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Order Quantities - Examples Order Quantities Order Quantities -- Examples Examples
Outline:Outline:I. Basic Inventory Planning QuestionsI. Basic Inventory Planning QuestionsII. Inventory ModelsII. Inventory ModelsIII. EOQ Model III. EOQ Model IV. EOQ Model ExampleIV. EOQ Model ExampleV. Production Order Quantity ModelV. Production Order Quantity ModelVI. POQ Model ExampleVI. POQ Model ExampleVII. Fixed Period Model.VII. Fixed Period Model.
KuliahKuliah keke--7: Rabu/5 Nov 20087: Rabu/5 Nov 2008
I. Basic Inventory Planning Questions
I. Basic Inventory Planning I. Basic Inventory Planning QuestionsQuestions
How much to order?How much to order?Purchase Order
Description Qty.Microwave 1000
How much to order?How much to order?When to order?When to order? Purchase Order
Description Qty.Microwave 1000
II. Inventory ModelII. Inventory ModelII. Inventory Model
We need Inventory Models:We need Inventory Models:1.1. Economic order quantityEconomic order quantity2.2. Production order quantityProduction order quantity3.3. Quantity discountQuantity discount
Help answer the inventory planning questions!
Help answer the inventory planning questions!
Why Carrying Cost Increases?Why Carrying Cost Increases?Why Carrying Cost Increases?
More units must be stored if more More units must be stored if more orderedordered
Purchase OrderDescription Qty.Microwave 1000
Purchase OrderDescription Qty.Microwave 1
Order Order quantityquantity
Order Order quantityquantity
Why Order Cost Decreases?Why Order Cost Decreases?Why Order Cost Decreases?
Cost is spread over more unitsCost is spread over more units
Example: You need 1000 microwave ovens Example: You need 1000 microwave ovens
Purchase OrderDescription Qty.Microwave 1000
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
1 Order (Postage $ 0.32)1 Order (Postage $ 0.32) 1000 Orders (Postage $320)1000 Orders (Postage $320)
Order Order quantityquantity
III. EOQ ModelIII. EOQ ModelIII. EOQ Model
Order QuantityOrder Quantity
Annual CostAnnual Cost 1. How much to order?
EOQ ModelEOQ ModelEOQ Model
Order QuantityOrder Quantity
Annual CostAnnual Cost
Carrying CostCarrying Cost
1. How much to order?
EOQ ModelEOQ ModelEOQ Model
Order QuantityOrder Quantity
Annual CostAnnual Cost
Carrying CostCarrying Cost
Order (Setup) CostOrder (Setup) Cost
1. How much to order?
EOQ ModelEOQ ModelEOQ Model
Order QuantityOrder Quantity
Annual CostAnnual Cost
Carrying CostCarrying Cost
Total Cost CurveTotal Cost Curve
Order (Setup) CostOrder (Setup) Cost
1. How much to order?
EOQ ModelEOQ ModelEOQ Model
Order QuantityOrder Quantity
Annual CostAnnual Cost
Carrying CostCarrying Cost
Total Cost CurveTotal Cost Curve
Order (Setup) CostOrder (Setup) Cost
Optimal Optimal Order Quantity (Q*)Order Quantity (Q*)
1. How much to order?
EOQ Model: When to Order?EOQ Model: When to Order?EOQ Model: When to Order?
Inventory LevelInventory Level
TimeTime
2. When to order?
EOQ Model EOQ Model EOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
Decrease due to Decrease due to constant demandconstant demand
TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
Instantaneous Instantaneous receipt of optimal receipt of optimal order quantityorder quantity
TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
Lead TimeLead Time TimeTime
2. When to order?
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order Quantity Quantity (Q*)(Q*)
Lead TimeLead Time
Reorder Reorder Point Point
(ROP)(ROP)TimeTime
2. When to order?
Reorder Reorder Point Point
(ROP)(ROP)TimeTime
EOQ ModelEOQ ModelEOQ Model
Inventory LevelInventory Level
Optimal Optimal Order Order QuantityQuantity(Q*)(Q*)
AverageAverageInventory (Q*/2)Inventory (Q*/2)
Lead TimeLead Time
2. When to order?
IV. EOQ Model Example IV. EOQ Model Example IV. EOQ Model Example
Problem 1Problem 1::When the inventory of microwaves gets When the inventory of microwaves gets down to 15 units (reorder point), order down to 15 units (reorder point), order 35 units (EOQ).35 units (EOQ).
15 left
Purchase OrderDescription Qty.Microwave 35
Problem 2:Problem 2:YouYou’’re a buyer for Walre a buyer for Wal--Mart. Mart. WalWal--Mart needs Mart needs 10001000 coffee coffee makers per year. The cost of makers per year. The cost of each coffee maker is each coffee maker is $78$78. . Ordering cost is Ordering cost is $100$100 per order. per order. Carrying cost is Carrying cost is 40%40% of per unit of per unit cost. Lead time is cost. Lead time is 55 days. Waldays. Wal--Mart is open Mart is open 365365 days/yr. What days/yr. What is the is the optimal order quantityoptimal order quantity & & ROPROP??
A = 1,000 unitA = 1,000 unitS = $ 100 per orderS = $ 100 per orderc = $ 78 per unitc = $ 78 per uniti = 0.40i = 0.40L = 5 daysL = 5 daysWorking days/year = 365 daysWorking days/year = 365 days
Question:Question:a.a. EOQ = ?EOQ = ?b.b. ROP = ?ROP = ?
EOQ Solution*EOQ Solution*EOQ Solution*
Qi X c
d A
ROP d L
*.
=2
.
. .
= =
= = =
= ⋅ = =
X1000X10040 (78)
80
1000365
2 74
2 74 X 5 13 7
units
units / day
units
Working Days/ Year
2 X A X S
V. Production Order Quantity ModelV. Production Order Quantity ModelV. Production Order Quantity Model
1.1. Answers how much to order & when to orderAnswers how much to order & when to order2.2. Allows partial receipt of material (other EOQ Allows partial receipt of material (other EOQ
assumptions apply)assumptions apply)3.3. Suited for production environmentSuited for production environment
•• Material produced, used immediatelyMaterial produced, used immediately•• Provides production lot sizeProvides production lot size
4.4. Lower carrying cost than EOQ model.Lower carrying cost than EOQ model.
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
Supply Supply EndsEnds
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
Supply Supply EndsEnds
Inventory level with NO Inventory level with NO demand during supply of demand during supply of optimum order quantityoptimum order quantity
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
Supply Supply EndsEnds
Inventory level with NO Inventory level with NO demand during supply of demand during supply of optimum order quantityoptimum order quantity
Q*Q*
Q* is optimum Q* is optimum order qtyorder qty
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
Supply Supply EndsEnds
Q*Q* Quantity used before Quantity used before becoming inventorybecoming inventory
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
Supply Supply EndsEnds
Decrease due to Decrease due to no supply & no supply & constant demandconstant demand
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory LevelNext CycleNext Cycle
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
Next CycleNext Cycle
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
Supply Supply EndsEnds
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Supply Supply BeginsBegins
Supply Supply EndsEnds
POQ Model: Inventory LevelsPOQ Model: Inventory LevelsPOQ Model: Inventory Levels
TimeTime
Inventory LevelInventory Level
Max. Inventory Max. Inventory Q*Q*··(1(1-- d/pd/p))
POQ Model EquationsPOQ Model EquationsPOQ Model Equations
Max. Inventory Level
Order Cost
Carrying Cost =
= −
=
Q dp
x 1
AQ
SxAA = Demand per year= Demand per yearSS = Order cost= Order costHH = Carrying cost (i X c)= Carrying cost (i X c)dd = Demand per day= Demand per dayp p = Production per day= Production per day
Optimal Order Quantity = Qp* = 2 x A x S
H x (1- d/p)
Q 1 - (d/p) H
VI. POQ Model ExampleVI. POQ Model ExampleVI. POQ Model Example
YouYou’’re a production planner re a production planner for Stanley Tools. Stanley for Stanley Tools. Stanley Tools makes Tools makes 30,00030,000 screw screw drivers per year. Demand is drivers per year. Demand is 100100 screw drivers per day & screw drivers per day & production is production is 300 300 per day. per day. Production setup cost is Production setup cost is $150 $150 per order. Carrying cost is per order. Carrying cost is $1.50 $1.50 per screw driver. What per screw driver. What is the is the optimal lot sizeoptimal lot size? ? Max. Max. Inv. Level?Inv. Level?
Production Order Quantity Model Solution*Production Order Quantity Model Solution*Production Order Quantity Model Solution*
Q A S
H dp
p * =⋅ ⋅
⋅=
⋅ ⋅
⋅ −=
= ⋅ − =
2 2 30000 150
1.5 1 100300
3000
3000 100300
2000Max. Inventory Level
AA = Demand Per Year = 30000 unit= Demand Per Year = 30000 unitSS = Order Cost = $ 150 per order= Order Cost = $ 150 per orderHH = Carrying Cost = $ 1,5 per unit= Carrying Cost = $ 1,5 per unitdd = Demand Per Day = 100 unit= Demand Per Day = 100 unitp p = Production Per Day = 300 unit= Production Per Day = 300 unit
1 -
1
Answers how much to orderAnswers how much to orderOrders placed at fixed intervalsOrders placed at fixed intervals
Inventory brought up to target amountInventory brought up to target amountAmount ordered variesAmount ordered varies
No continuous inventory countNo continuous inventory countPossibility of Possibility of stockoutstockout between intervalsbetween intervals
Useful when vendors visit routinelyUseful when vendors visit routinelyExample: P&G representative calls every 2 Example: P&G representative calls every 2 weeksweeks
VII. Fixed Period ModelVII. Fixed Period ModelVII. Fixed Period Model
Inventory Level in a Fixed Period SystemInventory Level in a Fixed Period SystemInventory Level in a Fixed Period System
Various amounts (Qi) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to
target maximum
pp pp pp
QQ11 QQ22
QQ33
QQ44
Target maximum
TimeTime
OnOn-- H
and I
nven
tory
Hand
Inve
ntory
Waktu
Inventory Level Target maximum
Periode PeriodePeriode
Sistem P (Periode Tetap)Kapan memesan?
SistemSistem P (P (PeriodePeriode TetapTetap))KapanKapan memesanmemesan??
Q1 Q2 Q3
VII. Quantity Discount ModelVII. Quantity Discount ModelVII. Quantity Discount Model
Answers how much to order & Answers how much to order & when to orderwhen to orderAllows quantity discountsAllows quantity discounts
Reduced price when item is purchased Reduced price when item is purchased in larger quantitiesin larger quantitiesOther EOQ assumptions applyOther EOQ assumptions apply
TradeTrade--off is between lower price & off is between lower price & increased holding costincreased holding cost
Quantity Discount ModelsQuantity Discount Models
•• Reduced prices are often available when Reduced prices are often available when larger quantities are purchasedlarger quantities are purchased
•• TradeTrade--off is between reduced product cost off is between reduced product cost and increased holding costand increased holding cost
Total cost = Setup cost + Holding cost + Product costTotal cost = Setup cost + Holding cost + Product cost
TC = S + + TC = S + + cAcAAAQQ
QHQH22
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
Discount Discount Quantity 1Quantity 1
Price 1Price 1
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
Discount Discount Quantity 1Quantity 1
Discount Discount Quantity 2Quantity 2
Price 1Price 1 Price 2Price 2
Order Order QuantityQuantity
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Total CostTotal Cost
Discount Discount Quantity 1Quantity 1
Discount Discount Quantity 2Quantity 2
Price 1Price 1 Price 2Price 2 Price 3Price 3
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost TC for TC for Discount 1Discount 1
Discount Discount Quantity 1Quantity 1
Discount Discount Quantity 2Quantity 2
Price 1Price 1 Price 2Price 2 Price 3Price 3
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost TC for TC for Discount 1Discount 1
Discount Discount Quantity 1Quantity 1
Discount Discount Quantity 2Quantity 2
Price 1Price 1 Price 2Price 2 Price 3Price 3
Q*Q*
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
Discount Discount Quantity 1Quantity 1
TC for TC for Discount 2Discount 2
Price 1Price 1 Price 2Price 2 Price 3Price 3
Discount Discount Quantity 2Quantity 2
TC for TC for Discount 1Discount 1
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
Disc Disc Qty 1Qty 1
TC for TC for Discount 2Discount 2
Discount Discount Quantity 2Quantity 2
Price 1Price 1 Price 2Price 2 Price 3Price 3
Q*Q*
TC for TC for Discount 1Discount 1
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
Disc Disc Qty 1Qty 1
TC for TC for Discount 2Discount 2
Discount Discount Quantity 2Quantity 2
Price 1Price 1 Price 2Price 2 Price 3Price 3
Q*Q*
Outside Outside discount discount rangerange
Outside Outside discount rangediscount range
TC for TC for Discount 1Discount 1
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
TC for TC for Discount 3Discount 3
Price 1Price 1 Price 2Price 2 Price 3Price 3
Discount Discount Quantity 2Quantity 2
Discount Discount Quantity 1Quantity 1
TC for TC for Discount 2Discount 2
TC for TC for Discount 1Discount 1
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
TC for TC for Discount 3Discount 3
Discount Discount Quantity 2Quantity 2
Price 1Price 1 Price 2Price 2 Price 3Price 3
Q*Q*Discount Discount Quantity 1Quantity 1
TC for TC for Discount 2Discount 2
TC for TC for Discount 1Discount 1
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost
TC for TC for Discount 3Discount 3
Discount Discount Quantity 2Quantity 2
Price 1Price 1 Price 2Price 2 Price 3Price 3
Disc Disc Qty 1Qty 1
Outside Outside discount rangediscount range Q*Q*
TC for TC for Discount 2Discount 2
TC for TC for Discount 1Discount 1
Quantity Discount Model: How Much to Order?
Quantity Discount Model: Quantity Discount Model: How Much to Order?How Much to Order?
Order Order QuantityQuantity
Total CostTotal Cost TC for TC for Discount 1Discount 1
Discount Discount Quantity 1Quantity 1
TC for TC for Discount 2Discount 2
TC for TC for Discount 3Discount 3
Discount Discount Quantity 2Quantity 2
Lowest cost not Lowest cost not in discount rangein discount range
Quantity Quantity OrderedOrdered
Price 1Price 1 Price 2Price 2 Price 3Price 3
Quantity Discount Model StepsQuantity Discount Model StepsQuantity Discount Model Steps
Compute EOQ for each quantity Compute EOQ for each quantity discount pricediscount priceIs computed EOQ in discount range?Is computed EOQ in discount range?
If not, use the lowest cost quantity in If not, use the lowest cost quantity in discount rangediscount range
Compute total cost for EOQ or lowest Compute total cost for EOQ or lowest cost quantity in discount rangecost quantity in discount rangeSelect quantity with lowest total costSelect quantity with lowest total cost
Contoh: Quantity Discount ScheduleContoh: Quantity Discount Schedule
Discount Number
Discount Quantity
Discount (%)
Discount Price (P)
1 0 to 999 No discount
$5.00
2 1,000 to 1,999 4 $4.803 2,000 and over 5 $4.75
Quantity Discount ModelsQuantity Discount Models
1.1. For each discount, calculate Q*For each discount, calculate Q*2.2. If Q* for a discount doesnIf Q* for a discount doesn’’t qualify, t qualify,
choose the smallest possible order size choose the smallest possible order size to get the discountto get the discount
3.3. Compute the total cost for each Q* or Compute the total cost for each Q* or adjusted value from Step 2adjusted value from Step 2
4.4. Select the Q* that gives the lowest total Select the Q* that gives the lowest total costcost
Steps in analyzing a quantity discountSteps in analyzing a quantity discount
Quantity Discount ExampleQuantity Discount Example
Calculate Q* for every discountCalculate Q* for every discount Q* = 2Sic
QQ11* * = = 700= = 700 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(5.00)(.2)(5.00)
QQ22* * = = 714= = 714 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(4.80)(.2)(4.80)
QQ33* * = = 718= = 718 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(4.75)(.2)(4.75)
1,0001,000 —— adjustedadjusted
2,0002,000 —— adjustedadjusted
Quantity Discount ExampleQuantity Discount Example
Discount Number
Unit Price
Order Quantity
Annual Product
Cost
Annual Ordering
Cost
Annual Holding
Cost Total
1 $5.00 700 $25,000 $350 $350 $25,700
2 $4.80 1,000 $24,000 $245 $480 $24,725
3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50
Table 12.3Table 12.3
Choose the price and quantity that gives Choose the price and quantity that gives the lowest total costthe lowest total cost
Buy Buy 1,0001,000 units at units at $4.80$4.80 per unitper unit
VIII. Probabilistic Models and Safety Stock
VIII. Probabilistic Models and Safety Stock
Answer how much and when to order Answer how much and when to order Used when demand is not constant or Used when demand is not constant or certaincertainUse safety stock to achieve a desired Use safety stock to achieve a desired service level and avoid stockoutsservice level and avoid stockouts
ROP ROP == d x Ld x L + + ssss
Annual stockout costs = the sum of the units short Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit x the probability x the stockout cost/unit
x the number of orders per yearx the number of orders per year
Safety Stock ExampleSafety Stock Example
Number of Units Probability30 .240 .2
ROP 50 .360 .270 .1
1.0
ROP ROP = 50= 50 unitsunits Stockout cost Stockout cost = $40= $40 per frameper frameOrders per year Orders per year = 6= 6 Carrying cost Carrying cost = $5= $5 per frame per yearper frame per year
Safety Stock ExampleSafety Stock Example
ROP ROP = 50= 50 unitsunits Stockout cost Stockout cost = $40= $40 per frameper frameOrders per year Orders per year = 6= 6 Carrying cost Carrying cost = $5= $5 per frame per yearper frame per year
Safety Stock
Additional Holding Cost Stockout Cost
Total Cost
20 (20)($5) = $100 $0 $100
10 (10)($5) = $50 (10)(.1)($40)(6) = $240 $290
0 $0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960
A safety stock of A safety stock of 2020 frames gives the lowest total costframes gives the lowest total costROP ROP = 50 + 20 = 70= 50 + 20 = 70 framesframes
Safety stock 16.5 units
ROP ROP
Place Place orderorder
Probabilistic DemandProbabilistic DemandIn
vent
ory
leve
lIn
vent
ory
leve
l
TimeTime00
Minimum demand during lead timeMinimum demand during lead time
Maximum demand during lead timeMaximum demand during lead time
Mean demand during lead timeMean demand during lead time
Normal distribution probability of Normal distribution probability of demand during lead timedemand during lead time
Expected demand during lead time Expected demand during lead time (350(350 kitskits))
ROP ROP = 350 += 350 + safety stock of safety stock of 16.5 = 366.516.5 = 366.5
Receive Receive orderorder
Lead Lead timetime
Figure 12.8Figure 12.8
Probabilistic DemandProbabilistic Demand
Use prescribed service levels to set safety Use prescribed service levels to set safety stock when the cost of stockouts cannot be stock when the cost of stockouts cannot be determineddetermined
ROP = demand during lead time + ZROP = demand during lead time + Zσσdltdlt
wherewhere Z Z == number of standard deviationsnumber of standard deviationsσσdltdlt == standard deviation of demand standard deviation of demand
during lead timeduring lead time
Probabilistic ExampleProbabilistic Example
Average demand Average demand = = μμ = 350= 350 kitskitsStandard deviation of demand during lead time Standard deviation of demand during lead time = = σσdltdlt = 10= 10 kitskits5%5% stockout policy stockout policy ((service level service level = 95%)= 95%)
Using Appendix I, for an area under the curve Using Appendix I, for an area under the curve of of 95%,95%, the Z the Z = 1.65= 1.65
Safety stock Safety stock == ZZσσdltdlt = 1.65(10) = 16.5= 1.65(10) = 16.5 kitskits
Reorder pointReorder point == expected demand during lead time expected demand during lead time + safety stock+ safety stock
== 350350 kits kits + 16.5+ 16.5 kits of safety stockkits of safety stock== 366.5366.5 or or 367367 kitskits