Inventory Management - Jeryfarel
Introduction to Management Science(8th Edition, Bernard W. Taylor III)Chapter 16Inventory ManagementChapter 16 - Inventory Management1
Chapter TopicsElements of Inventory ManagementInventory Control SystemsEconomic Order Quantity ModelsThe Basic EOQ ModelThe EOQ Model with Non-Instantaneous ReceiptThe EOQ Model with ShortagesEOQ Analysis with QM for WindowsEOQ Analysis with Excel and Excel QMQuantity DiscountsReorder PointDetermining Safety Stocks Using Service LevelsOrder Quantity for a Periodic Inventory SystemChapter 16 - Inventory Management2
Elements of Inventory ManagementRole of Inventory (1 of 2)Inventory is a stock of items kept on hand used to meetcustomer demand.A level of inventory is maintained that will meet anticipateddemand.If demand not known with certainty, safety (buffer) stocksare kept on hand.Additional stocks are sometimes built up to meet seasonalor cyclical demand.Large amounts of inventory sometimes purchased to takeadvantage of discounts.Chapter 16 - Inventory Management3
Elements of Inventory ManagementRole of Inventory (2 of 2)In-process inventories maintained to provide independencebetween operations.Raw materials inventory kept to avoid delays in case ofsupplier problems.Stock of finished parts kept to meet customer demand inevent of work stoppage.Chapter 16 - Inventory Management4
Elements of Inventory ManagementDemandInventory exists to meet the demand of customers.Customers can be external (purchasers of products) orinternal (workers using material).Management needs accurate forecast of demand.Items that are used internally to produce a final product arereferred to as dependent demand items.Items that are final products demanded by an externalcustomer are independent demand items.Chapter 16 - Inventory Management5
Elements of Inventory ManagementInventory Costs (1 of 3)Carrying costs - Costs of holding items in storage.Vary with level of inventory and sometimes with lengthof time held.Include facility operating costs, record keeping,interest, etc.Assigned on a per unit basis per time period, or aspercentage of average inventory value (usuallyestimated as 10% to 40%).Chapter 16 - Inventory Management6
Elements of Inventory ManagementInventory Costs (2 of 3)Ordering costs - costs of replenishing stock of inventory.Expressed as dollar amount per order, independent oforder size.Vary with the number of orders made.Include purchase orders, shipping, handling,inspection, etc.Chapter 16 - Inventory Management7
Elements of Inventory ManagementInventory Costs (3 of 3)Shortage, or stockout costs - Costs associated withinsufficient inventory.Result in permanent loss of sales and profits for itemsnot on hand.Sometimes penalties involved; if customer is internal,work delays could result.Chapter 16 - Inventory Management8
Inventory Control SystemsAn inventory control system controls the level of inventoryby determining how much (replenishment level) and whento order.Two basic types of systems -continuous (fixed-orderquantity) and periodic (fixed-time).In a continuous system, an order is placed for the sameconstant amount when inventory decreases to a specifiedlevel.In a periodic system, an order is placed for a variableamount after a specified period of time.Chapter 16 - Inventory Management9
Inventory Control SystemsContinuous Inventory SystemsA continual record of inventory level is maintained.Whenever inventory decreases to a predetermined level,the reorder point, an order is placed for a fixed amount toreplenish the stock.The fixed amount is termed the economic order quantity,whose magnitude is set at a level that minimizes the totalinventory carrying, ordering, and shortage costs.Because of continual monitoring, management is alwaysaware of status of inventory level and critical parts, butsystem is relatively expensive to maintain.Chapter 16 - Inventory Management10
Inventory Control SystemsPeriodic Inventory SystemsInventory on hand is counted at specific time intervals andan order placed that brings inventory up to a specified level.Inventory not monitored between counts and system istherefore less costly to track and keep account of.Results in less direct control by management and thusgenerally higher levels of inventory to guard againststockouts.System requires a new order quantity each time an order isplaced.Used in smaller retail stores, drugstores, grocery stores andoffices.Chapter 16 - Inventory Management11
Economic Order Quantity ModelsEconomic order quantity, or economic lot size, is thequantity ordered when inventory decreases to the reorderpoint.Amount is determined using the economic order quantity(EOQ) model.Purpose of the EOQ model is to determine the optimalorder size that will minimize total inventory costs.Three model versions to be discussed:Basic EOQ modelEOQ model without instantaneous receiptEOQ model with shortagesChapter 16 - Inventory Management12
Economic Order Quantity ModelsBasic EOQ Model (1 of 2)A formula for determining the optimal order size thatminimizes the sum of carrying costs and ordering costs.Simplifying assumptions and restrictions:Demand is known with certainty and is relativelyconstant over time.No shortages are allowed.Lead time for the receipt of orders is constant.The order quantity is received all at once andinstantaneously.Chapter 16 - Inventory Management13
Economic Order Quantity ModelsBasic EOQ Model (2 of 2)Figure 16.1The Inventory Order CycleChapter 16 - Inventory Management14
Basic EOQ ModelCarrying Cost (1 of 2)Carrying cost usually expressed on a per unit basis of time,traditionally one year.Annual carrying cost equals carrying cost per unit per yeartimes average inventory level:Carrying cost per unit per year CcAverage inventory Q/2Annual carrying cost CcQ/2.Chapter 16 - Inventory Management15
Basic EOQ ModelCarrying Cost (2 of 2)Figure 16.4Average InventoryChapter 16 - Inventory Management16
Basic EOQ ModelOrdering CostTotal annual ordering cost equals cost per order (Co) timesnumber of orders per year.Number of orders per year, with known and constantdemand, D, is D/Q, where Q is the order size:Annual ordering cost CoD/QOnly variable is Q, Co and D are constant parameters.Relative magnitude of the ordering cost is dependent onorder size.Chapter 16 - Inventory Management17
Basic EOQ ModelTotal Inventory Cost (1 of 2)Total annual inventory cost is sum of ordering and carryingcost:TC Co D Cc QQ2Chapter 16 - Inventory Management18
Basic EOQ ModelTotal Inventory Cost (2 of 2)Figure 16.5The EOQ Cost ModelChapter 16 - Inventory Management19
Basic EOQ ModelEOQ and Minimum Total CostEOQ occurs where total cost curve is at minimum valueand carrying cost equals ordering cost:TC min CoD Cc QoptQopt2Qopt 2CoDCcThe EOQ model is robust because Q is a square root anderrors in the estimation of D, Cc and Co are dampened.Chapter 16 - Inventory Management20
Basic EOQ ModelExample (1 of 2)I-75 Carpet Discount Store, Super Shag carpet sales.Given following data, determine number of orders to bemade annually and time between orders given store is openevery day except Sunday, Thanksgiving Day, andChristmas Day.Model parameters :Cc 0.75, Co 150, D 10,000ydOptimal order size :Qopt 2CoD 2(150)(10,000) 2,000 ydCc(0.75)Chapter 16 - Inventory Management21
Basic EOQ ModelExample (2 of 2)Total annual inventory cost :TC min Co D Cc Qopt (150)10,000 (0.75) (2,000) 1,500Qopt22,0002Number of orders per year :D 10,000 5Qopt 2,000Order cycle time 311 days 311 62.2 store daysD/ Qopt5Chapter 16 - Inventory Management22
Basic EOQ ModelEOQ Analysis Over Time (1 of 2)For any time period unit of analysis, EOQ is the same.Shag Carpet example on monthly basis:Model parameters :Cc 0.0625 per yd per monthCo 150 per orderD 833.3 yd per monthOptimal order size :Qopt 2CoD 2(150)(833.3) 2,000 ydCc(0.0625)Chapter 16 - Inventory Management23
Basic EOQ ModelEOQ Analysis Over Time (2 of 2)Total monthly inventory cost :TC min Co D Cc Qopt (150) (833.3) (0.0625) (2,000)Qopt22,0002 125 per monthTotal annual inventory cost ( 125)(12) 1,500Chapter 16 - Inventory Management24
EOQ ModelNon-Instantaneous Receipt Description (1 of 2)In the non-instantaneous receipt model the assumption thatorders are received all at once is relaxed. (Also known asgradual usage or production lot size model.)The order quantity is received gradually over time andinventory is drawn on at the same time it is beingreplenished.Chapter 16 - Inventory Management25
EOQ ModelNon-Instantaneous Receipt Description (2 of 2)Figure 16.6The EOQ Model with Non-Instantaneous Order ReceiptChapter 16 - Inventory Management26
Non-Instantaneous Receipt ModelModel Formulation (1 of 2)p daily rate at which the order is received over timed daily rate at which inventory is demanded dMaximum inventory level Q 1 p Q dAverage inventory level 1 p 2 Q dTotal carrying cost Cc 1 p 2 Q DdTotal annual inventory cost Co Cc 1 p Q2 Chapter 16 - Inventory Management27
Non-Instantaneous Receipt ModelModel Formulation (2 of 2) Q dCc 1 p Co D at lowest point of total cost curveQ2 Optimal order size : Qopt Chapter 16 - Inventory Management2CoDCc(1 d / p)28
Non-Instantaneous Receipt ModelExample (1 of 2)Super Shag carpet manufacturing facility:Co 150Cc 0.75 per unitD 10,000 yd per year 10,000/311 32.2 yd per dayp 150 yd per dayOptimal order size : Qopt 2CoD 2(150)(10,000) d32.2Cc 1 p 0.75 1 150 2,256.8 ydChapter 16 - Inventory Management29
Non-Instantaneous Receipt ModelExample (2 of 2) Q DdTotal minimum annual inventory cost Co Cc 1 p Q2 (10,000)(2,256.8) 32.2 (150) (.075) 1 1,329 (2,256.8)2150 2,256.8 15.05 daysProduction run length Q p150Number of orders per year (productio n runs) DQ 10,000 4.43 runs2,256.8 d32.2Maximum inventory level Q 1 p 2,256.8 1 1,772 yd 150 Chapter 16 - Inventory Management30
EOQ Model with ShortagesDescription (1 of 2)In the EOQ model with shortages, the assumption thatshortages cannot exist is relaxed.Assumed that unmet demand can be backordered with alldemand eventually satisfied.Chapter 16 - Inventory Management31
EOQ Model with ShortagesDescription (2 of 2)Figure 16.7The EOQ Model with ShortagesChapter 16 - Inventory Management32
EOQ Model with ShortagesModel Formulation (1 of 2)2STotal shortage costs Cs2Q2(Q S)Total carrying costs Cc2QTotal ordering cost C0 DQ22(Q S)STotal inventory cost Cs Cc Co DQ2Q2Q 2CoD Cs Cc Optimal order quantity Qopt Cc Cs Cc Shortage level Sopt QoptCc Cs Chapter 16 - Inventory Management33
EOQ Model with ShortagesModel Formulation (2 of 2)Figure 16.8Cost Model with ShortagesChapter 16 - Inventory Management34
EOQ Model with ShortagesModel Formulation (1 of 3)I-75 Carpet Discount Store allows shortages; shortage costCs, is 2/yard per year.Co 150Cc 0.75 per ydCs 2 per ydD 10,000 ydOptimal order quantity : 2(150)(10,000) 2 0.75 2CoD Cs Cc Qopt 2,345 .2 yd Cc Cs 0.752 Chapter 16 - Inventory Management35
EOQ Model with ShortagesModel Formulation (2 of 3)Shortage level: 0.75 Cc Sopt Qopt 639 .6 yd 2,345 .2 Cc Cs 2 0.75 Total inventory cost :22(Q S)STC Cs Cc Co DQ2Q2Q2 (0.75)(1,705.6)2 (150)(10,000)(2)(639.6) 2(2,345.2)2(2,345.2)2,345.2 174.44 465.16 639.60 1,279.20Chapter 16 - Inventory Management36
EOQ Model with ShortagesModel Formulation (3 of 3)Number of orders D 10,000 4.26 orders per yearQ 2,345.2Maximum inventory level Q S 2,345.2 639.6 1,705.6 ydTime between orders t days per year 311 73.0 daysnumber of orders 4.26Time during which inventory is on hand t1 Q S 2,345.2-639.6 0.171 or 53.2 daysD10,000Time during which the re is a shortage t 2 S 639.6 0.064 year or 19.9 daysD 10,000Chapter 16 - Inventory Management37
EOQ Analysis with QM for WindowsExhibit 16.1Chapter 16 - Inventory Management38
EOQ Analysis with Excel and Excel QM (1 of 2)Exhibit 16.2Chapter 16 - Inventory Management39
EOQ Analysis with Excel and Excel QM (2 of 2)Exhibit 16.3Chapter 16 - Inventory Management40
Quantity DiscountsPrice discounts are often offered if a predetermined number ofunits is ordered or when ordering materials in high volume.Basic EOQ model used with purchase price added:TC Co D Cc Q PDQ2where: P per unit price of the itemD annual demandQuantity discounts are evaluated under two differentscenarios:With constant carrying costsWith carrying costs as a percentage of purchase priceChapter 16 - Inventory Management41
Quantity Discounts with Constant Carrying CostsAnalysis ApproachOptimal order size is the same regardless of the discountprice.The total cost with the optimal order size must be comparedwith any lower total cost with a discount price to determinewhich is the lesser.Chapter 16 - Inventory Management42
Quantity Discounts with Constant Carrying CostsExample (1 of 2)University bookstore: For following discount scheduleoffered by Comptek, should bookstore buy at the discountterms or order the basic EOQ order size?Quantity Price1- 49 1,40050 – 891,10090 900Determine optimal order size and total cost:Co 2,500Cc 190 per unitD 200Qopt 2CoD 2(2,500)(200) 72.5190CcChapter 16 - Inventory Management43
Quantity Discounts with Constant Carrying CostsExample (2 of 2)Compute total cost at eligible discount price ( 1,100):TC min CoD Cc Qopt PDQopt2 (2,500)(200) (190) (72.5) (1,100)(200) 233,784(72.5)2Compare with total cost of with order size of 90 and priceof 900:TC CoD Cc Q PDQ2 (2,500)(200) (190)(90) (900)(200) 194,105(90)2Because 194,105 233,784, maximum discount priceshould be taken and 90 units ordered.Chapter 16 - Inventory Management44
Quantity Discounts with Carrying CostsPercentage of Price Example (1 of 3)University Bookstore example, but a different optimal ordersize for each price discount.Optimal order size and total cost determined using basicEOQ model with no quantity discount.This cost then compared with various discount quantityorder sizes to determine minimum cost order.This must be compared with EOQ-determined order size forspecific discount price.Data:Co 2,500D 200 computers per yearChapter 16 - Inventory Management45
Quantity Discounts with Carrying CostsPercentage of Price Example (2 of 3)QuantityPriceCarrying Cost0 - 4950 - 8990 1,4001,1009001,400(.15) 2101,100(.15) 165900(.15) 135Compute optimum order size for purchase price withoutdiscount and Cc 210:Qopt 2CoD 2(2,500)(200) 69Cc210Compute new order size:Qopt 2(2,500)(200) 77.8165Chapter 16 - Inventory Management46
Quantity Discounts with Carrying CostsPercentage of Price Example (3 of 3)Compute minimum total cost:TC CoD Cc Q PD (2,500)(200) 165 (77.8) (1,100)(200)Q277.82 232,845Compare with cost, discount price of 900, order quantity of90:TC (2,500)(200) (135)(90) (900)(200) 191,630902Optimal order size computed as follows:Qopt 2(2,500)(200) 86.1135Since this order size is less than 90 units , it is notfeasible,thus optimal order size is 90 units.Chapter 16 - Inventory Management47
Quantity Discount ModelSolution with QM for WindowsExhibit 16.4Chapter 16 - Inventory Management48
Reorder Point (1 of 4)The reorder point is the inventory level at which a neworder is placed.Order must be made while there is enough stock in place tocover demand during lead time.Formulation:R dLwhere d demand rate per time periodL lead timeFor Carpet Discount store problem:R dL (10,000/311)(10) 321.54Chapter 16 - Inventory Management49
Reorder Point (2 of 4)Figure 16.9Reorder Point and Lead TimeChapter 16 - Inventory Management50
Reorder Point (3 of 4)Inventory level might be depleted at slower or faster rateduring lead time.When demand is uncertain, safety stock is added as ahedge against stockout.Figure 16.10Inventory Model with Uncertain DemandChapter 16 - Inventory Management51
Reorder Point (4 of 4)Figure 16.11Inventory model with safety stockChapter 16 - Inventory Management52
Determining Safety Stocks Using Service LevelsService level is probability that amount of inventory on handis sufficient to meet demand during lead time (probabilitystockout will not occur).The higher the probability inventory will be on hand, themore likely customer demand will be met.Service level of 90% means there is a .90 probability thatdemand will be met during lead time and .10 probability of astockout.Chapter 16 - Inventory Management53
Reorder Point with Variable Demand (1 of 2)R d L Z d Lwhere:R reorder pointd average daily demandL lead time d the standard deviation of daily demandZ number of standard deviations correspond ingto service level probabilityZ d L safety stockChapter 16 - Inventory Management54
Reorder Point with Variable Demand (2 of 2)Figure 16.12Reorder Point for a Service LevelChapter 16 - Inventory Management55
Reorder Point with Variable Demand ExampleI-75 Carpet Discount Store Super Shag carpet.For following data, determine reorder point and safety stockfor service level of 95%.d 30 yd per dayL 10 days d 5 yd per dayFor 95% service level, Z 1.65 (Table A -1, appendix A )R d L Z d L 30(10) (1.65)(5)( 10 ) 300 26.1 326.1 ydSafety stock is second term in reorder point formula : 26.1.Chapter 16 - Inventory Management56
Determining Reorder Point with ExcelDetermining the Reorder Point with ExcelExhibit 16.5Chapter 16 - Inventory Management57
Reorder Point with Variable Lead TimeFor constant demand and variable lead time:R d L Zd Lwhere:d constant daily demandL average lead time L standard deviation of lead timed L standard deviation of demand during lead timeZd L safety stockChapter 16 - Inventory Management58
Reorder Point with Variable Lead Time ExampleCarpet Discount Store:d 30 yd per dayL 10 days L 3 daysZ 1.65 for a 95% service levelR d L Zd L (30)(10) (1.65)(30)(3) 300 148.5 448.5 ydChapter 16 - Inventory Management59
Reorder PointVariable Demand and Lead TimeWhen both demand and lead time are variable:22 2R d L Z ( d ) L ( L ) dwhere:d average daily demandL average lead time22 2( d ) L ( L) d standard deviation of demand during lead time22 2Z ( d ) L ( L ) d safety stockChapter 16 - Inventory Management60
Reorder PointVariable Demand and Lead Time ExampleCarpet Discount Store:d 30 yd per day d 5 yd per dayL 10 days L 3 daysZ 1.65 for 95% service level22 2R d L Z ( d ) L ( L ) d (30)(10) (1.65) (5)(5)(10) (3)(3)(30)(30) 300 150.8 450.8 ydsChapter 16 - Inventory Management61
Order Quantity for a Periodic Inventory SystemA periodic, or fixed-time period inventory system is one inwhich time between orders is constant and the order sizevaries.Vendors make periodic visits, and stock of inventory iscounted.An order is placed, if necessary, to bring inventory levelback up to some desired level.Inventory not monitored between visits.At times, inventory can be exhausted prior to the visit,resulting in a stockout.Larger safety stocks are generally required for the periodicinventory system.Chapter 16 - Inventory Management62
Order Quantity for Variable DemandFor normally distributed variable daily demand:Q d (tb L) Z d tb L Iwhere:d average demand ratetb the fixed time between ordersL lead time d standard deviation of demandZ d tb L safety stockI inventory in stockChapter 16 - Inventory Management63
Order Quantity for Variable Demand ExampleCorner Drug Store with periodic inventory
Introduction to Management Science (8th Edition, Bernard W. Taylor III) Chapter 16 Chapter 16 - Inventory Management 1 Inventory Management. Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Chapter Topics The Basic EOQ Model
An inventory valuation method that assumes the most recent products added to your inventory are the ones to be sold first. Average inventory cost . An inventory valuation method that bases its figure on the average cost of items throughout an accounting period. Average inventory . The average inventory on-hand over a given time period,
Balance sheet Inventory Cost / Unit Inventory Value x Holding Cost Inventory Turns Inventory Value Inventory Turns Wal Mart Stores Inc. Kmart Corp. . Restaurant; High Tech; Inventory decisions 1 Christmas Tree Problem 100 8 15 22 29 2 9 16 23 30 3 10 17 24 31 4 11 18 25 5 12 19 26 6 13 20 27 7 14 21 28
property inventory system. The PCO will also prepare annual inventory control printouts and furnish them to all ODOC facilities/units. III. Inventory Control Officers and Agents Each facility/unit will designate an inventory control officer (ICO) who may designate one or more inventory control agents (ICA) to maintain inventory records
19.Preferred Teaching Approach Inventory 20.Principles of Adult Learning Scale 21.Teacher BehaviorPreferences Survey 22.Teaching Goals Inventory 23.Teaching Methods Inventory 24.Trainer Style Inventory 25.Training Style Inventory 26.Trainer Type Inventory 27.Effective Teacher Inventory 28.Clinical Teacher Characteristics Instrument 29 .
Mississippi Forest Inventory (MFI) Inventory Unit First Inventory Second Inventory Southwest 2004 2012 Southeast 2005 2013 Central 2006 2014 North 2007 2015 Delta 2008 2016. USFS Forest Inventory and Analysis (FIA) Initiated in 1930's Continuous forest inventory Forest Area and Distribution Species, size and health of trees
The cost of ending inventory can be determined by using ABC Method of inventory accounting or the FIFO or LIFO inventory accounting methods, or any less ordinary technique. Beginning inventory for the financial year under study is ending inventory . Perpetual inventory systems provide the company owner with a proof of what is sold, when it .
Inventory Approver and an Inventory Administrator has reviewed it and marked it to be posted to the core AM tables. In Process: The inventory transaction is being posted. Posted: Inventory Code and asset information updates have been posted to the core AM tables. PS 1.Use the Inventory Status field to approve or reject an inventory .
Animal nutrition is gained from grasses, grain crops, and pro-cessed products. Objectives: 1. Explain the functions of feed. 2. Describe the various types of feed. Key Terms: Functions of Feed Feed is any product consumed by an animal to meet nutritional needs. Feed provides the animal with energy to be mobile, protein to grow new or repair damaged cells, and vitamins and minerals to support .
