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INVENTORY MODELING

INVENTORY MODELING. Basic Concepts. INVENTORY MODELING. What is inventory? Items in inventory in a store Manufactured items waiting to be shipped Employees in a firm Computer information in computer files Etc. COMPONENTS OF AN INVENTORY POLICY.

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INVENTORY MODELING

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  1. INVENTORY MODELING Basic Concepts

  2. INVENTORY MODELING What is inventory? • Items in inventory in a store • Manufactured items waiting to be shipped • Employees in a firm • Computer information in computer files • Etc.

  3. COMPONENTS OF AN INVENTORY POLICY • Q = the amount to order (the order quantity) • R = the number of items left in inventory when an order is placed (the reorder point)

  4. BASIC CONCEPT • Balance the cost of having goods in inventory (Holding Cost) to other costs such as: • Order Cost • Purchase Costs • Shortage Costs

  5. HOLDING COSTS • Costs of keeping goods in inventory • Cost of capital • Rent • Utilities • Insurance • Labor • Taxes • Shrinkage, Spoilage, Obsolescence

  6. Holding Cost RateAnnual Holding Cost Per Unit • These factors, individually are hard to determine • Management (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)

  7. ORDER/SETUP COSTS • When 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. • Labor • Communication • Some transportation

  8. ORDER/SETUP COSTS (Cont’d) • 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 machines • Calling in shift workers • Paperwork, communications involved

  9. PROCUREMENT/PRODUCTION COSTS • These 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

  10. CUSTOMER SATISFACTION COSTS • Shortage/Goodwill Costs associated with being out of stock • goodwill • loss of future sales • labor/communication • Fixed administrative costs = Cb ($/occurrence) • Annualized Customer Waiting Costs = Cs ($/item short/year)

  11. 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!!

  12. REVIEW SYSTEMS • Continuous Review -- • Items are monitored continuously • When 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

  13. TIME HORIZONS • Infinite Time Horizon • Assumes the process has and will continue “forever” • Single Period Models • Ordering for a one-time occurence

  14. EOQ-TYPE MODELS EOQ (Economic Order Quantity)-type models assume: • Infinite Time Horizon • Continuous Review • Demand is relatively constant

  15. THE BASIC EOQ MODEL • Order the same amount, Q, each time • Reordering is instantaneous • No shortages • Since reordering is instantaneous • Infinite Time Horizon • Continuous Review • Demand is relatively constant at D items/yr.

  16. AVERAGE INVENTORY Q/2 Q Q Q Average Inventory =Q/2 INVENTORY VS. TIME

  17. THE EOQ COST COMPONENTS • Total 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

  18. THE EOQ TOTAL COST EQUATION • TC(Q) = CO(D/Q) + Ch(Q/2) + CD • This a function in one unknown (Q) that we wish to minimize

  19. SOLVING FOR Q* • TC(Q) = CO(D/Q) + Ch(Q/2) + CD

  20. 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 stock • Then, r* = LD + SS

  21. TOTAL ANNUAL COST • The 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) PurchaseCosts SafetyStockCosts

  22. TOTAL VARIABLE COST CURVE CH(Q/2)Holding Costs CHQ/2 + COD/QTOTAL VARIABLE COSTS COD/QOrder Costs Ignoring purchase costs and safety stock costs: Q* Optimal Order Quantity occurs where Holding Costs = Reorder Costs

  23. EXAMPLE -- ALLEN APPLIANCE COMPANY • Juicer Sales For Past 10 weeks 1. 105 6. 120 2. 115 7. 135 3. 125 8. 115 4. 120 9. 110 5. 125 10. 130 • Using 10-period moving average method, D = (105 + 115 + …+ 130)/10 = 120/ wk = 6240/yr

  24. ALLEN APPLIANCE COSTS • Juicers cost $10 each and sell for $11.85 • Cost of money = 10% • Other misc. inventory = 4% • Labor, postage, telephone/order = $8 • Workers paid $12/hr.--20 min. to unload an order • Desires a safety stock = 13 • EOQ Model • D = 6240 • H = .10 + .04 = .14 • CH= .14(10) = $1.40 • CO = $8 + (1/3 hr.)*($12/hr.) = $8 + $4 = $12 • SS = 13

  25. OPTIMAL ORDER QUANTITY FOR ALLEN

  26. OPTIMAL QUANTITIES • Total Order Cost = CO(D/Q*) = (12)(6240)/327 = $228.99 • Total 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 = 19.08 • Time between orders (Cycle Time) = Q*/D = 327/6240 = .0524 years = 2.72 weeks • r* = SS = 13

  27. TOTAL ANNUAL COST • Total Variable Cost = Total Order Cost + Total Holding Cost = $228.99 + $228.90 = $457.89 • Total Purchase Cost = CD = 10(6240) = $62,400 • Total Safety Stock Cost =ChSS =(1.40)(13) = $18.20 Total Annual Cost = $457.89 + $62,400 + $18.20 = $62,876.09

  28. Using the Inventory Template Input Parameters Note: Ch is automaticallycalculated Optimal Quantities

  29. 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

  30. INSENSIVITY IN EOQ MODELS • We 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* = 327 TV(327) = ((12)(7500))/327 + (1.40/2)(327) = $504.13 Q* should have been: SQRT(2(12)(7500)/1.40) = 359 TV(359) = ((12)(7500))/359 + (1.40/2)(359) = $502.00 • This is only a 0.4% increase in the TVCost

  31. Review • Cost Components of Inventory Models • Holding, Order/Setup, Procurement, Shortage • Objective -- Minimize Total Annual Cost • Continuous Review/Infinite Time Horizon • Basic EOQ Assumptions • Basic EOQ Formula • Reorder Point and Safety Stock • Quantities of Interest • Use of Template • Importance of EOQ Models

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