INVENTORY -- Basic Concepts
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Transcript of INVENTORY -- Basic Concepts
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INVENTORY MODELINGBasic Concepts
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INVENTORY MODELINGWhat is inventory?Items in inventory in a storeManufactured items waiting to be shippedEmployees in a firmComputer information in computer filesEtc.
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COMPONENTS OF AN INVENTORY POLICYQ = the amount to order (the order quantity)
R = the number of items left in inventory when an order is placed (the reorder point)
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BASIC CONCEPTBalance the cost of having goods in inventory (Holding Cost) to other costs such as:
Order CostPurchase CostsShortage Costs
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HOLDING COSTSCosts of keeping goods in inventoryCost of capitalRentUtilitiesInsuranceLaborTaxesShrinkage, Spoilage, Obsolescence
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Holding Cost RateAnnual Holding Cost Per UnitThese factors, individually are hard to determineManagement (typically the CFO) assigns a holding cost rate, H, which is a percentage of the value of the item, C
Annual Holding Cost Per Unit, Ch
Ch = HC (in $/item in inv./year)
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ORDER/SETUP COSTSWhen purchasing items, this cost is known as the order cost, CO (in $/order) These are costs associated with the ordering process that are independent of the size of the order-- invoice processing, check writing, e-mails, phone calls, accounting etc. LaborCommunication Some transportation
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ORDER/SETUP COSTS (Contd)When these costs are associated with producing items for sale they are called set-up costs (still labeled CO-- in $/setup)Costs associated with getting the process ready for production (regardless of the production quantity)Readying machinesCalling in shift workersPaperwork, communications involved
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PROCUREMENT/PRODUCTION COSTSThese are the per unit purchase costs, C, if we are ordering the items from a supplier
These are the per unit production costs, C, if we are producing the items for sale
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CUSTOMER SATISFACTION COSTSShortage/Goodwill Costs associated with being out of stockgoodwillloss of future saleslabor/communication Fixed administrative costs = Cb ($/occurrence)Annualized Customer Waiting Costs =Cs ($/item short/year)
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BASIC INVENTORY EQUATION(Total Annual Inventory Costs) =(Total Annual Order/Setup-Up Costs) +(Total Annual Holding Costs) +(Total Annual Purchase/Production Costs) +(Total Annual Shortage/Goodwill Costs)This is a quantity we wish to minimize!!
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REVIEW SYSTEMSContinuous Review --Items are monitored continuouslyWhen inventory reaches some critical level, R, an order is placed for additional items
Periodic Review --Ordering is done periodically (every day, week, 2 weeks, etc.)Inventory is checked just prior to ordering to determine an order quantity
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TIME HORIZONSInfinite Time HorizonAssumes the process has and will continue forever
Single Period Models Ordering for a one-time occurence
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EOQ-TYPE MODELSEOQ (Economic Order Quantity)-type models assume:
Infinite Time Horizon
Continuous Review
Demand is relatively constant
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THE BASIC EOQ MODELOrder the same amount, Q, each timeReordering is instantaneousNo shortages Since reordering is instantaneousInfinite Time HorizonContinuous ReviewDemand is relatively constant at D items/yr.
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AVERAGE INVENTORYINVENTORY VS. TIME
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THE EOQ COST COMPONENTSTotal Annual Order Costs:(Cost/order)(average # orders per year) = CO(D/Q)
Total Annual Holding Costs:(Cost Per Item in inv./yr.)(Average inv.) = Ch(Q/2)
Total Annual Purchase Costs: (Cost Per Item)(Average # items ordered/yr.) = CD
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THE EOQ TOTAL COST EQUATIONTC(Q) = CO(D/Q) + Ch(Q/2) + CD
This a function in one unknown (Q) that we wish to minimize
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SOLVING FOR Q*TC(Q) = CO(D/Q) + Ch(Q/2) + CD
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THE REORDER POINT, r*Since reordering is instantaneous, r* = 0
MODIFICATION -- fixed lead time = L yrs.r* = LD But demand was only approximately constant so we may wish to carry some safety stock (SS) to lessen the likelihood of running out of stockThen,r* = LD + SS
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TOTAL ANNUAL COSTThe optimal policy is to order Q* when supply reaches r*
TC(Q*) = COD/Q* + Ch (Q*/2) + CD + ChSS
The optimal policy minimizes the total variable cost, hence the total annual cost Variable Costs TV(Q)Purchase CostsSafety Stock Costs
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TOTAL VARIABLE COST CURVEQ*Optimal Order Quantity occurs where Holding Costs = Reorder CostsIgnoring purchase costs and safety stock costs:
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The Total Variable Costs function
Constructing the Total Annual Variable Cost Curve
Add the two curves to one another
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Total Annual Holding and Ordering Costs
Q
TV(Q)
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EXAMPLE -- ALLEN APPLIANCE COMPANYJuicer Sales For Past 10 weeks1.1056.1202.1157.1353.1258.1154.1209.1105.12510.130
Using 10-period moving average method, D = (105 + 115 + + 130)/10 = 120/ wk = 6240/yr
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ALLEN APPLIANCE COSTSJuicers cost $10 each and sell for $11.85Cost of money = 10% Other misc. inventory = 4%Labor, postage, telephone/order = $8Workers paid $12/hr.--20 min. to unload an orderDesires a safety stock = 13 EOQ ModelD = 6240H = .10 + .04 = .14CH = .14(10) = $1.40CO = $8 + (1/3 hr.)*($12/hr.) = $8 + $4 = $12SS = 13
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OPTIMAL ORDER QUANTITY FOR ALLEN
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OPTIMAL QUANTITIESTotal Order Cost = CO(D/Q*) = (12)(6240)/327 = $228.99Total Holding Cost = Ch(Q*/2) = (1.40/2)(327) = $228.90(Total Order Cost = Total Holding Cost -- except for rounding error: actual Q* = 327.065)# Orders Per Year = D/Q* = 6240/327 = 19.08Time between orders (Cycle Time) = Q*/D = 327/6240 = .0524 years = 2.72 weeksr* = SS = 13
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TOTAL ANNUAL COSTTotal Variable Cost = Total Order Cost + Total Holding Cost = $228.99 + $228.90 = $457.89Total Purchase Cost = CD = 10(6240) = $62,400Total Safety Stock Cost =ChSS =(1.40)(13) = $18.20Total Annual Cost = $457.89 + $62,400 + $18.20 = $62,876.09
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Using the Inventory Template
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WHY IS THE EOQ MODEL IMPORTANT?No real-life model really is an EOQ model
Many models are variants of EOQ-type models
Many situations can be approximated by EOQ models
The EOQ model is relatively insensitive to some pretty major errors in input parameters
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INSENSIVITY IN EOQ MODELSWe cannot affect purchase costs and safety stock cost, only variable costs: TV(Q) = COD/Q + Ch(Q/2) Now, suppose D really = 7500 (>20% error)We did not know this and got Q* = 327TV(327) = ((12)(7500))/327 + (1.40/2)(327) = $504.13Q* should have been: SQRT(2(12)(7500)/1.40) = 359TV(359) = ((12)(7500))/359 + (1.40/2)(359) = $502.00This is only a 0.4% increase in the TVCost
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ReviewCost Components of Inventory ModelsHolding, Order/Setup, Procurement, ShortageObjective -- Minimize Total Annual CostContinuous Review/Infinite Time HorizonBasic EOQ AssumptionsBasic EOQ FormulaReorder Point and Safety StockQuantities of InterestUse of TemplateImportance of EOQ Models
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