1. 2 Dependent VS Independent E(1) Independent Demand (Demand not related to other items) Dependent...

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Independent Demand Ordering Independent Demand Ordering SystemsSystems

Chapter 11Chapter 11

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Dependent VS IndependentDependent VS Independent

E(1)

Independent Demand(Demand not related to other items)

Dependent Demand(Derived)

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Dependent VS IndependentDependent VS IndependentIndependent Demand

Dependent Demand

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• Main question now turns to when to place Main question now turns to when to place an order?an order?– Stock not ordered early enough may result in a Stock not ordered early enough may result in a

stockout situationstockout situation– Stock ordered too soon may result in excess Stock ordered too soon may result in excess

inventoryinventory– How do you balance the two?How do you balance the two?

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DefinitionsDefinitions

• Lead TimeLead Time : “The time between recognition of a need for : “The time between recognition of a need for an order and the receipt of the goods”an order and the receipt of the goods”

• Order PointOrder Point: “A set inventory level where, if the stock on : “A set inventory level where, if the stock on hand plus on-order falls to or below that point, action is hand plus on-order falls to or below that point, action is taken to replenish the stock.”taken to replenish the stock.”

• Safety StockSafety Stock: “In general, a quantity of stock planned to : “In general, a quantity of stock planned to be in inventory to protect against fluctuations in demand be in inventory to protect against fluctuations in demand and/or supplyand/or supply

• Service LevelService Level: “… the percentage of orders filled from : “… the percentage of orders filled from stock…”stock…”

APICS Dictionary7th Edition©1992

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• Reorder Systems Include:Reorder Systems Include:– Order Point SystemOrder Point System

– Periodic Review SystemPeriodic Review System

– MRPMRP• For dependent demand itemsFor dependent demand items

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• Order Point SystemsOrder Point Systems– A system where an order is placed whenever the on-A system where an order is placed whenever the on-

hand inventory level falls to a predetermined level hand inventory level falls to a predetermined level known as the order pointknown as the order point

• Quantity ordered is usually predetermined and based on the Quantity ordered is usually predetermined and based on the EOQEOQ

• An order must be placed when there is enough stock on hand An order must be placed when there is enough stock on hand to satisfy demand from the time the order is placed until new to satisfy demand from the time the order is placed until new stock arrivesstock arrives

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• The Order PointThe Order Point– The point where there exists enough inventory on hand The point where there exists enough inventory on hand

to equal the demand during the lead time plus some to equal the demand during the lead time plus some safety stock.safety stock.

Order Point = Demand During Lead Time + Safety StockOrder Point = Demand During Lead Time + Safety Stock

OP = DDLT + SSOP = DDLT + SS

– Note that the demand during lead time is important as this when a Note that the demand during lead time is important as this when a stockout could occur.stockout could occur.

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Example: Order PointExample: Order Point

Q: Demand is 100 units a week, the lead time is three Q: Demand is 100 units a week, the lead time is three weeks, and the safety stock has been established at weeks, and the safety stock has been established at 300 units. Calculate the order point.300 units. Calculate the order point.

A:A: Order Point = ?Order Point = ?

DDLT = (100 units per week x 3 weeks)DDLT = (100 units per week x 3 weeks)

SS = 300 unitsSS = 300 units

OP = DDLT + SS = (100 x 3) + 300 = OP = DDLT + SS = (100 x 3) + 300 = 600 units600 units

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• Order PointOrder Point

Average Inventory = Q/2 + SS

Lead Time

Q = Order Quantity

Order Point

Safety Stock

Un

its in

Sto

ck

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Example: Average inventoryExample: Average inventory

Q: Q: Order quantity is 7000 units and safety stock Order quantity is 7000 units and safety stock is 900 units. What is the average annual is 900 units. What is the average annual inventory?inventory?

A: A: Average inventory = Q/2 + SSAverage inventory = Q/2 + SS

= = 70007000 + 900 = + 900 = 4400 units4400 units

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• UncertaintyUncertainty– Quantity uncertaintyQuantity uncertainty

• When the amount of supply or demand variesWhen the amount of supply or demand varies

– Timing uncertaintyTiming uncertainty• Time of receipt of supply or demand differs from that expectedTime of receipt of supply or demand differs from that expected

– Two ways to protect:Two ways to protect:• Carry extra stock (safety stock)Carry extra stock (safety stock)

• Order early (safety lead time)Order early (safety lead time)

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• Safety StockSafety Stock– SS is used to protect against uncertainty in SS is used to protect against uncertainty in

supply and demand.supply and demand.

– SS depends on:SS depends on:• Variability of demand during lead timeVariability of demand during lead time

• Frequency of reorderFrequency of reorder

• Service level desiredService level desired

• Length of lead timeLength of lead time

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• Variability of DemandVariability of Demand– Actual demand will vary from the Actual demand will vary from the

forecast due to bias and random forecast due to bias and random fluctuations.fluctuations.

– Usually the variation of demand will Usually the variation of demand will follow a normal distribution (bell curve)follow a normal distribution (bell curve)

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• Variability of DemandVariability of Demand– Actual demand will beActual demand will be

+1Sigma

-1Sigma

-2Sigma

+2Sigma

-3Sigma

+3Sigma

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Average & DispersionAverage & Dispersion

Demand Dispersion

0

10

20

30

40

50

60

66 80 92 96 100 103 110 119 131

Demand

# o

f T

imes

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Mean Absolute DeviationMean Absolute DeviationForecast

Forecast DForecast D Actual DActual D DeviationDeviation

100100 6666 3434

100100 110110 1010

100100 131131 3131

100100 103103 33

100100 9696 44

100100 119119 1919

100100 9292 88

100100 100100 00

100100 8080 2020

n

periodsn for deviation absolute of Sum=MAD

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Standard Deviation (Sigma) Standard Deviation (Sigma) Forecast Forecast DemandDemand

Actual Actual DemandDemand

DeviationDeviation Dev SquaredDev Squared

100100 6666 3434 11561156

100100 110110 1010 100100

100100 131131 3131 961961

100100 103103 33 99

100100 9696 44 1616

100100 119119 1919 361361

100100 9292 88 6464

100100 100100 00 00

100100 8080 2020 400400

Total 3067

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• Determining Safety StockDetermining Safety Stock– SS is needed only to cover those periods in which SS is needed only to cover those periods in which

the demand during lead time is greater than the demand during lead time is greater than average.average.

– Service levelService level is a statement of the percentage of is a statement of the percentage of time there is no stockouttime there is no stockout

– Safety FactorSafety Factor is derived from the service level is derived from the service level

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• Safety Stock EquationSafety Stock Equation

• Safety Stock = (Sigma x Safety Factor)Safety Stock = (Sigma x Safety Factor)

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Example: Safety Stock & Order PointExample: Safety Stock & Order Point

Using the figures in the last example problem in which the sigma was Using the figures in the last example problem in which the sigma was calculated as 18.5 unitscalculated as 18.5 units Safety Stock = (Sigma x Safety Factor)Safety Stock = (Sigma x Safety Factor)

Q: a) Calculate the safety stock and order point for an 84% service Q: a) Calculate the safety stock and order point for an 84% service level.level.

A: A: Safety stock = Sigma x safety FactorSafety stock = Sigma x safety Factor

= 18.5 x 1.00 = = 18.5 x 1.00 = 18.5 units18.5 units

Order point = DDLT + SSOrder point = DDLT + SS

= 100 + 18.5 = = 100 + 18.5 = 118.5 units118.5 units

From safety factor on page 291

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Using the figures in the last example problem in which the sigma was Using the figures in the last example problem in which the sigma was calculated as 18.5 unitscalculated as 18.5 units Safety Stock = (Sigma x Safety Factor)Safety Stock = (Sigma x Safety Factor)

Q: b) If a safety stock equal to 95.5% is carried, calculate the safety stock Q: b) If a safety stock equal to 95.5% is carried, calculate the safety stock and the order point.and the order point.

A: A: Safety stock = Sigma x safety FactorSafety stock = Sigma x safety Factor

= 18.5 x 1.65 = 30.525 or= 18.5 x 1.65 = 30.525 or 31 units 31 units


= 100 + 31 = = 100 + 31 = 131 units131 units

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Safety Factor

Generated using Excel function NORMSINV

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Q: If the standard deviation is 18.5 units, what safety stock Q: If the standard deviation is 18.5 units, what safety stock should be carried to provide a service level of 90%? If the should be carried to provide a service level of 90%? If the expected demand during the lead-time is 500 units, what is expected demand during the lead-time is 500 units, what is the order point?the order point?

A: The safety factor for a service level of 90% is 1.28A: The safety factor for a service level of 90% is 1.28

Safety stock = sigma x safety factorSafety stock = sigma x safety factor

= 18.5 x 1.28 = 23.68 or = 18.5 x 1.28 = 23.68 or 24 units24 units


= 500 + 24 = = 500 + 24 = 524 units524 units

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• Service LevelService Level– Stockouts lead to costs such asStockouts lead to costs such as

• Back-order costsBack-order costs

• Lost SalesLost Sales

• Lost CustomersLost Customers

• Possible only when stock is running low, usually the time Possible only when stock is running low, usually the time when an order is placedwhen an order is placed

• Chances of a stockout are directly proportional to frequency of Chances of a stockout are directly proportional to frequency of reorderreorder

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• Service LevelService Level– The service level will determine the number of The service level will determine the number of

stockouts that will occur each year.stockouts that will occur each year.

– Service level decisions are the responsibility of Service level decisions are the responsibility of senior management and should reflect the senior management and should reflect the company’s corporate and marketing strategy.company’s corporate and marketing strategy.

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• Determining When the Order Point is ReachedDetermining When the Order Point is Reached

– Two-Bin SystemTwo-Bin System• A quantity of an item equal to the order point is set aside and A quantity of an item equal to the order point is set aside and

not touched until the main stock has been usednot touched until the main stock has been used

• Variations include tags and indicatorsVariations include tags and indicators

Full Empty

Order One Bin ofInventory

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• Determining When the Order Point is ReachedDetermining When the Order Point is Reached

– Perpetual Inventory SystemPerpetual Inventory System• A continual account of inventory transactions as they occurA continual account of inventory transactions as they occur

• Contains “permanent” and “variable” informationContains “permanent” and “variable” information– BarcodingBarcoding

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• Periodic Review SystemPeriodic Review System– The quantity on hand of a particular item is determined The quantity on hand of a particular item is determined

at specified, fixed-time intervals.at specified, fixed-time intervals.

– The review period is fixed and the order quantity is The review period is fixed and the order quantity is allowed to vary.allowed to vary.

– The quantity on hand plus the quantity ordered must be The quantity on hand plus the quantity ordered must be sufficient to last until next shipment is received.sufficient to last until next shipment is received.

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