeExpected volume = 2,000 = 2,000 unitsunits
FixedFixed VariableVariable TotalTotalCityCity CostCost CostCost CostCost
Total Cost = Fixed Cost + Variable Cost x VolumeTotal Cost = Fixed Cost + Variable Cost x Volume
Locational Break-Even Analysis Example
–$180,000 $180,000 –
–$160,000 $160,000 –$150,000 $150,000 –
–$130,000 $130,000 –
–$110,000 $110,000 –
––
$80,000 $80,000 ––
$60,000 $60,000 –––
$30,000 $30,000 ––
$10,000 $10,000 ––
An
nu
al c
ost
An
nu
al c
ost
| | | | | | |
00 500500 1,0001,000 1,5001,500 2,0002,000 2,5002,500 3,0003,000
VolumeVolume
Akron Akron lowest lowest costcost
Bowling Green Bowling Green lowest costlowest cost
Chicago Chicago lowest costlowest cost
Akron c
ost
Akron c
ost
curv
e
curv
e
Bowling Green
Bowling Green
cost curve
cost curve
Figure 8.2Figure 8.2
Center-of-Gravity Method
Finds location of distribution center Finds location of distribution center that minimizes distribution coststhat minimizes distribution costs
ConsidersConsiders Location of marketsLocation of markets
Volume of goods shipped to those Volume of goods shipped to those marketsmarkets
Shipping cost (or distance)Shipping cost (or distance)
Center-of-Gravity Method
Place existing locations on a Place existing locations on a coordinate gridcoordinate grid Grid origin and scale is arbitrary Grid origin and scale is arbitrary
Maintain relative distancesMaintain relative distances
Calculate X and Y coordinates for Calculate X and Y coordinates for ‘center of gravity’‘center of gravity’ Assumes cost is directly proportional to Assumes cost is directly proportional to
distance and volume shippeddistance and volume shipped
Center-of-Gravity Method
x - coordinate =x - coordinate =∑∑ddixixQQii
∑∑QQii
ii
ii
∑∑ddiyiyQQii
∑∑QQii
ii
ii
y - coordinate =y - coordinate =
wherewhere ddixix == x-coordinate of location ix-coordinate of location i
ddiyiy == y-coordinate of location iy-coordinate of location i
QQii == Quantity of goods moved to or Quantity of goods moved to or from location ifrom location i
Center-of-Gravity Method
North-SouthNorth-South
East-WestEast-West
120 120 –
90 90 –
60 60 –
30 30 –
–
| | | | | |
3030 6060 9090 120120 150150Arbitrary Arbitrary originorigin
Chicago Chicago (30, 120)(30, 120)New York New York (130, 130)(130, 130)
Pittsburgh Pittsburgh (90, 110)(90, 110)
Atlanta Atlanta (60, 40)(60, 40)
Center-of-Gravity Method
Number of ContainersNumber of ContainersStore LocationStore Location Shipped per MonthShipped per Month
Chicago Chicago (30, 120)(30, 120) 2,0002,000Pittsburgh Pittsburgh (90, 110)(90, 110) 1,0001,000New York New York (130, 130)(130, 130) 1,0001,000Atlanta Atlanta (60, 40)(60, 40) 2,0002,000
x-coordinate =x-coordinate =(30)(2000) + (90)(1000) + (130)(1000) + (60)(2000)(30)(2000) + (90)(1000) + (130)(1000) + (60)(2000)
2000 + 1000 + 1000 + 20002000 + 1000 + 1000 + 2000
= = 66.766.7
y-coordinate =y-coordinate =(120)(2000) + (110)(1000) + (130)(1000) + (40)(2000)(120)(2000) + (110)(1000) + (130)(1000) + (40)(2000)
2000 + 1000 + 1000 + 20002000 + 1000 + 1000 + 2000
= = 93.393.3
Center-of-Gravity Method
North-SouthNorth-South
East-WestEast-West
120 120 –
90 90 –
60 60 –
30 30 –
–
| | | | | |
3030 6060 9090 120120 150150Arbitrary Arbitrary originorigin
Chicago Chicago (30, 120)(30, 120)New York New York (130, 130)(130, 130)
Pittsburgh Pittsburgh (90, 110)(90, 110)
Atlanta Atlanta (60, 40)(60, 40)
Center of gravity Center of gravity (66.7, 93.3)(66.7, 93.3)+
Transportation Model
Finds amount to be shipped from Finds amount to be shipped from several points of supply to several several points of supply to several points of demandpoints of demand
Solution will minimize total production Solution will minimize total production and shipping costsand shipping costs
A special class of linear programming A special class of linear programming problemsproblems
Transportation Model
Service Location Strategy
1. Purchasing power of customer-drawing area1. Purchasing power of customer-drawing area
2. Service and image compatibility with demographics of 2. Service and image compatibility with demographics of the customer-drawing areathe customer-drawing area
3. Competition in the area3. Competition in the area
4. Quality of the competition4. Quality of the competition
5. Uniqueness of the firm’s and competitors’ locations5. Uniqueness of the firm’s and competitors’ locations
6. Physical qualities of facilities and neighboring 6. Physical qualities of facilities and neighboring businessesbusinesses
7. Operating policies of the firm7. Operating policies of the firm
8. Quality of management8. Quality of management
Location Strategies
Service/Retail/Professional LocationService/Retail/Professional Location Goods-Producing Location Goods-Producing Location
Revenue FocusRevenue Focus Cost Focus Cost Focus
Volume/revenueVolume/revenueDrawing area; purchasing powerDrawing area; purchasing powerCompetition; advertising/pricingCompetition; advertising/pricing
Physical qualityPhysical qualityParking/access; security/lighting; Parking/access; security/lighting; appearance/imageappearance/image
Cost determinantsCost determinantsRentRentManagement caliberManagement caliberOperations policies (hours, wage rates)Operations policies (hours, wage rates)
Tangible costsTangible costsTransportation cost of raw materialTransportation cost of raw materialShipment cost of finished goodsShipment cost of finished goodsEnergy and utility cost; labor; raw Energy and utility cost; labor; raw material; taxes, and so onmaterial; taxes, and so on
Intangible and future costsIntangible and future costsAttitude toward unionAttitude toward unionQuality of lifeQuality of lifeEducation expenditures by stateEducation expenditures by stateQuality of state and local governmentQuality of state and local government
Table 8.4Table 8.4
Location Strategies
Service/Retail/Professional LocationService/Retail/Professional Location Goods-Producing Location Goods-Producing Location
TechniquesTechniques Techniques Techniques
Regression models to determine Regression models to determine importance of various factorsimportance of various factors
Factor-rating methodFactor-rating methodTraffic countsTraffic countsDemographic analysis of drawing areaDemographic analysis of drawing areaPurchasing power analysis of areaPurchasing power analysis of areaCenter-of-gravity methodCenter-of-gravity methodGeographic information systemsGeographic information systems
Transportation methodsTransportation methodsFactor-rating methodFactor-rating methodLocational break-even analysisLocational break-even analysisCrossover chartsCrossover charts
Table 8.4Table 8.4
Location Strategies
Service/Retail/Professional LocationService/Retail/Professional Location Goods-Producing Location Goods-Producing Location
AssumptionsAssumptions Assumptions Assumptions
Location is a major determinant of Location is a major determinant of revenuerevenue
High customer-contact issues are criticalHigh customer-contact issues are criticalCosts are relatively constant for a given Costs are relatively constant for a given
area; therefore, the revenue function is area; therefore, the revenue function is criticalcritical
Location is a major determinant of costLocation is a major determinant of costMost major costs can be identified Most major costs can be identified
explicitly for each siteexplicitly for each siteLow customer contact allows focus on the Low customer contact allows focus on the
identifiable costsidentifiable costsIntangible costs can be evaluatedIntangible costs can be evaluated
Table 8.4Table 8.4
How Hotel Chains Select Sites
Location is a strategically important decision Location is a strategically important decision in the hospitality industryin the hospitality industry
La Quinta started with 35 independent La Quinta started with 35 independent variables and worked to refine a regression variables and worked to refine a regression model to predict profitabilitymodel to predict profitability
The final model had only four variablesThe final model had only four variables Price of the innPrice of the inn
Median income levelsMedian income levels
State population per innState population per inn
Location of nearby collegesLocation of nearby colleges
r2 = .5151% of the
profitability is predicted by
just these four variables!