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10/16/2010
1
1212 Inventory Management
Inventory Management
12 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall
PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, 10e Operations Management, 10e Principles of Operations Management, 8ePrinciples of Operations Management, 8e
PowerPoint slides by Jeff Heyl
OutlineOutlineGlobal Company Profile: Amazon.comThe Importance of Inventory
Functions of Inventory
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Functions of InventoryTypes of Inventory
Outline Outline –– ContinuedContinuedManaging Inventory
ABC AnalysisRecord AccuracyCycle Counting
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Cycle CountingControl of Service Inventories
Inventory ModelsIndependent vs. Dependent DemandHolding, Ordering, and Setup Costs
Outline Outline –– ContinuedContinued
Inventory Models for Independent Demand
The Basic Economic Order Quantity (EOQ) Model
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(EOQ) ModelMinimizing CostsReorder PointsProduction Order Quantity ModelQuantity Discount Models
Outline Outline –– ContinuedContinued
Probabilistic Models and Safety Stock
Other Probabilistic Models
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Single-Period ModelFixed-Period (P) Systems
Learning ObjectivesLearning ObjectivesWhen you complete this chapter you When you complete this chapter you should be able to:should be able to:
1. Conduct an ABC analysis
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2. Explain and use cycle counting3. Explain and use the EOQ model for
independent inventory demand4. Compute a reorder point and safety
stock
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Learning ObjectivesLearning ObjectivesWhen you complete this chapter you When you complete this chapter you should be able to:should be able to:
5. Apply the production order quantity model
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model6. Explain and use the quantity
discount model7. Understand service levels and
probabilistic inventory models
Amazon.comAmazon.com
Amazon.com started as a “virtual” retailer – no inventory, no warehouses, no overhead; just computers taking orders to be filled
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computers taking orders to be filled by othersGrowth has forced Amazon.com to become a world leader in warehousing and inventory management
Amazon.comAmazon.com1. Each order is assigned by computer to
the closest distribution center that has the product(s)
2. A “flow meister” at each distribution center assigns work crews
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center assigns work crews3. Lights indicate products that are to be
picked and the light is reset4. Items are placed in crates on a conveyor,
bar code scanners scan each item 15 times to virtually eliminate errors
Amazon.comAmazon.com
5. Crates arrive at central point where items are boxed and labeled with new bar code
6. Gift wrapping is done by hand at 30 packages per hour
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packages per hour7. Completed boxes are packed, taped,
weighed and labeled before leaving warehouse in a truck
8. Order arrives at customer within 2 - 3 days
Inventory ManagementInventory Management
The objective of inventory The objective of inventory management is to strike a balance management is to strike a balance between inventory investment andbetween inventory investment and
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between inventory investment and between inventory investment and customer servicecustomer service
Importance of InventoryImportance of Inventory
One of the most expensive assets of many companies representing as much as 50% of total invested
it l
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capitalOperations managers must balance inventory investment and customer service
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Functions of InventoryFunctions of Inventory1. To decouple or separate various
parts of the production process2. To decouple the firm from
fluctuations in demand and
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fluctuations in demand and provide a stock of goods that will provide a selection for customers
3. To take advantage of quantity discounts
4. To hedge against inflation
Types of InventoryTypes of InventoryRaw material
Purchased but not processedWork-in-process
Undergone some change but not completed
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A function of cycle time for a productMaintenance/repair/operating (MRO)
Necessary to keep machinery and processes productive
Finished goodsCompleted product awaiting shipment
The Material Flow CycleThe Material Flow Cycle
Cycle time
95% 5%
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Figure 12.1
Input Wait for Wait to Move Wait in queue Setup Run Outputinspection be moved time for operator time time
Managing Inventory Managing Inventory
1. How inventory items can be classified
2 How accurate inventory records
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2. How accurate inventory records can be maintained
ABC AnalysisABC AnalysisDivides inventory into three classes based on annual dollar volume
Class A - high annual dollar volumeClass B - medium annual dollar
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Class B medium annual dollar volumeClass C - low annual dollar volume
Used to establish policies that focus on the few critical parts and not the many trivial ones
ABC AnalysisABC Analysis
Item Stock
Number
Percent of Number of
Items Stocked
Annual Volume (units) x
Unit Cost =
Annual Dollar
Volume
Percent of Annual Dollar
Volume Class
#10286 20% 1,000 $ 90.00 $ 90,000 38.8% A72%
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#11526 500 154.00 77,000 33.2% A
#12760 1,550 17.00 26,350 11.3% B
#10867 30% 350 42.86 15,001 6.4% B
#10500 1,000 12.50 12,500 5.4% B
23%
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ABC AnalysisABC Analysis
Item Stock
Number
Percent of Number of
Items Stocked
Annual Volume (units) x
Unit Cost =
Annual Dollar
Volume
Percent of Annual Dollar
Volume Class
#12572 600 $ 14.17 $ 8,502 3.7% C
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#14075 2,000 .60 1,200 .5% C
#01036 50% 100 8.50 850 .4% C
#01307 1,200 .42 504 .2% C
#10572 250 .60 150 .1% C
8,550 $232,057 100.0%
5%
ABC AnalysisABC Analysis
A Items
al d
olla
r usa
ge
80 –70 –60 –50 –
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C ItemsB Items
Perc
ent o
f ann
ua
50 40 –30 –20 –10 –0 – | | | | | | | | | |
10 20 30 40 50 60 70 80 90 100
Percent of inventory itemsFigure 12.2
ABC AnalysisABC Analysis
Other criteria than annual dollar volume may be used
Anticipated engineering changes
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Delivery problemsQuality problemsHigh unit cost
ABC AnalysisABC Analysis
Policies employed may includeMore emphasis on supplier development for A items
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Tighter physical inventory control for A itemsMore care in forecasting A items
Record AccuracyRecord AccuracyAccurate records are a critical ingredient in production and inventory systemsAllows organization to focus on what is needed
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Necessary to make precise decisions about ordering, scheduling, and shippingIncoming and outgoing record keeping must be accurateStockrooms should be secure
Cycle CountingCycle CountingItems are counted and records updated on a periodic basisOften used with ABC analysis to determine cycleHas several advantages
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1. Eliminates shutdowns and interruptions2. Eliminates annual inventory adjustment3. Trained personnel audit inventory accuracy4. Allows causes of errors to be identified and
corrected5. Maintains accurate inventory records
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Cycle Counting ExampleCycle Counting Example5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C itemsPolicy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days)
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Item Class Quantity Cycle Counting Policy
Number of Items Counted per Day
A 500 Each month 500/20 = 25/day
B 1,750 Each quarter 1,750/60 = 29/day
C 2,750 Every 6 months 2,750/120 = 23/day77/day
Control of Service Control of Service InventoriesInventories
Can be a critical component of profitabilityLosses may come from shrinkage or pilferage
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shrinkage or pilferageApplicable techniques include
1. Good personnel selection, training, and discipline
2. Tight control on incoming shipments3. Effective control on all goods leaving
facility
Independent Versus Independent Versus Dependent DemandDependent Demand
Independent demandIndependent demand - the demand for item is independent of the demand for any other
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o t e de a d o a y ot eitem in inventoryDependent demandDependent demand - the demand for item is dependent upon the demand for some other item in the inventory
Holding, Ordering, and Holding, Ordering, and Setup CostsSetup Costs
Holding costsHolding costs - the costs of holding or “carrying” inventory over timeOrdering costsOrdering costs the costs of
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Ordering costsOrdering costs - the costs of placing an order and receiving goodsSetup costsSetup costs - cost to prepare a machine or process for manufacturing an order
Holding CostsHolding Costs
Category
Cost (and range) as a Percent of Inventory Value
Housing costs (building rent or depreciation, operating costs, taxes, insurance)
6% (3 - 10%)
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Material handling costs (equipment lease or depreciation, power, operating cost)
3% (1 - 3.5%)
Labor cost 3% (3 - 5%)Investment costs (borrowing costs, taxes, and insurance on inventory)
11% (6 - 24%)
Pilferage, space, and obsolescence 3% (2 - 5%)Overall carrying cost 26%
Table 12.1
Holding CostsHolding Costs
Category
Cost (and range) as a Percent of Inventory Value
Housing costs (building rent or depreciation, operating costs, taxes, insurance)
6% (3 - 10%)
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Material handling costs (equipment lease or depreciation, power, operating cost)
3% (1 - 3.5%)
Labor cost 3% (3 - 5%)Investment costs (borrowing costs, taxes, and insurance on inventory)
11% (6 - 24%)
Pilferage, space, and obsolescence 3% (2 - 5%)Overall carrying cost 26%
Table 12.1
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Inventory Models for Inventory Models for Independent DemandIndependent Demand
Need to determine when and how Need to determine when and how much to ordermuch to order
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1. Basic economic order quantity2. Production order quantity3. Quantity discount model
Basic EOQ ModelBasic EOQ Model
1. Demand is known, constant, and independent
2. Lead time is known and constant
Important assumptions
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3. Receipt of inventory is instantaneous and complete
4. Quantity discounts are not possible5. Only variable costs are setup and holding6. Stockouts can be completely avoided
Inventory Usage Over TimeInventory Usage Over Time
Order quantity = Q(maximum inventory
Usage rate Average inventory on hand
Q2ry
leve
l
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Figure 12.3
level) 2
Minimum inventory
Inve
ntor
Time0
Minimizing CostsMinimizing CostsObjective is to minimize total costs
Total cost of holding and setup (order)
Minimum t t l t
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Table 12.4(c)
Annu
al c
ost
Order quantity
Holding cost
Setup (or order) cost
total cost
Optimal order quantity (Q*)
The EOQ ModelThe EOQ ModelQ = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per year
Annual setup cost = SDQ
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Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order)
Annual demandNumber of units in each order
Setup or order cost per order=
= (S)DQ
The EOQ ModelThe EOQ ModelQ = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per year
Annual setup cost = SDQ
Annual holding cost = HQ2
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Annual holding cost = (Average inventory level) x (Holding cost per unit per year)
Order quantity2= (Holding cost per unit per year)
= (H)Q2
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The EOQ ModelThe EOQ ModelQ = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per year
O ti l d tit i f d h l t t
Annual setup cost = SDQ
Annual holding cost = HQ2
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Optimal order quantity is found when annual setup cost equals annual holding cost
DQ S = HQ
2Solving for Q* 2DS = Q2H
Q2 = 2DS/HQ* = 2DS/H
An EOQ ExampleAn EOQ ExampleDetermine optimal number of needles to orderD = 1,000 unitsS = $10 per orderH = $.50 per unit per year
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Q* = 2DSH
Q* = 2(1,000)(10)0.50 = 40,000 = 200 units
An EOQ ExampleAn EOQ ExampleDetermine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = $10 per orderH = $.50 per unit per year
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= N = =Expected number of
orders
DemandOrder quantity
DQ*
N = = 5 orders per year 1,000200
An EOQ ExampleAn EOQ ExampleDetermine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = $10 per order N = 5 orders per yearH = $.50 per unit per year
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= T =Expected
time between orders
Number of working days per year
N
T = = 50 days between orders2505
An EOQ ExampleAn EOQ ExampleDetermine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = $10 per order N = 5 orders per yearH = $.50 per unit per year T = 50 days
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Total annual cost = Setup cost + Holding cost
TC = S + HDQ
Q2
TC = ($10) + ($.50)1,000200
2002
TC = (5)($10) + (100)($.50) = $50 + $50 = $100
Robust ModelRobust Model
The EOQ model is robustIt works even if all parameters and assumptions are not met
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and assumptions are not metThe total cost curve is relatively flat in the area of the EOQ
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An EOQ ExampleAn EOQ Example
Management underestimated demand by 50%D = 1,000 units Q* = 200 unitsS = $10 per order N = 5 orders per yearH = $.50 per unit per year T = 50 days
1,500 units
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TC = S + HDQ
Q2
TC = ($10) + ($.50) = $75 + $50 = $1251,500200
2002
Total annual cost increases by only 25%
An EOQ ExampleAn EOQ Example
Actual EOQ for new demand is 244.9 unitsD = 1,000 units Q* = 244.9 unitsS = $10 per order N = 5 orders per yearH = $.50 per unit per year T = 50 days
1,500 units
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TC = S + HDQ
Q2
TC = ($10) + ($.50)1,500244.9
244.92
TC = $61.24 + $61.24 = $122.48
Only 2% less than the total cost of $125
when the order quantity
was 200
Reorder PointsReorder Points
EOQ answers the “how much” questionThe reorder point (ROP) tells “when” to order
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ROP = Lead time for a new order in days
Demand per day
= d x L
d = DNumber of working days in a year
Reorder Point CurveReorder Point CurveQ*
leve
l (un
its)
Slope = units/day = d
Resupply takes place as order arrives
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ROP (units)Inve
ntor
y
Time (days)Figure 12.5 Lead time = L
Reorder Point ExampleReorder Point ExampleDemand = 8,000 iPods per year250 working day yearLead time for orders is 3 working days
dD
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ROP = d x L
d = Number of working days in a year
= 8,000/250 = 32 units
= 32 units per day x 3 days = 96 units
Production Order Quantity Production Order Quantity ModelModel
Used when inventory builds up over a period of time after an order is placed
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order is placedUsed when units are produced and sold simultaneously
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Production Order Quantity Production Order Quantity ModelModel
leve
l
Part of inventory cycle during which production (and usage) is taking place
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Inve
ntor
y l
Time
Demand part of cycle with no production
t
Maximum inventory
Figure 12.6
Production Order Quantity Production Order Quantity ModelModel
Q = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage ratet = Length of the production run in days
= (Average inventory level) xAnnual inventory holding cost
Holding cost per unit per year
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(Average inventory level) xholding cost per unit per year
= (Maximum inventory level)/2Annual inventory level
= –Maximum inventory level
Total produced during the production run
Total used during the production run
= pt – dt
Production Order Quantity Production Order Quantity ModelModel
Q = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage ratet = Length of the production run in days
= –Maximum i t l l
Total produced during th d ti
Total used during th d ti
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inventory level the production run the production run= pt – dt
However, Q = total produced = pt ; thus t = Q/p
Maximum inventory level = p – d = Q 1 –Q
pQp
dp
Holding cost = (H) = 1 – Hdp
Q2
Maximum inventory level2
Production Order Quantity Production Order Quantity ModelModel
Q = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage rateD = Annual demand
Setup cost = (D/Q)S
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Q2 = 2DSH[1 - (d/p)]
Q* = 2DSH[1 - (d/p)]p
Holding cost = HQ[1 - (d/p)]12
(D/Q)S = HQ[1 - (d/p)]12
Production Order Quantity Production Order Quantity ExampleExample
D = 1,000 units p = 8 units per dayS = $10 d = 4 units per dayH = $0.50 per unit per year
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Q* = 2DSH[1 - (d/p)]
= 282.8 or 283 hubcaps
Q* = = 80,0002(1,000)(10)
0.50[1 - (4/8)]
Production Order Quantity Production Order Quantity ModelModel
Note:
d = 4 = =D
Number of days the plant is in operation1,000250
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When annual data are used the equation becomes
Q* = 2DSannual demand rate
annual production rateH 1 –
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Quantity Discount ModelsQuantity Discount Models
Reduced prices are often available when larger quantities are purchasedTrade-off is between reduced product cost and increased holding cost
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and increased holding cost
Total cost = Setup cost + Holding cost + Product cost
TC = S + H + PDDQ
Q2
Quantity Discount ModelsQuantity Discount Models
Discount Number Discount Quantity Discount (%)
Discount Price (P)
A typical quantity discount schedule
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Number Discount Quantity Discount (%) Price (P)1 0 to 999 no discount $5.00
2 1,000 to 1,999 4 $4.80
3 2,000 and over 5 $4.75
Table 12.2
Quantity Discount ModelsQuantity Discount Models
1. For each discount, calculate Q*2. If Q* for a discount doesn’t qualify,
Steps in analyzing a quantity discountSteps in analyzing a quantity discount
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ychoose the smallest possible order size to get the discount
3. Compute the total cost for each Q* or adjusted value from Step 2
4. Select the Q* that gives the lowest total cost
Quantity Discount ModelsQuantity Discount Modelst $
Total cost curve for
discount 1
Total cost curve for discount 2
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1,000 2,000
Tota
l cos
t
0Order quantity
Q* for discount 2 is below the allowable range at point aand must be adjusted upward to 1,000 units at point b
ab
1st price break
2nd price break
Total cost curve for discount 3
Figure 12.7
Quantity Discount ExampleQuantity Discount ExampleCalculate Q* for every discount Q* = 2DS
IP
Q1* = = 700 cars/order2(5,000)(49)( 2)(5 00)
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1 (.2)(5.00)
Q2* = = 714 cars/order2(5,000)(49)(.2)(4.80)
Q3* = = 718 cars/order2(5,000)(49)(.2)(4.75)
Quantity Discount ExampleQuantity Discount ExampleCalculate Q* for every discount Q* = 2DS
IP
Q1* = = 700 cars/order2(5,000)(49)( 2)(5 00)
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1 (.2)(5.00)
Q2* = = 714 cars/order2(5,000)(49)(.2)(4.80)
Q3* = = 718 cars/order2(5,000)(49)(.2)(4.75)
1,000 — adjusted
2,000 — adjusted
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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
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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 12.3
Choose the price and quantity that gives the lowest total cost
Buy 1,000 units at $4.80 per unit
Probabilistic Models and Probabilistic Models and Safety StockSafety Stock
Used when demand is not constant or certainUse safety stock to achieve a desired
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service level and avoid stockouts
ROP = d x L + ss
Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit
x the number of orders per year
Safety Stock ExampleSafety Stock Example
Number of Units Probability
ROP = 50 units Stockout cost = $40 per frameOrders per year = 6 Carrying cost = $5 per frame per year
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30 .240 .2
ROP 50 .360 .270 .1
1.0
Safety Stock ExampleSafety Stock ExampleROP = 50 units Stockout cost = $40 per frameOrders per year = 6 Carrying cost = $5 per frame per year
Safety Stock
Additional Holding Cost Stockout Cost
Total Cost
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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 20 frames gives the lowest total costROP = 50 + 20 = 70 frames
Probabilistic DemandProbabilistic Demand
y le
vel Minimum demand during lead time
Maximum demand during lead time
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Safety stock 16.5 units
ROP
Place order
Inve
ntor
y
Time0
Mean demand during lead time
Normal distribution probability of demand during lead time
Expected demand during lead time (350 kits)
ROP = 350 + safety stock of 16.5 = 366.5
Receive order
Lead time
Figure 12.8
Probabilistic DemandProbabilistic Demand
Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined
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ROP = demand during lead time + ZσdLT
where Z = number of standard deviationsσdLT = standard deviation of demand
during lead time
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Probabilistic DemandProbabilistic Demand
Probability ofno stockout
95% of the time
Risk of a stockout (5% of area of normal curve)
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Safety stock
95% of the time
Mean demand
350
ROP = ? kits Quantity
Number of standard deviations
0 z
)
Probabilistic ExampleProbabilistic ExampleAverage demand = μ = 350 kitsStandard deviation of demand during lead time = σdLT = 10 kits5% stockout policy (service level = 95%)
Using Appendix I, for an area under the curve
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of 95%, the Z = 1.65
Safety stock = ZσdLT = 1.65(10) = 16.5 kits
Reorder point = expected demand during lead time + safety stock
= 350 kits + 16.5 kits of safety stock= 366.5 or 367 kits
Other Probabilistic ModelsOther Probabilistic Models
1 When demand is variable and lead
When data on demand during lead time is not available, there are other models available
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1. When demand is variable and lead time is constant
2. When lead time is variable and demand is constant
3. When both demand and lead time are variable
Other Probabilistic ModelsOther Probabilistic ModelsDemand is variable and lead time is constant
ROP = (average daily demand x lead time in days) + ZσdLT
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x lead time in days) + ZσdLT
where σd = standard deviation of demand per dayσdLT = σd lead time
Probabilistic ExampleProbabilistic ExampleAverage daily demand (normally distributed) = 15Standard deviation = 5Lead time is constant at 2 days90% service level desired
Z for 90% = 1.28From Appendix I
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ROP = (15 units x 2 days) + ZσdLT
= 30 + 1.28(5)( 2)= 30 + 9.02 = 39.02 ≈ 39
Safety stock is about 9 iPods
Other Probabilistic ModelsOther Probabilistic ModelsLead time is variable and demand is constant
ROP = (daily demand x average lead time in days)
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time in days)= Z x (daily demand) x σLT
where σLT = standard deviation of lead time in days
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Probabilistic ExampleProbabilistic Example
Daily demand (constant) = 10Average lead time = 6 daysStandard deviation of lead time = σLT = 398% service level desired
Z for 98% = 2.055From Appendix I
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ROP = (10 units x 6 days) + 2.055(10 units)(3)= 60 + 61.65 = 121.65
Reorder point is about 122 cameras
Other Probabilistic ModelsOther Probabilistic ModelsBoth demand and lead time are variable
ROP = (average daily demand x average lead time) + ZσdLT
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x average lead time) + ZσdLT
where σd = standard deviation of demand per dayσLT = standard deviation of lead time in daysσdLT = (average lead time x σd
2) + (average daily demand)2 x σLT
2
Probabilistic ExampleProbabilistic ExampleAverage daily demand (normally distributed) = 150Standard deviation = σd = 16Average lead time 5 days (normally distributed)Standard deviation = σLT = 1 day95% service level desired Z for 95% = 1 65
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Z for 95% = 1.65From Appendix I
ROP = (150 packs x 5 days) + 1.65σdLT
= (150 x 5) + 1.65 (5 days x 162) + (1502 x 12)= 750 + 1.65(154) = 1,004 packs
Single Period ModelSingle Period ModelOnly one order is placed for a productUnits have little or no value at the end of the sales period
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Cs = Cost of shortage = Sales price/unit – Cost/unitCo = Cost of overage = Cost/unit – Salvage value
Service level =Cs
Cs + Co
Single Period ExampleSingle Period ExampleAverage demand = μ = 120 papers/dayStandard deviation = σ = 15 papersCs = cost of shortage = $1.25 - $.70 = $.55Co = cost of overage = $.70 - $.30 = $.40
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Service level = Cs
Cs + Co
.55.55 + .40.55.95
=
= = .578
Service level
57.8%
Optimal stocking levelμ = 120
Single Period ExampleSingle Period Example
From Appendix I, for the area .578, Z ≅ .20The optimal stocking level
= 120 copies + (.20)(σ)
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120 copies + (.20)(σ)
= 120 + (.20)(15) = 120 + 3 = 123 papers
The stockout risk = 1 – service level
= 1 – .578 = .422 = 42.2%
10/16/2010
14
FixedFixed--Period (P) SystemsPeriod (P) Systems
Orders placed at the end of a fixed periodInventory counted only at end of periodOrder brings inventory up to target level
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g y p g
Only relevant costs are ordering and holdingLead times are known and constantItems are independent from one another
FixedFixed--Period (P) SystemsPeriod (P) Systems
tory
Q2
Target quantity (T)
Q4
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On-
hand
inve
n
Time
Q1
P
Q3
P
P
Figure 12.9
FixedFixed--Period (P) ExamplePeriod (P) Example
Order amount (Q) = Target (T) On
3 jackets are back ordered No jackets are in stockIt is time to place an order Target value = 50
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Order amount (Q) = Target (T) - On-hand inventory - Earlier orders not yet
received + Back orders
Q = 50 - 0 - 0 + 3 = 53 jackets
FixedFixed--Period SystemsPeriod Systems
Inventory is only counted at each review periodMay be scheduled at convenient times
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yAppropriate in routine situationsMay result in stockouts between periodsMay require increased safety stock
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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
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