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Inventory Management
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IntroductionInventories are assets of the firm and assuch they represent an Investment.Because such investment requirescommitment of funds, managers mustensure that the firm maintainsinventories at Optimal Level.Inventory is one of the most expensive
assets of many companies.It represents as much as 40% of totalinvested capital.
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Types of InventoriesRaw materials & purchased partsPartially completed goods called work in
progressFinished-goods inventories(manufacturing firms ) or merchandise(retail stores)
Replacement parts, tools & SuppliesGoods-in-transit to warehouses orcustomers
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Two Fundamental
Inventory DecisionsHow much to order of eachmaterial when orders are placedwith either outside suppliers orproduction departments withinorganizations
When to place the orders
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Why We Want to Hold
InventoriesImprove customer serviceReduce certain costs such as
ordering costsstockout costsacquisition costsstart-up quality costs
Contribute to the efficient and effectiveoperation of the production system
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Inventory and Supply Chain
ManagementBullwhip effect
demand information is distorted as it movesaway from the end-use customer
higher safety stock inventories to are stored tocompensateSeasonal or cyclical demandInventory provides independence fromvendors
Take advantage of price discountsInventory provides independence betweenstages and avoids work stop-pages
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Inventory and Quality
ManagementCustomers usually perceive qualityservice as availability of goodsthey want when they want themInventory must be sufficient toprovide high-quality customerservice in TQM
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Inventory Costs
Carrying costCarrying costcost of holding an item in inventorycost of holding an item in inventory
Ordering costOrdering costcost of replenishing inventory.cost of replenishing inventory.
These costs are opposing costs, i.e., as These costs are opposing costs, i.e., asone increases the other decreasesone increases the other decreases
Shortage costShortage costtemporary or permanent loss of salestemporary or permanent loss of saleswhen demand cannot be metwhen demand cannot be met
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Inventory Control Systems
Continuous system (fixed-Continuous system (fixed-order-quantity)order-quantity)
constant amount orderedconstant amount orderedwhen inventory declines towhen inventory declines topredetermined levelpredetermined level
Periodic system (fixed-time-Periodic system (fixed-time-period)period)
order placed for variableorder placed for variableamount after fixed passage of amount after fixed passage of timetime
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Economic Order
Quantity (EOQ) ModelsEOQ
optimal order quantity thatwill minimize total inventorycosts
EOQ= 2DO/C
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Assumptions of BasicEOQ Model
Demand is known with certainty andDemand is known with certainty and
is constant over timeis constant over timeNo shortages are allowedNo shortages are allowedLead time for the receipt of orders isLead time for the receipt of orders isconstantconstantOrder quantity is received all at onceOrder quantity is received all at once
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Model I: Basic EOQ Typical assumptions made
annual demand (D), carrying cost (C) and
ordering cost (O) can be estimatedaverage inventory level is the fixed orderquantity (Q) divided by 2 which implies
no safety stock
orders are received all at oncedemand occurs at a uniform rateno inventory when an order arrives
. . . more
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Model I: Basic EOQAssumptions (continued)
Stockout, customer responsiveness, and other
costs are inconsequentialacquisition cost is fixed, i.e., no quantitydiscounts
Annual carrying cost = (average inventory level) x
(carrying cost) = (Q/2)CAnnual ordering cost = (average number of ordersper year) x (ordering cost) = (D/Q)O
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EOQ Cost Model
C C oo - cost of placing order - cost of placing order DD - annual demand- annual demandC C cc - annual per-unit carrying cost- annual per-unit carrying cost QQ - order quantity- order quantity
Annual ordering cost =Annual ordering cost =C C oo DD
Annual carrying cost =Annual carrying cost =C C cc QQ
22
Total cost = +Total cost = +C C oo DD
C C cc QQ
22
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EOQ Cost Model (cont.)
Order Quantity,Order Quantity, QQ
AnnualAnnualcost ($)cost ($) Total CostTotal Cost
Carrying Cost =Carrying Cost =C C cc QQ
22
Slope = 0Slope = 0
MinimumMinimumtotal costtotal cost
Optimal order Optimal order QQ optopt
Ordering Cost =Ordering Cost = C C
oo DD
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EOQ Example
C C cc = $0.75 per yard= $0.75 per yard C C oo = $150= $150 DD = 10,000 yards= 10,000 yards
QQ optopt ==22C C oo DD
C C cc
QQ optopt ==2(150)(10,000)2(150)(10,000)
(0.75)(0.75)
QQ optopt = 2,000 yards= 2,000 yards
TC TC minmin = += +C C oo DD
C C cc QQ
22
TC TC minmin = += +(150)(10,000)(150)(10,000)
2,0002,000(0.75)(2,000)(0.75)(2,000)
22
TC TC minmin = $750 + $750 = $1,500= $750 + $750 = $1,500
Orders per year =Orders per year = DD //QQ optopt== 10,000/2,00010,000/2,000== 5 orders/year 5 orders/year
Order cycle time =Order cycle time = 311 days/(311 days/( DD //QQ optopt ))
== 311/5311/5== 62.2 store days62.2 store days
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Quantity Discounts
Price per unit decreases as order Price per unit decreases as order
quantity increasesquantity increases
TC TC = + += + + PDPDC C oo DD
C C cc QQ
22
wherewhereP P = per unit price of the item= per unit price of the item
DD = annual demand= annual demand
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Quantity Discount:Example
QUANTITYQUANTITY PRICEPRICE
1 - 491 - 49 $1,400$1,40050 - 8950 - 89 1,1001,100
90+90+ 900900
C C oo == $2,500$2,500
C C c c == $190 per computer $190 per computer
DD == 200200
QQ optopt = = = 72.5 PCs= = = 72.5 PCs22C C oo DD
C C cc
2(2500)(200)2(2500)(200)190190
TC TC = + += + + PDPD = $233,784= $233,784C C oo DD
QQ optopt
C C cc QQoptopt
22
For For QQ = 72.5= 72.5
TC TC = + += + + PDPD = $194,105= $194,105C C oo DD
C C cc QQ
22
For For QQ = 90= 90
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Reorder Point
Level of inventory at which a new order Level of inventory at which a new order is placed is placed
R R == d X Ld X Lwherewhere
d d = demand rate per period= demand rate per periodLL = lead time= lead time
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Reorder Point: Example
Demand = 10,000 yards/year Demand = 10,000 yards/year
Store open 311 days/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154Daily demand = 10,000 / 311 = 32.154yards/dayyards/dayLead time = L = 10 daysLead time = L = 10 days
R = d X L = (32.154)(10) = 321.54 yardsR = d X L = (32.154)(10) = 321.54 yards
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Inventory Management Techniques
Reorder point under certaintylead time
average usageReorder point = Lead time x average usage
Reorder point under uncertaintysafety stock
Reorder point = (Lead time x average usage)+ safety stock
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Safety Stocks
Safety stockSafety stockbuffer added to on hand inventory during leadbuffer added to on hand inventory during lead
timetimeStockoutStockout
an inventory shortagean inventory shortage
Service levelService levelprobability that the inventory available duringprobability that the inventory available duringlead time will meet demandlead time will meet demand
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Reorder Point witha Safety Stock
Reorder Reorder point,point, R R
Q Q
LTLTTimeTime
LTLT
Inventory
level
Inventory
level
00Safety Stock
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ABC ClassificationClass A
5 15 % of units70 80 % of value
Class B30 % of units15 % of value
Class C
50 60 % of units5 10 % of value
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ABC Classification: Example
11 $ 60$ 60 909022 350350 4040
33 3030 13013044 8080 606055 3030 10010066 2020 180180
77 1010 17017088 320320 505099 510510 6060
1010 2020 120120
PARTPART UNIT COSTUNIT COST ANNUAL USAGEANNUAL USAGE
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ABC Classification:Example (cont.)
Example 10.1Example 10.1
11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 180180
77 1010 17017088 320320 505099 510510 6060
1010 2020 120120
PARTPART UNIT COSTUNIT COST ANNUAL USAGEANNUAL USAGETOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.0
2 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.0
5 3,000 3.5 13.0 71.010 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0
$85,400
A A
BB
C C
% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY
A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0C 6, 5, 10, 7 12.5 60.0
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Just-in-Time Inventory
Just in Time
Inventory is theminimuminventory that
is necessary tokeep a systemperfectlyrunning.
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Just-in-Time Inventory
With just in time (JIT) inventory,
The exact amount of items arriveat the moment they areneeded , Not a minute before ORnot a minute after.
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Just-in-Time Inventory
To achieve JIT inventory, Managersshould Reduce the Variability Caused by some Internal andExternal Factors.Existence of Inventory hides the
variability. What causesvariability?
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Just-in-Time Inventory
Most variability is caused bytolerating waste (inventory).
(1) For example, employees ormachines produce units that do notconform to standards. These arewaste. And they cause variability.
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Just-in-Time Inventory
(2) Or, engineering drawings areinaccurate, Again resulting in loss of
production And consecutivelyresulting in Variability. These are the internal (controllable)factors that cause Variability.However, Some of the variability iscaused by some external factors.
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Just-in-Time Inventory
For example, customer demandsmay change due to some externalfactors (such as competitorsactions or promotions)In summary, To achieve JIT
inventory, Managers must beginwith Reducing Inventory.
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Just-in-Time Inventory
Reducing Inventory uncovers theRocks located along the way on ariver, And the water streambecomes more clear.
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Just-in-Time Inventory
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Just-in-Time Inventory
In the figure, the section calledOthers are the Rocks on theriver.
Those rocks include QualityVariability, In-transit Delays,
Machine Breakdowns, Large Lot-sizes, Inaccurate drawings,Employee attendance variability.
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Just-In-Time Production JIT production means (1) Elimination of Waste, (2) Synchronized Manufacturing, and(3) Little Inventory.Reducing the order batch size can be a majorhelp in reducing inventory.Average Inventory = (Maximum Inventory +
Minimum Inventory) / 2
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Just-In-Time Production
Average Inventory drops as theinventory re-order quantity drops
because the maximum inventorylevel drops. (show by drawing)Moreover, the smaller the lot size,the fewer the problems are hidden.One way to achieve small lot sizesis to Move Inventory through theshop Only as needed.
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Just-In-Time Production
Sending a card authorizes theprevious work center to send its
finished batch to the subsequentwork center.Batches are typically very small.
Such a system requires tightschedules and frequent set-ups formachines.
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Just-In-Time Production
This is called a pull system. In thissystem, Ideal Lot size is 1.
Japanese call this system asKanban system.Kanban is a Japanese word for Card.
A card is used to signal the need formaterial in a work center.
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Just-In-Time Production
On the other hand,Small batches allow a
very limited amountof faulty material,less damages, lessspace occupation,less materialhandling, lessaccidents, etc.