1 1 2002 South-Western/Thomson Learning 2002 South-Western/Thomson Learning TMTM
Slides preparedSlides preparedby John Loucksby John Loucks
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Chapter 14Chapter 14Chapter 14Chapter 14
Inventory ManagementInventory Management
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OverviewOverviewOverviewOverview
Opposing Views of InventoriesOpposing Views of Inventories Nature of InventoriesNature of Inventories Fixed Order Quantity SystemsFixed Order Quantity Systems Fixed Order Period SystemsFixed Order Period Systems Other Inventory ModelsOther Inventory Models Some Realities of Inventory PlanningSome Realities of Inventory Planning Wrap-Up: What World-Class Companies DoWrap-Up: What World-Class Companies Do
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Opposing Views of InventoryOpposing Views of InventoryOpposing Views of InventoryOpposing Views of Inventory
Why We Want to Hold InventoriesWhy We Want to Hold Inventories Why We Not Want to Hold InventoriesWhy We Not Want to Hold Inventories
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Why We Want to Hold InventoriesWhy We Want to Hold InventoriesWhy We Want to Hold InventoriesWhy We Want to Hold Inventories
Improve customer serviceImprove customer service Reduce certain costs such asReduce certain costs such as
ordering costsordering costs stockout costsstockout costs acquisition costsacquisition costs start-up quality costsstart-up quality costs
Contribute to the efficient and effective operation of Contribute to the efficient and effective operation of the production systemthe production system
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Why We Want to Hold InventoriesWhy We Want to Hold InventoriesWhy We Want to Hold InventoriesWhy We Want to Hold Inventories
Finished GoodsFinished Goods Essential in produce-to-stock positioning strategiesEssential in produce-to-stock positioning strategies Necessary in level aggregate capacity plansNecessary in level aggregate capacity plans Products can be displayed to customersProducts can be displayed to customers
Work-in-ProcessWork-in-Process Necessary in process-focused productionNecessary in process-focused production May reduce material-handling & production costsMay reduce material-handling & production costs
Raw MaterialRaw Material Suppliers may produce/ship materials in batchesSuppliers may produce/ship materials in batches Quantity discounts and freight/handling $$ savingsQuantity discounts and freight/handling $$ savings
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Why We Do Not Want to Hold InventoriesWhy We Do Not Want to Hold InventoriesWhy We Do Not Want to Hold InventoriesWhy We Do Not Want to Hold Inventories
Certain costs increase such asCertain costs increase such as carrying costscarrying costs cost of customer responsivenesscost of customer responsiveness cost of coordinating productioncost of coordinating production cost of diluted return on investmentcost of diluted return on investment reduced-capacity costsreduced-capacity costs large-lot quality costlarge-lot quality cost cost of production problemscost of production problems
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InventoryInventoryInventoryInventory
Current trends in inventory managementCurrent trends in inventory management
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Nature of InventoryNature of InventoryNature of InventoryNature of Inventory
Two Fundamental Inventory DecisionsTwo Fundamental Inventory Decisions Terminology of InventoriesTerminology of Inventories Independent Demand Inventory SystemsIndependent Demand Inventory Systems Dependent Demand Inventory SystemsDependent Demand Inventory Systems Inventory CostsInventory Costs
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Two Fundamental Inventory DecisionsTwo Fundamental Inventory DecisionsTwo Fundamental Inventory DecisionsTwo Fundamental Inventory Decisions
How muchHow much to order of each material when orders are to order of each material when orders are placed with either outside suppliers or production placed with either outside suppliers or production departments within organizationsdepartments within organizations
WhenWhen to place the orders to place the orders
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Independent Demand Inventory SystemsIndependent Demand Inventory SystemsIndependent Demand Inventory SystemsIndependent Demand Inventory Systems
Demand for an item carried in inventory is Demand for an item carried in inventory is independent of the demand for any other item in independent of the demand for any other item in inventoryinventory
Finished goods inventory is an exampleFinished goods inventory is an example Demands are estimated from forecasts (Chapter 3) Demands are estimated from forecasts (Chapter 3)
and/or customer ordersand/or customer orders
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Dependent Demand Inventory SystemsDependent Demand Inventory SystemsDependent Demand Inventory SystemsDependent Demand Inventory Systems
Items whose demand depends on the demands for Items whose demand depends on the demands for other itemsother items
For example, the demand for raw materials and For example, the demand for raw materials and components can be calculated from the demand for components can be calculated from the demand for finished goodsfinished goods
The systems used to manage these inventories The systems used to manage these inventories (Chapter 15) are different from those used to manage (Chapter 15) are different from those used to manage independent demand itemsindependent demand items
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Independent vs. Dependent DemandIndependent vs. Dependent Demand
A
Independent Demand(finished goods and spare parts)
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand(components)
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Inventory CostsInventory CostsInventory CostsInventory Costs
Costs associated with ordering too much (represented Costs associated with ordering too much (represented by carrying costs)by carrying costs)
Costs associated with ordering too little (represented Costs associated with ordering too little (represented by ordering costs)by ordering costs)
These costs are opposing costs, i.e., as one increases These costs are opposing costs, i.e., as one increases the other decreasesthe other decreases
. . . more. . . more
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Inventory Costs (continued)Inventory Costs (continued)Inventory Costs (continued)Inventory Costs (continued)
The sum of the two costs is the total stocking cost The sum of the two costs is the total stocking cost (TSC)(TSC)
When plotted against order quantity, the TSC When plotted against order quantity, the TSC decreases to a minimum cost and then increasesdecreases to a minimum cost and then increases
This cost behavior is the basis for answering the first This cost behavior is the basis for answering the first fundamental question: how much to orderfundamental question: how much to order
It is known as the economic order quantity (EOQ)It is known as the economic order quantity (EOQ)
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Balancing Carrying against Ordering CostsBalancing Carrying against Ordering CostsBalancing Carrying against Ordering CostsBalancing Carrying against Ordering Costs
Annual Cost ($)Annual Cost ($)
Order QuantityOrder Quantity
MinimumMinimumTotal AnnualTotal Annual
Stocking CostsStocking Costs
AnnualAnnualCarrying CostsCarrying Costs
AnnualAnnualOrdering CostsOrdering Costs
Total AnnualTotal AnnualStocking CostsStocking Costs
SmallerSmaller LargerLarger
Low
erL
ower
Hig
her
Hig
her
EOQEOQ
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InventoryInventoryInventoryInventory
Inventory CostsInventory Costs
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Fixed Order Quantity SystemsFixed Order Quantity SystemsFixed Order Quantity SystemsFixed Order Quantity Systems
Behavior of Economic Order Quantity (EOQ) Behavior of Economic Order Quantity (EOQ) SystemsSystems
Determining Order QuantitiesDetermining Order Quantities Determining Order PointsDetermining Order Points
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Behavior of EOQ SystemsBehavior of EOQ SystemsBehavior of EOQ SystemsBehavior of EOQ Systems
As demand for the inventoried item occurs, the As demand for the inventoried item occurs, the inventory level dropsinventory level drops
When the inventory level drops to a critical point, the When the inventory level drops to a critical point, the order point, the ordering process is triggered order point, the ordering process is triggered
The amount ordered each time an order is placed is The amount ordered each time an order is placed is fixed or constantfixed or constant
When the ordered quantity is received, the inventory When the ordered quantity is received, the inventory level increaseslevel increases
. . . more. . . more
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Behavior of EOQ SystemsBehavior of EOQ SystemsBehavior of EOQ SystemsBehavior of EOQ Systems
An application of this type system is the two-bin An application of this type system is the two-bin systemsystem
A perpetual inventory accounting system is usually A perpetual inventory accounting system is usually associated with this type of systemassociated with this type of system
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Determining Order QuantitiesDetermining Order QuantitiesDetermining Order QuantitiesDetermining Order Quantities
Basic EOQBasic EOQ EOQ for Production LotsEOQ for Production Lots EOQ with Quantity DiscountsEOQ with Quantity Discounts
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Model I: Basic EOQ Model I: Basic EOQ Model I: Basic EOQ Model I: Basic EOQ
Typical assumptions madeTypical assumptions made annual demand (D), carrying cost (C) and ordering annual demand (D), carrying cost (C) and ordering
cost (S) can be estimatedcost (S) can be estimated average inventory level is the fixed order quantity average inventory level is the fixed order quantity
(Q) divided by 2 which implies(Q) divided by 2 which implies no safety stockno safety stock orders are received all at onceorders are received all at once demand occurs at a uniform ratedemand occurs at a uniform rate no inventory when an order arrivesno inventory when an order arrives
. . . more. . . more
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Model I: Basic EOQModel I: Basic EOQModel I: Basic EOQModel I: Basic EOQ
Assumptions (continued)Assumptions (continued) Stockout, customer responsiveness, and other costs Stockout, customer responsiveness, and other costs
are inconsequentialare inconsequential acquisition cost is fixed, i.e., no quantity discountsacquisition cost is fixed, i.e., no quantity discounts
Annual carrying cost = (average inventory level) x Annual carrying cost = (average inventory level) x (carrying cost) = (Q/2)C(carrying cost) = (Q/2)C
Annual ordering cost = (average number of orders per Annual ordering cost = (average number of orders per year) x (ordering cost) = (D/Q)Syear) x (ordering cost) = (D/Q)S
. . . more. . . more
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CDS /2 = EOQ CDS /2 = EOQ
Model I: Basic EOQModel I: Basic EOQModel I: Basic EOQModel I: Basic EOQ
Total annual stocking cost (TSC) = annual carrying Total annual stocking cost (TSC) = annual carrying cost + annual ordering cost = (Q/2)C + (D/Q)Scost + annual ordering cost = (Q/2)C + (D/Q)S
The order quantity where the TSC is at a minimum The order quantity where the TSC is at a minimum (EOQ) can be found using calculus (take the first (EOQ) can be found using calculus (take the first derivative, set it equal to zero and solve for Q) derivative, set it equal to zero and solve for Q)
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Example: Basic EOQExample: Basic EOQExample: Basic EOQExample: Basic EOQ
Zartex Co. produces fertilizer to sell to Zartex Co. produces fertilizer to sell to wholesalers. One raw material – calcium nitrate – is wholesalers. One raw material – calcium nitrate – is purchased from a nearby supplier at $22.50 per ton. purchased from a nearby supplier at $22.50 per ton. Zartex estimates it will need 5,750,000 tons of Zartex estimates it will need 5,750,000 tons of calcium nitrate next year.calcium nitrate next year.
The annual carrying cost for this material is The annual carrying cost for this material is 40% of the acquisition cost, and the ordering cost is 40% of the acquisition cost, and the ordering cost is $595. $595. a) What is the most economical order quantity?a) What is the most economical order quantity?b) How many orders will be placed per year?b) How many orders will be placed per year?c) How much time will elapse between orders?c) How much time will elapse between orders?
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Example: Basic EOQExample: Basic EOQExample: Basic EOQExample: Basic EOQ
Economical Order Quantity (EOQ)Economical Order Quantity (EOQ)
D = 5,750,000 tons/yearD = 5,750,000 tons/year
C = .40(22.50) = $9.00/ton/yearC = .40(22.50) = $9.00/ton/year
S = $595/orderS = $595/order
= 27,573.135 tons per order= 27,573.135 tons per order
EOQ = 2DS/CEOQ = 2DS/C
EOQ = 2(5,750,000)(595)/9.00EOQ = 2(5,750,000)(595)/9.00
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Example: Basic EOQExample: Basic EOQExample: Basic EOQExample: Basic EOQ
Total Annual Stocking Cost (TSC)Total Annual Stocking Cost (TSC)
TSC = (Q/2)C + (D/Q)STSC = (Q/2)C + (D/Q)S
= (27,573.135/2)(9.00) = (27,573.135/2)(9.00)
+ (5,750,000/27,573.135)(595)+ (5,750,000/27,573.135)(595)
= 124,079.11 + 124,079.11= 124,079.11 + 124,079.11
= $248,158.22= $248,158.22Note: Total Carrying CostNote: Total Carrying Costequals Total Ordering Costequals Total Ordering Cost
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Example: Basic EOQExample: Basic EOQExample: Basic EOQExample: Basic EOQ
Number of Orders Per YearNumber of Orders Per Year= D/Q = D/Q = 5,750,000/27,573.135 = 5,750,000/27,573.135 = 208.5 orders/year= 208.5 orders/year
Time Between OrdersTime Between Orders= Q/D= Q/D= 1/208.5= 1/208.5= .004796 years/order= .004796 years/order= .004796(365 days/year) = 1.75 days/order= .004796(365 days/year) = 1.75 days/order
Note: This is the inverseNote: This is the inverse of the formula above.of the formula above.
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Model II: EOQ for Production LotsModel II: EOQ for Production LotsModel II: EOQ for Production LotsModel II: EOQ for Production Lots
Used to determine the order size, production lot, if an Used to determine the order size, production lot, if an item is produced at one stage of production, stored in item is produced at one stage of production, stored in inventory, and then sent to the next stage or the inventory, and then sent to the next stage or the customercustomer
Differs from Model I because orders are assumed to Differs from Model I because orders are assumed to be supplied or produced at a uniform rate (p) rate be supplied or produced at a uniform rate (p) rate rather than the order being received all at oncerather than the order being received all at once
. . . more. . . more
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Model II: EOQ for Production LotsModel II: EOQ for Production LotsModel II: EOQ for Production LotsModel II: EOQ for Production Lots
It is also assumed that the supply rate, p, is greater It is also assumed that the supply rate, p, is greater than the demand rate, dthan the demand rate, d
The change in maximum inventory level requires The change in maximum inventory level requires modification of the TSC equationmodification of the TSC equation
TSC = (Q/2)[(p-d)/p]C + (D/Q)STSC = (Q/2)[(p-d)/p]C + (D/Q)S The optimization results inThe optimization results in
dp
p
C
DS2 = EOQ
dp
p
C
DS2 = EOQ
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Example: EOQ for Production LotsExample: EOQ for Production LotsExample: EOQ for Production LotsExample: EOQ for Production Lots
Highland Electric Co. buys coal from Cedar Highland Electric Co. buys coal from Cedar Creek Coal Co. to generate electricity. CCCC can Creek Coal Co. to generate electricity. CCCC can supply coal at the rate of 3,500 tons per day for supply coal at the rate of 3,500 tons per day for $10.50 per ton. HEC uses the coal at a rate of 800 $10.50 per ton. HEC uses the coal at a rate of 800 tons per day and operates 365 days per year.tons per day and operates 365 days per year.
HEC’s annual carrying cost for coal is 20% of HEC’s annual carrying cost for coal is 20% of the acquisition cost, and the ordering cost is $5,000.the acquisition cost, and the ordering cost is $5,000.
a) What is the economical production lot size?a) What is the economical production lot size?
b) What is HEC’s maximum inventory level for coal?b) What is HEC’s maximum inventory level for coal?
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Example: EOQ for Production LotsExample: EOQ for Production LotsExample: EOQ for Production LotsExample: EOQ for Production Lots
Economical Production Lot SizeEconomical Production Lot Size
d = 800 tons/day; D = 365(800) = 292,000 tons/yeard = 800 tons/day; D = 365(800) = 292,000 tons/year
p = 3,500 tons/dayp = 3,500 tons/day
S = $5,000/order C = .20(10.50) = $2.10/ton/yearS = $5,000/order C = .20(10.50) = $2.10/ton/year
= 42,455.5 tons per order= 42,455.5 tons per order
EOQ = (2DS/C)[p/(p-d)]EOQ = (2DS/C)[p/(p-d)]
EOQ = 2(292,000)(5,000)/2.10[3,500/(3,500-800)]EOQ = 2(292,000)(5,000)/2.10[3,500/(3,500-800)]
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Example: EOQ for Production LotsExample: EOQ for Production LotsExample: EOQ for Production LotsExample: EOQ for Production Lots
Total Annual Stocking Cost (TSC)Total Annual Stocking Cost (TSC)
TSC = (Q/2)((p-d)/p)C + (D/Q)STSC = (Q/2)((p-d)/p)C + (D/Q)S
= (42,455.5/2)((3,500-800)/3,500)(2.10) = (42,455.5/2)((3,500-800)/3,500)(2.10)
+ (292,000/42,455.5)(5,000)+ (292,000/42,455.5)(5,000)
= 34,388.95 + 34,388.95= 34,388.95 + 34,388.95
= $68,777.90= $68,777.90Note: Total Carrying CostNote: Total Carrying Costequals Total Ordering Costequals Total Ordering Cost
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Example: EOQ for Production LotsExample: EOQ for Production LotsExample: EOQ for Production LotsExample: EOQ for Production Lots
Maximum Inventory LevelMaximum Inventory Level
= Q(p-d)/p = Q(p-d)/p
= 42,455.5(3,500 – 800)/3,500= 42,455.5(3,500 – 800)/3,500
= 42,455.5(.771429)= 42,455.5(.771429)
= 32,751.4 tons= 32,751.4 tons Note: HEC will use 23%Note: HEC will use 23%of the production lot by theof the production lot by thetime it receives the full lot.time it receives the full lot.
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Model III: EOQ with Quantity DiscountsModel III: EOQ with Quantity DiscountsModel III: EOQ with Quantity DiscountsModel III: EOQ with Quantity Discounts
Under quantity discounts, a supplier offers a lower Under quantity discounts, a supplier offers a lower unit price if larger quantities are ordered at one timeunit price if larger quantities are ordered at one time
This is presented as a price or discount schedule, i.e., This is presented as a price or discount schedule, i.e., a certain unit price over a certain order quantity rangea certain unit price over a certain order quantity range
This means this model differs from Model I because This means this model differs from Model I because the acquisition cost (ac) may vary with the quantity the acquisition cost (ac) may vary with the quantity ordered, i.e., it is not necessarily constantordered, i.e., it is not necessarily constant
. . . more. . . more
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Model III: EOQ with Quantity DiscountsModel III: EOQ with Quantity DiscountsModel III: EOQ with Quantity DiscountsModel III: EOQ with Quantity Discounts
Under this condition, acquisition cost becomes an Under this condition, acquisition cost becomes an incremental cost and must be considered in the incremental cost and must be considered in the determination of the EOQdetermination of the EOQ
The total annual material costs (TMC) = Total annual The total annual material costs (TMC) = Total annual stocking costs (TSC) + annual acquisition coststocking costs (TSC) + annual acquisition cost
TSC = (Q/2)C + (D/Q)S + (D)acTSC = (Q/2)C + (D/Q)S + (D)ac
. . . more. . . more
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Model III: EOQ with Quantity DiscountsModel III: EOQ with Quantity DiscountsModel III: EOQ with Quantity DiscountsModel III: EOQ with Quantity Discounts
To find the EOQ, the following procedure is used:To find the EOQ, the following procedure is used:
1.1. Compute the EOQ using the lowest acquisition cost. Compute the EOQ using the lowest acquisition cost. If the resulting EOQ is feasible (the quantity can If the resulting EOQ is feasible (the quantity can
be purchased at the acquisition cost used), this be purchased at the acquisition cost used), this quantity is optimal and you are finished.quantity is optimal and you are finished.
If the resulting EOQ is If the resulting EOQ is notnot feasible, go to Step 2 feasible, go to Step 22.2. Identify the Identify the nextnext higher acquisition cost. higher acquisition cost.
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Model III: EOQ with Quantity DiscountsModel III: EOQ with Quantity DiscountsModel III: EOQ with Quantity DiscountsModel III: EOQ with Quantity Discounts
3.3. Compute the EOQ using the acquisition cost from Compute the EOQ using the acquisition cost from Step 2.Step 2. If the resulting EOQ is feasible, go to Step 4.If the resulting EOQ is feasible, go to Step 4. Otherwise, go to Step 2. Otherwise, go to Step 2.
4.4. Compute the TMC for the feasible EOQ (just found Compute the TMC for the feasible EOQ (just found in Step 3) and its corresponding acquisition cost.in Step 3) and its corresponding acquisition cost.
5.5. Compute the TMC for each of the lower acquisition Compute the TMC for each of the lower acquisition costs using the minimum allowed order quantity for costs using the minimum allowed order quantity for each cost. each cost.
6.6. The quantity with the lowest TMC is optimal. The quantity with the lowest TMC is optimal.
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Example: EOQ with Quantity DiscountsExample: EOQ with Quantity DiscountsExample: EOQ with Quantity DiscountsExample: EOQ with Quantity Discounts
A-1 Auto Parts has a regional tire warehouse in A-1 Auto Parts has a regional tire warehouse in Atlanta. One popular tire, the XRX75, has estimated Atlanta. One popular tire, the XRX75, has estimated demand of 25,000 next year. It costs A-1 $100 to demand of 25,000 next year. It costs A-1 $100 to place an order for the tires, and the annual carrying place an order for the tires, and the annual carrying cost is 30% of the acquisition cost. The supplier cost is 30% of the acquisition cost. The supplier quotes these prices for the tire:quotes these prices for the tire:
QQ acac
1 – 4991 – 499 $21.60$21.60500 – 999500 – 999 20.9520.951,000 +1,000 + 20.9020.90
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Example: EOQ with Quantity DiscountsExample: EOQ with Quantity DiscountsExample: EOQ with Quantity DiscountsExample: EOQ with Quantity Discounts
Economical Order QuantityEconomical Order Quantity
This quantity is not feasible, so try ac = $20.95This quantity is not feasible, so try ac = $20.95
This quantity is feasible, so there is no reason to try This quantity is feasible, so there is no reason to try ac = $21.60ac = $21.60
i iEOQ = 2DS/Ci iEOQ = 2DS/C
3EOQ = 2(25,000)100/(.3(20.90) = 893.003EOQ = 2(25,000)100/(.3(20.90) = 893.00
2EOQ = 2(25,000)100/(.3(20.95) = 891.932EOQ = 2(25,000)100/(.3(20.95) = 891.93
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Example: EOQ with Quantity DiscountsExample: EOQ with Quantity DiscountsExample: EOQ with Quantity DiscountsExample: EOQ with Quantity Discounts
Compare Total Annual Material Costs (TMCs)Compare Total Annual Material Costs (TMCs)
TMC = (Q/2)C + (D/Q)S + (D)acTMC = (Q/2)C + (D/Q)S + (D)ac
Compute TMC for Q = 891.93 and ac = $20.95Compute TMC for Q = 891.93 and ac = $20.95
TMCTMC22 = (891.93/2)(.3)(20.95) + (25,000/891.93)100 = (891.93/2)(.3)(20.95) + (25,000/891.93)100
+ (25,000)20.95+ (25,000)20.95
= 2,802.89 + 2,802.91 + 523,750= 2,802.89 + 2,802.91 + 523,750
= $529,355.80= $529,355.80
… … moremore
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Example: EOQ with Quantity DiscountsExample: EOQ with Quantity DiscountsExample: EOQ with Quantity DiscountsExample: EOQ with Quantity Discounts
Compute TMC for Q = 1,000 and ac = $20.90Compute TMC for Q = 1,000 and ac = $20.90
TMCTMC33 = (1,000/2)(.3)(20.90) + (25,000/1,000)100 = (1,000/2)(.3)(20.90) + (25,000/1,000)100
+ (25,000)20.90+ (25,000)20.90
= 3,135.00 + 2,500.00 + 522,500= 3,135.00 + 2,500.00 + 522,500
= $528,135.00 (lower than TMC= $528,135.00 (lower than TMC22))
The EOQ is 1,000 tiresThe EOQ is 1,000 tires
at an acquisition cost of $20.90.at an acquisition cost of $20.90.
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Determining Order PointsDetermining Order PointsDetermining Order PointsDetermining Order Points
Basis for Setting the Order PointBasis for Setting the Order Point DDLT DistributionsDDLT Distributions Setting Order PointsSetting Order Points
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Basis for Setting the Order PointBasis for Setting the Order PointBasis for Setting the Order PointBasis for Setting the Order Point
In the fixed order quantity system, the ordering In the fixed order quantity system, the ordering process is triggered when the inventory level drops to process is triggered when the inventory level drops to a critical point, the order pointa critical point, the order point
This starts the lead time for the item.This starts the lead time for the item. Lead time is the time to complete all activities Lead time is the time to complete all activities
associated with placing, filling and receiving the associated with placing, filling and receiving the order. order.
. . . more. . . more
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Basis for Setting the Order PointBasis for Setting the Order PointBasis for Setting the Order PointBasis for Setting the Order Point
During the lead time, customers continue to draw During the lead time, customers continue to draw down the inventorydown the inventory
It is during this period that the inventory is vulnerable It is during this period that the inventory is vulnerable to stockout (run out of inventory)to stockout (run out of inventory)
Customer service level is the probability that a Customer service level is the probability that a stockout will not occur during the lead timestockout will not occur during the lead time
. . . more. . . more
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Basis for Setting the Order PointBasis for Setting the Order PointBasis for Setting the Order PointBasis for Setting the Order Point
The order point is set based onThe order point is set based on the demand during lead time (DDLT) andthe demand during lead time (DDLT) and the desired customer service levelthe desired customer service level
Order point (OP) = Expected demand during lead Order point (OP) = Expected demand during lead time (EDDLT) + Safety stock (SS)time (EDDLT) + Safety stock (SS)
The amount of safety stock needed is based on the The amount of safety stock needed is based on the degree of uncertainty in the DDLT and the customer degree of uncertainty in the DDLT and the customer service level desiredservice level desired
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DDLT DistributionsDDLT DistributionsDDLT DistributionsDDLT Distributions
If there is variability in the DDLT, the DDLT is If there is variability in the DDLT, the DDLT is expressed as a distributionexpressed as a distribution discretediscrete continuouscontinuous
In a discrete DDLT distribution, values (demands) In a discrete DDLT distribution, values (demands) can only be integerscan only be integers
A continuous DDLT distribution is appropriate when A continuous DDLT distribution is appropriate when the demand is very highthe demand is very high
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Setting Order PointSetting Order Pointfor a Discrete DDLT Distributionfor a Discrete DDLT Distribution
Setting Order PointSetting Order Pointfor a Discrete DDLT Distributionfor a Discrete DDLT Distribution
Assume a probability distribution of actual DDLTs is Assume a probability distribution of actual DDLTs is given or can be developed from a frequency given or can be developed from a frequency distributiondistribution
Starting with the lowest DDLT, accumulate the Starting with the lowest DDLT, accumulate the probabilities. These are the service levels for DDLTsprobabilities. These are the service levels for DDLTs
Select the DDLT that will provide the desired Select the DDLT that will provide the desired customer level as the order pointcustomer level as the order point
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Example: OP for Discrete DDLT DistributionExample: OP for Discrete DDLT DistributionExample: OP for Discrete DDLT DistributionExample: OP for Discrete DDLT Distribution
One of Sharp Retailer’s inventory items is now One of Sharp Retailer’s inventory items is now being analyzed to determine an appropriate level of being analyzed to determine an appropriate level of safety stock. The manager wants an 80% service safety stock. The manager wants an 80% service level during lead time. The item’s historical DDLT level during lead time. The item’s historical DDLT is:is:
DDLT (cases)DDLT (cases) OccurrencesOccurrences33 8844 6655 4466 22
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OP for Discrete DDLT DistributionOP for Discrete DDLT DistributionOP for Discrete DDLT DistributionOP for Discrete DDLT Distribution
Construct a Cumulative DDLT DistributionConstruct a Cumulative DDLT Distribution
ProbabilityProbability Probability ofProbability of
DDLT (cases)DDLT (cases) of DDLTof DDLT DDLT or LessDDLT or Less22 00 0033 .4.4 .4.444 .3.3 .7.755 .2.2 .9.966 .1.1 1.01.0
To provide 80% service level, OP = 5 casesTo provide 80% service level, OP = 5 cases
.8.8
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OP for Discrete DDLT DistributionOP for Discrete DDLT DistributionOP for Discrete DDLT DistributionOP for Discrete DDLT Distribution
Safety Stock (SS)Safety Stock (SS)
OP = EDDLT + SSOP = EDDLT + SS
SS = OP SS = OP EDDLT EDDLT
EDDLT = .4(3) + .3(4) + .2(5) + .1(6) = 4.0EDDLT = .4(3) + .3(4) + .2(5) + .1(6) = 4.0
SS = 5 – 4 = 1SS = 5 – 4 = 1
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Setting Order PointSetting Order Pointfor a Continuous DDLT Distributionfor a Continuous DDLT Distribution
Setting Order PointSetting Order Pointfor a Continuous DDLT Distributionfor a Continuous DDLT Distribution
Assume that the lead time (LT) is constantAssume that the lead time (LT) is constant Assume that the demand per day is normally Assume that the demand per day is normally
distributed with the mean (d ) and the standard distributed with the mean (d ) and the standard deviation (deviation (dd ) )
The DDLT distribution is developed by “adding” The DDLT distribution is developed by “adding” together the daily demand distributions across the together the daily demand distributions across the lead timelead time
. . . more. . . more
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Setting Order PointSetting Order Pointfor a Continuous DDLT Distributionfor a Continuous DDLT Distribution
Setting Order PointSetting Order Pointfor a Continuous DDLT Distributionfor a Continuous DDLT Distribution
The resulting DDLT distribution is a normal The resulting DDLT distribution is a normal distribution with the following parameters:distribution with the following parameters:
EDDLT = LT(d) EDDLT = LT(d)
DDLTDDLT = = LT d( ) 2
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Setting Order PointSetting Order Pointfor a Continuous DDLT Distributionfor a Continuous DDLT Distribution
Setting Order PointSetting Order Pointfor a Continuous DDLT Distributionfor a Continuous DDLT Distribution
The customer service level is converted into a Z value The customer service level is converted into a Z value using the normal distribution tableusing the normal distribution table
The safety stock is computed by multiplying the Z The safety stock is computed by multiplying the Z value by value by DDLTDDLT..
The order point is set using OP = EDDLT + SS, or by The order point is set using OP = EDDLT + SS, or by substitutionsubstitution
2dOP = LT(d) + z LT(σ )2dOP = LT(d) + z LT(σ )
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Auto Zone sells auto parts and supplies Auto Zone sells auto parts and supplies including a popular multi-grade motor oil. When the including a popular multi-grade motor oil. When the stock of this oil drops to 20 gallons, a replenishment stock of this oil drops to 20 gallons, a replenishment order is placed. The store manager is concerned that order is placed. The store manager is concerned that sales are being lost due to stockouts while waiting sales are being lost due to stockouts while waiting for an order. It has been determined that lead time for an order. It has been determined that lead time demand is normally distributed with a mean of 15 demand is normally distributed with a mean of 15 gallons and a standard deviation of 6 gallons. gallons and a standard deviation of 6 gallons.
The manager would like to know the The manager would like to know the probability of a stockout during lead time. probability of a stockout during lead time.
Example: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT Distribution
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Example: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT Distribution
EDDLT = 15 gallonsEDDLT = 15 gallons DDLTDDLT = 6 gallons = 6 gallons
OP = EDDLT + Z(OP = EDDLT + Z(DDLTDDLT ) )
20 = 15 + Z(6)20 = 15 + Z(6)
5 = Z(6)5 = Z(6)
Z = 5/6Z = 5/6
Z = .833Z = .833
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Example: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT Distribution
Standard Normal DistributionStandard Normal Distribution
00 .833.833
Area = .2967Area = .2967
Area = .5Area = .5
Area = .2033Area = .2033
zz
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Example: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT DistributionExample: OP - Continuous DDLT Distribution
The Standard Normal table shows an area of .2967 The Standard Normal table shows an area of .2967 for the region between the for the region between the zz = 0 line and the = 0 line and the z z = .833 = .833 line. The shaded tail area is .5 - .2967 = .2033.line. The shaded tail area is .5 - .2967 = .2033.
The probability of a stockout during lead time The probability of a stockout during lead time is .2033is .2033
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Example: Setting Order PointsExample: Setting Order PointsExample: Setting Order PointsExample: Setting Order Points
We can also use Excel to get the stockout risk and the We can also use Excel to get the stockout risk and the corresponding customer service level given the value corresponding customer service level given the value of Zof Z
CSL = CSL =
SR = 1-.7976 = .2024SR = 1-.7976 = .2024
Normsdist(0.833)= 0.7976
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Set safety stock level at a Set safety stock level at a percentagepercentage of EDDLT of EDDLT
OP = EDDLT + j(EDDLT)OP = EDDLT + j(EDDLT)
where j is a factor between 0 and 3.where j is a factor between 0 and 3.
Set safety stock level at Set safety stock level at square rootsquare root of EDDLT of EDDLT
OP = EDDLTOP = EDDLT + +
Rules of Thumb in Setting OPRules of Thumb in Setting OPRules of Thumb in Setting OPRules of Thumb in Setting OP
EDDLTEDDLT
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Fixed Order Period SystemsFixed Order Period SystemsFixed Order Period SystemsFixed Order Period Systems
Behavior of Economic Order Period (EOP) SystemsBehavior of Economic Order Period (EOP) Systems Economic Order Period ModelEconomic Order Period Model
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Behavior of Economic Order Period SystemsBehavior of Economic Order Period SystemsBehavior of Economic Order Period SystemsBehavior of Economic Order Period Systems
As demand for the inventoried item occurs, the As demand for the inventoried item occurs, the inventory level dropsinventory level drops
When a prescribed period of time (EOP) has elapsed, When a prescribed period of time (EOP) has elapsed, the ordering process is triggered, i.e., the time the ordering process is triggered, i.e., the time between orders is fixed or constant between orders is fixed or constant
At that time the order quantity is determined using At that time the order quantity is determined using order quantity = upper inventory target - inventory order quantity = upper inventory target - inventory level + EDDLTlevel + EDDLT
. . . more. . . more
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Behavior of Economic Order Period SystemsBehavior of Economic Order Period SystemsBehavior of Economic Order Period SystemsBehavior of Economic Order Period Systems
After the lead time elapses, the ordered quantity is After the lead time elapses, the ordered quantity is received , and the inventory level increasesreceived , and the inventory level increases
The upper inventory level may be determined by the The upper inventory level may be determined by the amount of space allocated to an itemamount of space allocated to an item
This system is used where it is desirable to physically This system is used where it is desirable to physically count inventory each time an order is placedcount inventory each time an order is placed
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EOP = 2S / DCEOP = 2S / DC
Determining the EOPDetermining the EOPDetermining the EOPDetermining the EOP
Using an approach similar to that used to derive Using an approach similar to that used to derive EOQ, the optimal value of the fixed time between EOQ, the optimal value of the fixed time between orders is derived to beorders is derived to be
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Other Inventory ModelsOther Inventory ModelsOther Inventory ModelsOther Inventory Models
Hybrid Inventory ModelsHybrid Inventory Models Single-Period Inventory ModelsSingle-Period Inventory Models
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Hybrid Inventory ModelsHybrid Inventory ModelsHybrid Inventory ModelsHybrid Inventory Models
Optional replenishment modelOptional replenishment model Similar to the fixed order period modelSimilar to the fixed order period model Unless inventory has dropped below a prescribed Unless inventory has dropped below a prescribed
level when the order period has elapsed, no order level when the order period has elapsed, no order is placedis placed
Protects against placing very small ordersProtects against placing very small orders Attractive when review and ordering costs are Attractive when review and ordering costs are
largelarge . . . more. . . more
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Hybrid Inventory ModelsHybrid Inventory ModelsHybrid Inventory ModelsHybrid Inventory Models
Base stock modelBase stock model Start with a certain inventory level Start with a certain inventory level Whenever a withdrawal is made, an order of equal Whenever a withdrawal is made, an order of equal
size is placedsize is placed Ensures that inventory maintained at an Ensures that inventory maintained at an
approximately constant levelapproximately constant level Appropriate for very expensive items with small Appropriate for very expensive items with small
ordering costsordering costs
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Single Period Inventory ModelsSingle Period Inventory ModelsSingle Period Inventory ModelsSingle Period Inventory Models
Order quantity decision covers only one periodOrder quantity decision covers only one period Appropriate for perishable items, e.g., fashion goods, Appropriate for perishable items, e.g., fashion goods,
certain foods, magazinescertain foods, magazines Payoff tables may be used to analyze the decision Payoff tables may be used to analyze the decision
under uncertaintyunder uncertainty . . . more. . . more
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Single Period Inventory ModelsSingle Period Inventory ModelsSingle Period Inventory ModelsSingle Period Inventory Models
One of the following rules can be used in the analysisOne of the following rules can be used in the analysis greatest profitgreatest profit least total expected long and short costsleast total expected long and short costs least total expected costsleast total expected costs
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Some Realities of Inventory PlanningSome Realities of Inventory PlanningSome Realities of Inventory PlanningSome Realities of Inventory Planning
ABC ClassificationABC Classification EOQ and UncertaintyEOQ and Uncertainty Dynamics of Inventory PlanningDynamics of Inventory Planning
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ABC ClassificationABC ClassificationABC ClassificationABC Classification
Start with the inventoried items ranked by dollar Start with the inventoried items ranked by dollar value in inventory in descending ordervalue in inventory in descending order
Plot the cumulative dollar value in inventory versus Plot the cumulative dollar value in inventory versus the cumulative items in inventorythe cumulative items in inventory
. . . more. . . more
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ABC ClassificationABC ClassificationABC ClassificationABC Classification
Typical observationsTypical observations A small percentage of the items (Class A) make up A small percentage of the items (Class A) make up
a large percentage of the inventory valuea large percentage of the inventory value A large percentage of the items (Class C) make up A large percentage of the items (Class C) make up
a small percentage of the inventory valuea small percentage of the inventory value These classifications determine how much attention These classifications determine how much attention
should be given to controlling the inventory of should be given to controlling the inventory of different items different items
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ABC Classification SystemABC Classification System
Items kept in inventory are not of equal importance in Items kept in inventory are not of equal importance in terms of:terms of:
dollars investeddollars invested
profit potentialprofit potential
sales or usage volumesales or usage volume
stock-out penalties stock-out penalties
0
30
60
30
60
AB
C
% of $ Value
% of Use
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EOQ and UncertaintyEOQ and UncertaintyEOQ and UncertaintyEOQ and Uncertainty
The TSC and TMC curves are relatively flat, The TSC and TMC curves are relatively flat, therefore moving left or right of the optimal order therefore moving left or right of the optimal order quantity on the order quantity axis has little effect on quantity on the order quantity axis has little effect on the coststhe costs
Estimation errors of the values of parameter used to Estimation errors of the values of parameter used to compute an EOQ usually do not have a significant compute an EOQ usually do not have a significant impact on total costsimpact on total costs
. . . more. . . more
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EOQ and UncertaintyEOQ and UncertaintyEOQ and UncertaintyEOQ and Uncertainty
Many costs are not directly incorporated in the EOQ Many costs are not directly incorporated in the EOQ and EOP formulas, but could be important factorsand EOP formulas, but could be important factors
Emergency procedures to replenish inventories Emergency procedures to replenish inventories quickly should be establishedquickly should be established
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Dynamics of Inventory PlanningDynamics of Inventory PlanningDynamics of Inventory PlanningDynamics of Inventory Planning
Continually review ordering practices and decisionsContinually review ordering practices and decisions Modify to fit the firm’s demand and supply patternsModify to fit the firm’s demand and supply patterns Constraints, such as storage capacity and available Constraints, such as storage capacity and available
funds, can impact inventory planningfunds, can impact inventory planning Computers and information technology are used Computers and information technology are used
extensively in inventory planningextensively in inventory planning
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Miscellaneous Systems:Miscellaneous Systems:Optional Replenishment SystemOptional Replenishment System
Maximum Inventory Level, M
MActual Inventory Level, I
q = M - I
I
Q = minimum acceptable order quantityDecision rule: If q > Q, order q, otherwise do not order any
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Miscellaneous Systems: Miscellaneous Systems: Bin SystemsBin Systems
Two-Bin System
Full
Empty
Order One Bin ofInventory when one is emptied
One-Bin System
Periodic Check
Order Enough toRefill Bin (e.g. check book)
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Wrap-Up: World-Class PracticeWrap-Up: World-Class PracticeWrap-Up: World-Class PracticeWrap-Up: World-Class Practice
Inventory cycle is the central focus of independent Inventory cycle is the central focus of independent demand inventory systemsdemand inventory systems
Production planning and control systems are Production planning and control systems are changing to support lean inventory strategieschanging to support lean inventory strategies
Information systems electronically link supply chainInformation systems electronically link supply chain
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End of Chapter 14End of Chapter 14