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Production Planning and Control
Production Planning and Control
Allocate the company’s ressources
Taking into account : Strategic and operational objectives
(quantity, quality, lead time, costs)
Existing constraints
Forecasted demand
Lon
g t
erm
Business Plan Determine the long-term strategies for production and capacity
Source : Stevenson W., Benedetti, (2001), p 426
Inte
rmeti
ate
term
Sh
ort
term
Externalenvironment
Forecast ofdemand
Strategies andpolicies
Material Requirements Planning (MRP)
Determine the needs for components and raw materials
Aggregate Plan Determine production capacity
Master ProductionSchedule (MPS)
Determine the production schedule for specific products
SchedulingDetailed planning of orders
Aggregate planning
Masterscheduling
Slide 11.4
Slide 11.5
LinkagesFacilitiesPlanning
AggregatePlanning
Scheduling
Time FrameFacilities Planning
Aggregate PlanningScheduling
Time
Slide 11.6
Aggregation is done according to:ProductsLaborTime
Aggregation????????
Slide 11.7
Long Range Planning Strategic planning (1-5 years)
Medium Range Planning Employment, output, and inventory levels
(2-18 months) Short Range Planning
Job scheduling, machine loading, and job sequencing (0-2 months)
Aggregate Plan
Demandforecast
I nventory
Machinecapacitiesand costs
Laborcapacitiesand costs
Outsourcingcapacitiesand costs
Aggregate Plan
Amount toproduce
Amount oflabor andovertimerequired
ProjectedI nventories
Amount tooutsource
Demandforecast
I nventory
Machinecapacitiesand costs
Laborcapacitiesand costs
Outsourcingcapacitiesand costs
Aggregate Plan
Managerial InputsManagerial Inputs
Supplier capabilities Storage capacity Materials availability
Materials
Current machine capacities Plans for future capacities Workforce capacities Current staffing level
Operations
New products Product design changes Machine standards
EngineeringLabor-market conditions Training capacity
Human resources
Cost data Financial condition of firm
Accounting and financeAggregate
plan
Customer needs Demand forecasts Competition behavior
Distribution and marketing
Minimize Costs/Maximize ProfitsMinimize Costs/Maximize Profits Maximize Customer ServiceMaximize Customer Service Minimize Inventory InvestmentMinimize Inventory Investment Minimize Changes in Production RatesMinimize Changes in Production Rates Minimize Changes in Workforce Minimize Changes in Workforce
LevelsLevels Maximize Utilization of Plant and Maximize Utilization of Plant and
EquipmentEquipment
Slide 11.13
Work force levelsWork force levels - the number of workers required for production.
Production ratesProduction rates - the number of units produced per time period.
Inventory levelsInventory levels - the balance of unused units carried forward from the previous period.
MINIMIZE:MINIMIZE:cost, inventory levels, changes in work force levels, use of overtime, use of subcontracting, changes in production rates, changes in production rates, plant/personnel idle time
MAXIMIZE:MAXIMIZE:profits, customer service
Price Incentives Reservations Backlogs Complementary Products or Services Advertising/promotion
Hiring/firing workers Overtime/slack time Part time/temporary labor Subcontracting Cooperative arrangements Inventories
Slide 11.17
Hiring/firing costs Overtime/slack time costs Part time/temporary labor costs Subcontracting costs Cooperative arrangements costs Inventory carrying costs Backorder or stock out costs
Washing machineModel Number
Required labor time(hrs)
Item demand as % ofaggregate demand
A5532 4.2 32
K4242 4.9 21
L9898 5.1 17
3800 5.2 14
M2624 5.4 10
M3880 5.8 06
Aggregate unit labor time = (.32)(4.2)+(.21)(4.9)+(.17)(5.1)+(.14)(5.2)+(.10)(5.4)+(.06)(5.8) = 4.856 hrs
1. Demand Chasing: Vary the Workforce Level
D(t) P(t) = D(t)
W(t)
PC WC HC FC
•D(t): Aggregate demand series•P(t): Aggregate production levels•W(t): Required Workforce levels•Costs Involved:
•PC: Production Costs•fixed (setup, overhead)•variable (materials, consumables, etc.)
•WC: Regular labor costs•HC: Hiring costs: e.g., advertising, interviewing, training•FC: Firing costs: e.g., compensation, social cost
2. Varying Production Capacity with Constant Workforce:
D(t) P(t)
O(t)
PC WC OC UC
U(t)
S(t)
SC
W = constant•S(t): Subcontracted quantities•O(t): Overtime levels•U(t): Undertime levels•Costs involved:
•PC, WC: as before•SC: subcontracting costs: e.g., purchasing, transport, quality, etc.•OC: overtime costs: incremental cost of producing one unit in overtime•(UC: undertime costs: this is hidden in WC)
3. Accumulating (Seasonal) Inventories:
D(t) P(t)
I(t)
PC WC IC
W(t), O(t), U(t), S(t) = constant
•I(t): Accumulated Inventory levels•Costs involved:
•PC, WC: as before•IC: inventory holding costs: e.g., interest lost, storage space, pilferage, obsolescence, etc.
4. Backlogging:
D(t) P(t)
B(t)
PC WC BC
W(t), O(t), U(t), S(t) = constant
•B(t): Accumulated Backlog levels•Costs involved:
•PC, WC: as before•BC: backlog (handling) costs: e.g., expediting costs, penalties, lost sales (eventually), customer dissatisfaction
A “mixture” of the previously discussed pure options:
D
PC WC HC FC
OCUC SC IC BC
PWHFOUSIB
+Additional constraints arising from the company strategy; e.g.,
•maximal allowed subcontracting•maximal allowed workforce variation in two consecutive periods•maximal allowed overtime•safety stocks•etc.
Io
Wo
Slide 11.24
Trial-and-error method Mathematical techniques
Materials $5/unitHolding costs $1/unit per mo.Marginal cost of stock-out $1.25/unit per mo.Hiring and training cost $200/workerLayoff costs $250/workerLabor hours required .15 hrs/unitStraight time labor cost $8/hourBeginning inventory 250 unitsProductive hours/worker/day 7.25Paid straight hrs/day 8
Suppose we have the following unit demand and cost information:Demand/mo Jan Feb Mar Apr May Jun
4500 5500 7000 10000 8000 6000
Jan Feb Mar Apr May JunDays/mo 22 19 21 21 22 20Hrs/worker/moUnits/worker$/worker
Productive hours/worker/day 7.25Paid straight hrs/day 8
Demand/mo Jan Feb Mar Apr May Jun
4500 5500 7000 10000 8000 6000
Given the demand and cost information below, what are the aggregate hours/worker/month, units/worker, and dollars/worker?
Jan Feb Mar Apr May JunDays/mo 22 19 21 21 22 20Hrs/worker/mo 159.5 137.75 152.25 152.25 159.5 145Units/worker 1063.33 918.33 1015 1015 1063.33 966.67$/worker $1,408 1,216 1,344 1,344 1,408 1,280
Productive hours/worker/day 7.25Paid straight hrs/day 8
Demand/mo Jan Feb Mar Apr May Jun
4500 5500 7000 10000 8000 6000
Given the demand and cost information below, what are the aggregate hours/worker/month, units/worker, and dollars/worker?
7.25x22
7.25/0.15=48.33 & 48.33x22=1063.3322x8hrsx$8=$140
8
JanDays/mo 22Hrs/worker/mo 159.5Units/worker 1,063.33$/worker $1,408
JanDemand 4,500Beg. inv. 250Net req.Req. workersHiredFiredWorkforceEnding inventory 0
Lets assume our current workforce is 7 workers.
First, calculate net requirements for production, or Demand-Begin Inv.
Then, calculate number of workers needed to produce the net requirements, or Net req/Units per worker or # workers
Finally, determine the number of workers to hire/fire. Current Workers-Required = (-) hire or (+) fire
JanDays/mo 22Hrs/worker/mo 159.5Units/worker 1,063.33$/worker $1,408
JanDemand 4,500Beg. inv. 250Net req. 4,250Req. workers 3.997HiredFired 3Workforce 4Ending inventory 0
Lets assume our current workforce is 7 workers.
First, calculate net requirements for production, or 4500-250=4250 units
Then, calculate number of workers needed to produce the net requirements, or 4250/1063.33=3.997 or 4 workers **Round-up
Finally, determine the number of workers to hire/fire. In this case we only need 4 workers, we have 7, so 3 can be fired.
Jan Feb Mar Apr May JunDays/mo 22 19 21 21 22 20Hrs/worker/mo 159.5 137.75 152.25 152.25 159.5 145Units/worker 1,063 918 1,015 1,015 1,063 967$/worker $1,408 1,216 1,344 1,344 1,408 1,280
Jan Feb Mar Apr May JunDemand 4,500 5,500 7,000 10,000 8,000 6,000Beg. inv. 250Net req. 4,250 5,500 7,000 10,000 8,000 6,000Req. workers 3.997 5.989 6.897 9.852 7.524 6.207Hired 2 1 3Fired 3 2 1Workforce 4 6 7 10 8 7Ending inventory 0 0 0 0 0 0
Below are the complete calculations for the remaining months in the six month planning horizon.
Jan Feb Mar Apr May JunDemand 4,500 5,500 7,000 10,000 8,000 6,000Beg. inv. 250Net req. 4,250 5,500 7,000 10,000 8,000 6,000Req. workers 3.997 5.989 6.897 9.852 7.524 6.207Hired 2 1 3Fired 3 2 1Workforce 4 6 7 10 8 7Ending inventory 0 0 0 0 0 0
Jan Feb Mar Apr May Jun CostsMaterial $21,250.00 $27,500.00 $35,000.00 $50,000.00 $40,000.00 $30,000.00 203,750.00Labor 5,627.59 7,282.76 9,268.97 13,241.38 10,593.10 7,944.83 53,958.62Hiring cost 400.00 200.00 600.00 1,200.00Firing cost 750.00 500.00 250.00 1,500.00
$260,408.62
Below are the complete calculations for the remaining months in the six month planning horizon with the other costs included.
JanDemand 4,500Beg. inv. 250Net req. 4,250Workers 6Production 6,380Ending inventory 2,130Surplus 2,130Shortage
Lets take the same problem as before but this time use the Level Workforce strategy.
This time we will seek to use a workforce level of 6 workers.
Jan Feb Mar Apr May JunDemand 4,500 5,500 7,000 10,000 8,000 6,000Beg. inv. 250 2,130 2,140 1,230 -2,680 -1,300Net req. 4,250 3,370 4,860 8,770 10,680 7,300Workers 6 6 6 6 6 6Production 6,380 5,510 6,090 6,090 6,380 5,800Ending inventory 2,130 2,140 1,230 -2,680 -1,300 -1,500Surplus 2,130 2,140 1,230Shortage 2,680 1,300 1,500
Note, if we recalculate this sheet with 7 workers we would have a surplus.
Below are the complete calculations for the remaining months in the six month planning horizon.
Jan Feb Mar Apr May Jun4,500 5,500 7,000 10,000 8,000 6,000
250 2,130 10 -910 -3,910 -1,6204,250 3,370 4,860 8,770 10,680 7,300
6 6 6 6 6 66,380 5,510 6,090 6,090 6,380 5,8002,130 2,140 1,230 -2,680 -1,300 -1,5002,130 2,140 1,230
2,680 1,300 1,500
Jan Feb Mar Apr May Jun$8,448 $7,296 $8,064 $8,064 $8,448 $7,680 $48,000.0031,900 27,550 30,450 30,450 31,900 29,000 181,250.002,130 2,140 1,230 5,500.00
3,350 1,625 1,875 6,850.00
$241,600.00
Below are the complete calculations for the remaining months in the six month planning horizon with the other costs included.
LaborMaterialStorageStock-out
Note, the total costs under this strategy are less than under Chase.
Chase strategyChase strategy Match output rates to demand Match output rates to demand
forecast for each periodforecast for each period Vary workforce levels or vary Vary workforce levels or vary
production rateproduction rate Favored by many service Favored by many service
organizationsorganizations
Level strategyLevel strategy Daily production is uniformDaily production is uniform Use inventory or idle time as Use inventory or idle time as
bufferbuffer Stable production leads to Stable production leads to
better quality and productivitybetter quality and productivity
Some combination of Some combination of capacity options, a mixed capacity options, a mixed strategy, might be the best strategy, might be the best solutionsolution
Popular techniquesPopular techniques Easy to understand and useEasy to understand and use Trial-and-error approaches Trial-and-error approaches
that do not guarantee an that do not guarantee an optimal solutionoptimal solution
Require only limited Require only limited computationscomputations
1.1. Determine the demand for each Determine the demand for each periodperiod
2.2. Determine the capacity for regular Determine the capacity for regular time, overtime, and subcontracting time, overtime, and subcontracting each periodeach period
3.3. Find labor costs, hiring and layoff Find labor costs, hiring and layoff costs, and inventory holding costscosts, and inventory holding costs
4.4. Consider company policy on Consider company policy on workers and stock levelsworkers and stock levels
5.5. Develop alternative plans and Develop alternative plans and examine their total costsexamine their total costs
MonthMonth Expected DemandExpected DemandProduction Production
DaysDaysDemand Per Day Demand Per Day
(computed)(computed)
JanJan 900900 2222 4141
FebFeb 700700 1818 3939
MarMar 800800 2121 3838
AprApr 1,2001,200 2121 5757
MayMay 1,5001,500 2222 6868
JuneJune 1,1001,100 2020 5555
6,2006,200 124124
= = 50 units per day= = 50 units per day6,2006,200
124124
Average Average requiremerequireme
ntnt==
Total expected demandTotal expected demand
Number of production daysNumber of production days
Figure 13.3Figure 13.3
70 70 –
60 60 –
50 50 –
40 40 –
30 30 –
0 0 –JanJan FebFeb MarMar AprApr MayMay JuneJune == MonthMonth
2222 1818 2121 2121 2222 2020 == Number ofNumber ofworking daysworking days
Pro
du
cti
on
rate
per
work
ing
day
Pro
du
cti
on
rate
per
work
ing
day
Level production using Level production using average monthly forecast average monthly forecast
demanddemand
Forecast demandForecast demand
Cost InformationCost Information
Inventory carrying costInventory carrying cost $ 5$ 5 per unit per month per unit per month
Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit
Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per day per day))
Overtime pay rateOvertime pay rate $ 7$ 7 per hour per hour ((above above 88 hours per day hours per day))
Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit
Cost of increasing daily production rate Cost of increasing daily production rate (hiring and training)(hiring and training)
$300$300 per unit per unit
Cost of decreasing daily production rate Cost of decreasing daily production rate (layoffs)(layoffs)
$600$600 per unit per unit
Plan 1 – constant workforce
Plan 1 – constant workforce
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carry costInventory carry cost $ 5$ 5 per unit per month per unit per month
Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit
Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per day per day))
Overtime pay rateOvertime pay rate $ 7$ 7 per hour per hour ((above above 88 hours per day hours per day))
Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit
Cost of increasing daily production rate Cost of increasing daily production rate (hiring and training)(hiring and training)
$300$300 per unit per unit
Cost of decreasing daily production rate Cost of decreasing daily production rate (layoffs)(layoffs)
$600$600 per unit per unit
Plan 1 – constant workforce
Plan 1 – constant workforce
MonthProduction at
50 Units per DayDemand Forecast
Monthly Inventory Change
Ending Inventory
Jan 1,100 900 +200 200
Feb 900 700 +200 400
Mar 1,050 800 +250 650
Apr 1,050 1,200 -150 500
May 1,100 1,500 -400 100
June 1,000 1,100 -100 0
1,850
Total units of inventory carried over from onemonth to the next = 1,850
unitsWorkforce required to produce 50 units per day = 10 workers
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carry costInventory carry cost $ 5$ 5 per unit per month per unit per month
Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit
Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per day per day))
Overtime pay rateOvertime pay rate $ 7$ 7 per hour per hour ((above above 88 hours per day hours per day))
Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit
Cost of increasing daily production rate Cost of increasing daily production rate (hiring and training)(hiring and training)
$300$300 per unit per unit
Cost of decreasing daily production rate Cost of decreasing daily production rate (layoffs)(layoffs)
$600$600 per unit per unit
MonthProduction at
50 Units per DayDemand Forecast
Monthly Inventory Change
Ending Inventory
Jan 1,100 900 +200 200
Feb 900 700 +200 400
Mar 1,050 800 +250 650
Apr 1,050 1,200 -150 500
May 1,100 1,500 -400 100
June 1,000 1,100 -100 0
1,850
Total units of inventory carried over from onemonth to the next = 1,850
unitsWorkforce required to produce 50 units per day = 10 workers
Costs Calculations
Inventory carrying $9,250 (= 1,850 units carried x $5 per unit)
Regular-time labor 49,600 (= 10 workers x $40 per day x 124 days)
Other costs (overtime, hiring, layoffs, subcontracting) 0
Total cost $58,850
Cu
mu
lati
ve d
em
an
d u
nit
sC
um
ula
tive d
em
an
d u
nit
s7,000 7,000 –
6,000 6,000 –
5,000 5,000 –
4,000 4,000 –
3,000 3,000 –
2,000 –
1,000 –
–JanJan FebFeb MarMar AprApr MayMay JuneJune
Cumulative Cumulative forecast forecast requirementsrequirements
Cumulative Cumulative level level
production production using average using average
monthly monthly forecast forecast
requirementsrequirements
Reduction Reduction of of
inventoryinventory
Excess inventoryExcess inventory
6,200 units6,200 units
MonthMonth Expected DemandExpected DemandProduction Production
DaysDaysDemand Per Day Demand Per Day
(computed)(computed)
JanJan 900900 2222 4141
FebFeb 700700 1818 3939
MarMar 800800 2121 3838
AprApr 1,2001,200 2121 5757
MayMay 1,5001,500 2222 6868
JuneJune 1,1001,100 2020 5555
6,2006,200 124124
Minimum requirement = 38 units per dayMinimum requirement = 38 units per day
Plan 2 – subcontracting
Plan 2 – subcontracting
70 70 –
60 60 –
50 50 –
40 40 –
30 30 –
0 0 –JanJan FebFeb MarMar AprApr MayMay JuneJune == MonthMonth
2222 1818 2121 2121 2222 2020 == Number ofNumber ofworking daysworking days
Pro
du
cti
on
rate
per
work
ing
day
Pro
du
cti
on
rate
per
work
ing
day
Level Level production production
using lowest using lowest monthly monthly forecast forecast demanddemand
Forecast demandForecast demand
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carrying costInventory carrying cost $ 5$ 5 per unit per month per unit per month
Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit
Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per day per day))
Overtime pay rateOvertime pay rate $ 7$ 7 per hour per hour ((above above 88 hours per day hours per day))
Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit
Cost of increasing daily production rate Cost of increasing daily production rate (hiring and training)(hiring and training)
$300$300 per unit per unit
Cost of decreasing daily production rate Cost of decreasing daily production rate (layoffs)(layoffs)
$600$600 per unit per unit
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carry costInventory carry cost $ 5$ 5 per unit per month per unit per month
Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit
Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per day per day))
Overtime pay rateOvertime pay rate $ 7$ 7 per hour per hour ((above above 88 hours per day hours per day))
Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit
Cost of increasing daily production rate Cost of increasing daily production rate (hiring and training)(hiring and training)
$300$300 per unit per unit
Cost of decreasing daily production rate Cost of decreasing daily production rate (layoffs)(layoffs)
$600$600 per unit per unit
In-house production = 38 units per day x 124 days
= 4,712 units
Subcontract units = 6,200 - 4,712= 1,488 units
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carry costInventory carry cost $ 5$ 5 per unit per month per unit per month
Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit
Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per day per day))
Overtime pay rateOvertime pay rate $ 7$ 7 per hour per hour ((above above 88 hours per day hours per day))
Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit
Cost of increasing daily production rate Cost of increasing daily production rate (hiring and training)(hiring and training)
$300$300 per unit per unit
Cost of decreasing daily production rate Cost of decreasing daily production rate (layoffs)(layoffs)
$600$600 per unit per unit
In-house production = 38 units per day x 124 days
= 4,712 units
Subcontract units = 6,200 - 4,712= 1,488 units
Costs Calculations
Regular-time labor $37,696 (= 7.6 workers x $40 per day x 124 days)
Subcontracting 14,880 (= 1,488 units x $10 per unit)
Total cost $52,576
MonthMonth Expected DemandExpected DemandProduction Production
DaysDaysDemand Per Day Demand Per Day
(computed)(computed)
JanJan 900900 2222 4141
FebFeb 700700 1818 3939
MarMar 800800 2121 3838
AprApr 1,2001,200 2121 5757
MayMay 1,5001,500 2222 6868
JuneJune 1,1001,100 2020 5555
6,2006,200 124124
Production = Expected DemandProduction = Expected DemandPlan 3 – hiring and firing
Plan 3 – hiring and firing
70 70 –
60 60 –
50 50 –
40 40 –
30 30 –
0 0 –JanJan FebFeb MarMar AprApr MayMay JuneJune == MonthMonth
2222 1818 2121 2121 2222 2020 == Number ofNumber ofworking daysworking days
Pro
du
cti
on
rate
per
work
ing
day
Pro
du
cti
on
rate
per
work
ing
day
Forecast demand Forecast demand and monthly and monthly productionproduction
Cost InformationCost Information
Inventory carrying costInventory carrying cost $ 5$ 5 per unit per month per unit per month
Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit
Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per day per day))
Overtime pay rateOvertime pay rate $ 7$ 7 per hour per hour ((above above 88 hours per day hours per day))
Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit
Cost of increasing daily production rate Cost of increasing daily production rate (hiring and training)(hiring and training)
$300$300 per unit per unit
Cost of decreasing daily production rate Cost of decreasing daily production rate (layoffs)(layoffs)
$600$600 per unit per unit
Table 13.3Table 13.3
Cost InformationCost Information
Inventory carrying costInventory carrying cost $ 5$ 5 per unit per month per unit per month
Subcontracting cost per unitSubcontracting cost per unit $10$10 per unit per unit
Average pay rateAverage pay rate $ 5$ 5 per hour per hour ($40($40 per day per day))
Overtime pay rateOvertime pay rate $ 7$ 7 per hour per hour ((above above 88 hours per day hours per day))
Labor-hours to produce a unitLabor-hours to produce a unit 1.61.6 hours per unit hours per unit
Cost of increasing daily production rate Cost of increasing daily production rate (hiring and training)(hiring and training)
$300$300 per unit per unit
Cost of decreasing daily production rate Cost of decreasing daily production rate (layoffs)(layoffs)
$600$600 per unit per unit
MonthForecast
(units)
Daily Prod Rate
Basic Production
Cost (demand x
1.6 hrs/unit x $5/hr)
Extra Cost of Increasing Production (hiring cost)
Extra Cost of Decreasing Production (layoff cost) Total Cost
Jan 900 41 $ 7,200 — — $ 7,200
Feb 700 39 5,600 — $1,200 (= 2 x $600) 6,800
Mar 800 38 6,400 — $600 (= 1 x $600) 7,000
Apr 1,200 57 9,600 $5,700 (= 19 x $300) — 15,300
May 1,500 68 12,000 $3,300 (= 11 x $300) — 15,300
June 1,100 55 8,800 — $7,800 (= 13 x $600) 16,600
$49,600 $9,000 $9,600 $68,200
Table 13.4Table 13.4
Table 13.5Table 13.5
CostCost Plan 1Plan 1 Plan 2Plan 2 Plan 3Plan 3
Inventory carryingInventory carrying $ 9,250$ 9,250 $ 0$ 0 $ 0$ 0
Regular laborRegular labor 49,60049,600 37,69637,696 49,60049,600
Overtime laborOvertime labor 00 00 00
HiringHiring 00 00 9,0009,000
LayoffsLayoffs 00 00 9,6009,600
SubcontractingSubcontracting 00 14,88014,880 00
Total costTotal cost $58,850$58,850 $52,576$52,576 $68,200$68,200
Plan 2 is the lowest cost optionPlan 2 is the lowest cost option
Useful for generating Useful for generating strategiesstrategies Transportation Method of Transportation Method of
Linear ProgrammingLinear Programming Produces an optimal planProduces an optimal plan
Management Coefficients Management Coefficients ModelModel
Model built around manager’s experience Model built around manager’s experience and performanceand performance
Other ModelsOther Models Linear Decision RuleLinear Decision Rule SimulationSimulation