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Published byRoberto Yelvington Modified about 1 year ago

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Module C4 Inventory Modeling Concepts

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

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COMPONENTS OF AN INVENTORY POLICY Q = the amount to order (the order quantity) R = when to reorder (the reorder point)

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BASIC CONCEPT Balance the cost of having goods in inventory to other costs such as: –Order Cost –Purchase Costs –Shortage Costs

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

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Holding Cost Rate Annual 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, C h C h = HC (in $/item in inv./year)

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ORDER/SETUP COSTS When purchasing items, this cost is known as the order cost, C O (in $/order) These are costs associated with the ordering process that are independent of the size of the order-- invoice writing or checking, phone calls, etc. – Labor –Communication –Some transportation

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ORDER/SETUP COSTS (Cont’d) When these costs are associated with producing items for sale they are called set-up costs (still labeled C O -- 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

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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

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CUSTOMER SATISFACTION COSTS Shortage/Goodwill Costs associated with being out of stock –goodwill –loss of future sales –labor/communication Fixed administrative costs = C b ($/occurrence) Annualized Customer Waiting Costs = C s ($/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 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

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

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

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

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

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THE EOQ COST COMPONENTS Total Annual Order Costs: –(Cost/order)(average # orders per year) = C O (D/Q) Total Annual Holding Costs: –(Cost Per Item in inv./yr.)(Average inv.) = C h (Q/2) Total Annual Purchase Costs: –(Cost Per Item)(Average # items ordered/yr.) = CD

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THE EOQ TOTAL COST EQUATION TC(Q) = C O (D/Q) + C h (Q/2) + CD This a function in one unknown (Q) that we wish to minimize

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SOLVING FOR Q* TC(Q) = C O (D/Q) + C h (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 stock Then,r* = LD + SS

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TOTAL ANNUAL COST The optimal policy is to order Q* when supply reaches r* TC(Q*) = C O D/Q* + (C h /2)(Q*) + CD + C h SS fixed safety cost stock cost The optimal policy minimizes the total variable cost, hence the total annual cost

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TOTAL VARIABLE COST CURVE Ignoring fixed costs and safety stock costs:

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EXAMPLE -- ALLEN APPLIANCE COMPANY Juicer Sales For Past 10 weeks 1.1056.120 2.1157.135 3.1258.115 4.1209.110 5.12510.130 Using 10-period moving average method, D = (105 + 115 + …+ 130)/10 = 120/ wk = 6240/yr

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ALLEN APPLIANCE COSTS Juicers cost $10 each and sell for $11.85 Cost of money = 10% Other misc. costs associated with inventory = 4% Labor, postage, telephone charges/order = $8 Workers paid $12/hr. -- 20 min. to unload an order Desires a safety stock = 13 This is an EOQ Model with: H =.10 +.04 =.14; C h =.14(10) = $1.40 C O = $8 + (1/3 hr.)*($12/hr.) = $8 + $4 = $12 SS = 13

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OPTIMAL ORDER QUANTITY FOR ALLEN

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OPTIMAL QUANTITIES Total Order Cost = C O D/Q* = (12)(6240)/327 = $228.99 Total Holding Cost = (C h /2)Q* = (1.40/2)(327) = $228.90 –(Total Order Cost = Total Holding Cost -- except for roundoff) # 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

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TOTAL ANNUAL COST Total Variable Cost = Total Order Cost + Total Holding Cost = $228.99 + $228.90 = $457.89 Total Fixed Cost = CD = 10(6240) = $62,400 Total Safety Stock Cost =C h SS =(1.40)(13) = $18.20 Total Annual Cost = $457.89 + $62,400 + $18.20 = $62,876.09

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Using the Inventory Template Input Parameters Note: C h is automatically calculated Optimal Quantities

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WHY IS 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 MODELS We cannot affect fixed costs, only variable costs TV(Q) = C O D/Q + (C h /2)(Q) 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

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Module C4 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 Quantities of Interest Use of Template Importance of EOQ Models

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