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InventoryInventory
ManagementManagement
Probabilistic ModelsProbabilistic ModelsINTRODUCTIONINTRODUCTION
Prepared by: RAPrepared by: RA IIdoydoy
AMAT 167AMAT 167
Operations Research 1Operations Research 1
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The realityThe reality
The models and environments discussed in theThe models and environments discussed in the
deterministic models of inventory management have alldeterministic models of inventory management have all
been based on the premise that thebeen based on the premise that the demand process isdemand process is
deterministicdeterministic..
In most real situations, this assumption is violated.In most real situations, this assumption is violated.
However,However, mostmost companies treat the world as if it werecompanies treat the world as if it werepredictable.predictable.
Production and inventory planning are based on forecasts ofProduction and inventory planning are based on forecasts of
demand made far in advance of the selling season.demand made far in advance of the selling season.
Companies are aware of demand uncertainty when they create aCompanies are aware of demand uncertainty when they create a
forecast, but they design their planning process as if the forecastforecast, but they design their planning process as if the forecasttrul re resents realittrul re resents realit
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The realityThe reality
Recent technological advances have increased the level ofRecent technological advances have increased the level of
demand uncertainty:demand uncertainty:
Short product life cyclesShort product life cycles
Increasing product varietyIncreasing product variety
The three principles of all forecastingThe three principles of all forecasting techniques:techniques: Forecasting is always wrongForecasting is always wrong
TheThe longer the forecast horizon the worst is the forecastlonger the forecast horizon the worst is the forecast
Aggregate forecasts are more accurateAggregate forecasts are more accurate
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RealReal--Life Application :Life Application :
Inventory Decisions in Dells SupplyInventory Decisions in Dells Supply
ChainChain
Dell, Inc., implements a directDell, Inc., implements a direct--sales business model insales business model in
which personal computers are sold directly to customerswhich personal computers are sold directly to customers
in US.in US.
When an order arrives from a customer, the specificationsWhen an order arrives from a customer, the specifications
are sent to a manufacturing plant in Austin, Texas.are sent to a manufacturing plant in Austin, Texas.
Suppliers are located in Southeast Asia and are required toSuppliers are located in Southeast Asia and are required tokeep a revolving inventory in revolvers (which arekeep a revolving inventory in revolvers (which are
owned by Dell).owned by Dell).
Dell then pulls parts as needed from the revolvers, thus it isDell then pulls parts as needed from the revolvers, thus it isthe suppliers responsibility to replenish the inventory tothe suppliers responsibility to replenish the inventory to
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RealReal--Life Application :Life Application :
Inventory Decisions in Dells SupplyInventory Decisions in Dells Supply
ChainChain
Although Dell does not own the inventory in the revolvers,Although Dell does not own the inventory in the revolvers,
its cost is indirectly passed on to customers throughits cost is indirectly passed on to customers through
component pricing.component pricing.
Thus, any reduction in inventory directly benefits Dell'sThus, any reduction in inventory directly benefits Dell's
customers by reducing product prices.customers by reducing product prices.
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ScenariosScenarios to ponderto ponder
PlayTimePlayTime ToysToys
Toys have short life cycles, high variety of competitorsToys have short life cycles, high variety of competitors
New designs are completedNew designs are completed
One production opportunityOne production opportunity
Based on past sales, knowledge of the industry, andBased on past sales, knowledge of the industry, andeconomic conditions, the marketing department has aeconomic conditions, the marketing department has aprobabilistic forecastprobabilistic forecast
The forecast averages about 13,000, but there is aThe forecast averages about 13,000, but there is achance that demand will be greater or less than this.chance that demand will be greater or less than this.
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ScenariosScenarios to ponderto ponder
PlayTimePlayTime ToysToys
Demand Scenarios
0%
5%
10%
15%
20%25%
30%
8000
10000
12000
14000
16000
18000
Sales
Probab
ili
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ScenariosScenarios to ponderto ponder
PlayTimePlayTime ToysToys
Production cost per unit (c): P80Production cost per unit (c): P80
Selling price per unit (p): P125Selling price per unit (p): P125
Salvage value per unit (g): P20Salvage value per unit (g): P20
Fixed production cost (K): P100,000Fixed production cost (K): P100,000
Q is production(order) quantity, D demandQ is production(order) quantity, D demand
Profit =RevenueProfit =Revenue Variable CostVariable Cost Fixed Cost +Fixed Cost +
SalvageSalvage
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ScenariosScenarios to ponderto ponder
PlayTimePlayTime ToysToys
Scenario One:Scenario One:
Suppose you make 12,000 toys and demand ends upSuppose you make 12,000 toys and demand ends up
being 13,000 toys.being 13,000 toys.
ProfitProfit == 125(12,000)125(12,000) -- 80(12,000)80(12,000) -- 100,000 = P440,000100,000 = P440,000
Scenario Two:Scenario Two:
Suppose you make 12,000 toys and demand ends upSuppose you make 12,000 toys and demand ends up
being 11,000 toys.being 11,000 toys. Profit = 125(11,000)Profit = 125(11,000) -- 80(12,000)80(12,000) -- 100,000 + 20(1000) = P 335,000100,000 + 20(1000) = P 335,000
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ScenariosScenarios to ponderto ponder
PlayTimePlayTime ToysToys
Find order quantity that maximizes average profit.Find order quantity that maximizes average profit.
Question:Question:
Will this quantity be less than, equal to, or greater thanWill this quantity be less than, equal to, or greater than
average demand?average demand?
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ScenariosScenarios to ponderto ponder
PlayTimePlayTime ToysToys
TradeTrade--off between ordering enough to meetoff between ordering enough to meet
demand and ordering too muchdemand and ordering too much
Several quantities have the same average profitSeveral quantities have the same average profit
Average profit does not tell the whole storyAverage profit does not tell the whole story
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ObservationsObservations
The optimal order quantity isThe optimal order quantity is not necessarilynot necessarily equal toequal toaverage forecast demandaverage forecast demand
The optimal quantity depends on the relationshipThe optimal quantity depends on the relationshipbetween marginal profit and marginal costbetween marginal profit and marginal cost
As order quantity increases, average profit firstAs order quantity increases, average profit firstincreases and then decreasesincreases and then decreases
As production quantity increases, risk increases. InAs production quantity increases, risk increases. Inother words, the probability of large gainsother words, the probability of large gains andandof largeof largelosses increaseslosses increases
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Inventory Management withInventory Management with StochasticStochastic
DemandDemand
Demand is NOT known for sureDemand is NOT known for sure
StochasticStochastic
ProbabilisticProbabilistic
UncertainUncertain
We have some idea about the average (mean) demandWe have some idea about the average (mean) demand
We may also know the probability distribution of theWe may also know the probability distribution of thedemanddemand
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Inventory Management withInventory Management with StochasticStochastic
DemandDemand
Decisions to make:Decisions to make:
How often we review the inventory?How often we review the inventory?
When we should issue a (replenishment/production)When we should issue a (replenishment/production)
order?order? How large the order should be?How large the order should be?
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Probabilistic ModelProbabilistic Model
Continuous Review ModelContinuous Review Model
ProbabilitizedProbabilitized EOQ modelEOQ model
Probabilistic EOQ ModelProbabilistic EOQ Model
SingleSingle--Period ModelsPeriod Models
Instantaneous Demand, No SetInstantaneous Demand, No Set--up Costup Cost
Instantaneous Demand, SetInstantaneous Demand, Set--up Cost (sup Cost (s--S Policy)S Policy)