probabilistic model - 0 introduction

8/6/2019 Probabilistic Model - 0 Introduction

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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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Demand Scenarios

0%

5%

10%

15%

20%25%

30%

8000

10000

12000

14000

16000

18000

Sales

Probab

ili


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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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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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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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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)

probabilistic model - 0 introduction

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