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Muhammad ShakeelMS IEM (PU) MS IT (PIMSAT)BE (Av) (NED)Supply Chain ManagementInventory ManagementFriday, March 6, 20152Supply Chain Management By:- Muhammad ShakeelWhat Is Inventory?Stock of items kept to meet future demandPurpose of inventory managementhow many units to orderwhen to orderFriday, March 6, 20153Supply Chain Management By:- Muhammad ShakeelInventory ManagementEconomic Order Quantity ModelsReorder PointOrder Quantity for a Periodic Inventory SystemFriday, March 6, 20154Supply Chain Management By:- Muhammad ShakeelInventory Control SystemsFriday, March 6, 20155Supply Chain Management By:- Muhammad ShakeelContinuous system (fixed-order-quantity)Constant amount ordered when inventory declines to predetermined level

Periodic system (fixed-time-period)Order placed for variable amount after fixed passage of time5Inventory ManagementAn OverviewFriday, March 6, 20156Supply Chain Management By:- Muhammad ShakeelRaw materialsPurchased parts and suppliesWork-in-process (partially completed) products (WIP)Items being transportedTools and equipmentTypes of InventoryFriday, March 6, 20157Supply Chain Management By:- Muhammad ShakeelClass A5 15 % of units70 80 % of value Class B30 % of units15 % of valueClass C50 60 % of units 5 10 % of valueABC Classification

Friday, March 6, 20158Supply Chain Management By:- Muhammad ShakeelABC Classification: Example1$ 6090235040330130480605301006201807101708320509510601020120PARTUNIT COSTANNUAL USAGEFriday, March 6, 20159Supply Chain Management By:- Muhammad Shakeel9ABC Classification: Example (cont.)Example 10.11$ 6090235040330130480605301006201807101708320509510601020120PARTUNIT COSTANNUAL USAGETOTAL% OF TOTAL% OF TOTALPARTVALUEVALUEQUANTITY% CUMMULATIVE9$30,60035.96.06.0816,00018.75.011.0214,00016.44.015.015,4006.39.024.044,8005.66.030.033,9004.610.040.063,6004.218.058.053,0003.513.071.0102,4002.812.083.071,7002.017.0100.0

$85,400ABCFriday, March 6, 201510Supply Chain Management By:- Muhammad Shakeel% OF TOTAL% OF TOTALCLASSITEMSVALUEQUANTITYA9, 8, 271.015.0B1, 4, 316.525.0C6, 5, 10, 712.560.010

Friday, March 6, 2015Supply Chain Management By:- Muhammad Shakeel11Two Forms of DemandDependentDemand for items used to produce final products Tires stored at a Goodyear plant are an example of a dependent demand itemIndependentDemand for items used by external customersCars, appliances, computers, and houses are examples of independent demand inventory11Carrying costCost of holding an item in inventory CcOrdering costCost of replenishing inventory c.Shortage costTemporary or permanent loss of sales when demand cannot be met Could be tangible or intangible

Inventory CostsFriday, March 6, 201512Supply Chain Management By:- Muhammad Shakeel12Bullwhip effectdemand information is distorted as it moves away from the end-use customerhigher safety stock inventories are stored to compensateSeasonal or cyclical demandInventory provides independence from vendorsTake advantage of price discountsInventory provides independence between stages and avoids work stoppagesInventory vs Supply Chain ManagementFriday, March 6, 201513Supply Chain Management By:- Muhammad ShakeelQuality in Supply ChainAvailability of needed goods when neededInventory must be sufficient to provide high-quality customer service in QMInventory vs Quality Management in the Supply ChainFriday, March 6, 201514Supply Chain Management By:- Muhammad ShakeelInventory ManagementEconomic Order Quantity ModelsFriday, March 6, 201515Supply Chain Management By:- Muhammad ShakeelEOQoptimal order quantity that will minimize total inventory costsBasic EOQ modelProduction quantity model

Economic Order Quantity (EOQ) ModelsFriday, March 6, 201516Supply Chain Management By:- Muhammad ShakeelDemand is known with certainty and is constant over timeNo shortages are allowedLead time for the receipt of orders is constantOrder quantity is received all at once

Assumptions of Basic EOQ ModelFriday, March 6, 201517Supply Chain Management By:- Muhammad Shakeel17Inventory Order CycleDemand rateTimeLead timeLead timeOrder placedOrder placedOrder receiptOrder receiptInventory LevelReorder point, ROrder quantity, Q0Average inventory Q2Friday, March 6, 201518Supply Chain Management By:- Muhammad Shakeel18EOQ Cost ModelCo - cost of placing orderD - annual demandCc - annual per-unit carrying costQ - order quantityAnnual ordering cost =CoDQAnnual carrying cost =CcQ2Total cost = +CoDQCcQ2Friday, March 6, 201519Supply Chain Management By:- Muhammad Shakeel+19EOQ Cost Model (cont.)Order Quantity, QAnnual cost ($)Total CostCarrying Cost =CcQ2Slope = 0Minimum total costOptimal order QoptOrdering Cost =CoDQFriday, March 6, 201520Supply Chain Management By:- Muhammad Shakeel20EOQ Cost Model(cont.)TC = +CoDQCcQ2= +CoDQ2Cc2TCQ0 = +C0DQ2Cc2Qopt =2CoDCcDeriving QoptProving equality of costs at optimal point=CoDQCcQ2Q2 =2CoDCcQopt =2CoDCcFriday, March 6, 201521Supply Chain Management By:- Muhammad Shakeel21EOQ ExampleCc = $0.75 per gallonCo = $150D = 10,000 gallonsQopt =2CoDCcQopt =2(150)(10,000)(0.75)Qopt = 2,000 gallonsTCmin = +CoDQCcQ2TCmin = +(150)(10,000)2,000(0.75)(2,000)2TCmin = $750 + $750 = $1,500Orders per year =D/Qopt=10,000/2,000=5 orders/yearOrder cycle time =311 days/(D/Qopt)=311/5=62.2 store daysFriday, March 6, 201522Supply Chain Management By:- Muhammad Shakeel22An inventory system in which an order is received gradually, as inventory is simultaneously being depletedAKA non-instantaneous receipt modelassumption that Q is received all at once is relaxedp - daily rate at which an order is received over time, a.k.a. production rated - daily rate at which inventory is demandedProduction QuantityModelFriday, March 6, 201523Supply Chain Management By:- Muhammad ShakeelProduction Quantity Model (cont.)Q(1-d/p)Inventorylevel(1-d/p)Q2Time0Orderreceipt periodBeginorderreceiptEndorderreceiptMaximuminventory levelAverageinventory levelFriday, March 6, 201524Supply Chain Management By:- Muhammad Shakeel24Production Quantity Model (cont.)p = production rated = demand rateMaximum inventory level =Q -

=Q 1 -Q dpdpAverage inventory level = 1 -Q2dpTC = + 1 -dpCoDQCcQ2Qopt =2CoD

Cc 1 - dpFriday, March 6, 201525Supply Chain Management By:- Muhammad Shakeel1. Q is the total quantity produced 2. p is the production rate 3. Q/p is the number of days needed to produce Q 4. (Q/p)*d is the number of units consumed during period Q/p25Production Quantity Model: ExampleCc = $0.75 per gallonCo = $150D = 10,000 gallonsd = 10,000/311 = 32.2 gallons per dayp = 150 gallons per dayQopt = = = 2,256.8 gallons2CoD

Cc 1 - dp2(150)(10,000)

0.75 1 - 32.2150TC = + 1 - = $1,329dpCoDQCcQ2Production run = = = 15.05 days per orderQp2,256.8150Friday, March 6, 201526Supply Chain Management By:- Muhammad Shakeel26Production Quantity Model: Example (cont.)Number of production runs = = = 4.43 runs/yearDQ10,0002,256.8Maximum inventory level = Q 1 - = 2,256.8 1 -

=1,772 gallonsdp32.2150Friday, March 6, 201527Supply Chain Management By:- Muhammad Shakeel27Quantity DiscountsPrice per unit decreases as order quantity increasesTC = + + PDCoDQCcQ2whereP = per unit price of the itemD = annual demandFriday, March 6, 201528Supply Chain Management By:- Muhammad Shakeel28Quantity Discount Model (cont.)QoptCarrying cost Ordering cost Inventory cost ($)Q(d1 ) = 100Q(d2 ) = 200TC (d2 = $6 ) TC (d1 = $8 ) TC = ($10 ) ORDER SIZE PRICE0 - 99 $10100 199 8 (d1)200+ 6 (d2)Friday, March 6, 201529Supply Chain Management By:- Muhammad Shakeel29Quantity Discount: ExampleQUANTITYPRICE

1 - 49$1,40050 - 891,10090+900Co =$2,500 Cc =$190 per TV D =200 TVs per yearQopt = = = 72.5 TVs2CoDCc2(2500)(200)190TC = + + PD = $233,784 CoDQoptCcQopt2For Q = 72.5TC = + + PD = $194,105

CoDQCcQ2For Q = 90Friday, March 6, 201530Supply Chain Management By:- Muhammad Shakeel30Inventory ManagementReorder PointFriday, March 6, 201531Supply Chain Management By:- Muhammad ShakeelLevel of inventory at which a new order is placed

Reorder PointR = dLwhere

d = demand rate per periodL = lead timeFriday, March 6, 201532Supply Chain Management By:- Muhammad Shakeel32Demand = 10,000 gallons/yearStore open 311 days/yearDaily demand = 10,000 / 311 = 32.154 gallons/dayLead time = L = 10 days

R = dL = (32.154)(10) = 321.54 gallons

Reorder Point: ExampleFriday, March 6, 201533Supply Chain Management By:- Muhammad Shakeel33Reorder Point with a Variable DemandReorderpoint, RQLTTimeLTInventory level0Friday, March 6, 201534Supply Chain Management By:- Muhammad Shakeel34Reorder Point with a Safety StockReorderpoint, RQLTTimeLTInventory level0Safety StockFriday, March 6, 201535Supply Chain Management By:- Muhammad Shakeel35Safety stockbuffer added to on hand inventory during lead timeStock out an inventory shortageService level probability that the inventory available during lead time will meet demandSafety Stocks Friday, March 6, 201536Supply Chain Management By:- Muhammad Shakeel36Reorder Point With Variable DemandR = dL + zd Lwhere

d=average daily demandL=lead timed=the standard deviation of daily demand z=number of standard deviationscorresponding to the service levelprobabilityzd L=safety stock

Friday, March 6, 201537Supply Chain Management By:- Muhammad Shakeel37Reorder Point for a Service LevelProbability of meeting demand during lead time = service levelProbability of a stockoutRSafety stockdLDemandzd LFriday, March 6, 201538Supply Chain Management By:- Muhammad Shakeel38Reorder Point for Variable DemandThe paint store wants a reorder point with a 95% service level and a 5% stockout probabilityd= 30 gallons per dayL= 10 daysd= 5 gallons per dayFor a 95% service level, z = 1.65R= dL + z d L= 30(10) + (1.65)(5)( 10)= 326.1 gallonsSafety stock= z d L= (1.65)(5)( 10)= 26.1 gallonsFriday, March 6, 201539Supply Chain Management By:- Muhammad Shakeel39Inventory ManagementPeriodic Inventory SystemFriday, March 6, 201540Supply Chain Management By:- Muhammad ShakeelOrder Quantity for a Periodic Inventory SystemQ = d(tb + L) + zd t + L - Iwhere

d= average demand ratetb= the fixed time between ordersL= lead timesd= standard deviation of demand zd tb + L= safety stockI= inventory levelFriday, March 6, 201541Supply Chain Management By:- Muhammad Shakeel41Periodic Inventory System

Friday, March 6, 201542Supply Chain Management By:- Muhammad ShakeelFixed-Period Model with Variable Demandd= 6 packages per daysd= 1.2 packagestb= 60 daysL= 5 daysI= 8 packagesz= 1.65 (for a 95% service level)

Q= d(tb + L) + zd tb + L - I= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8= 397.96 packagesFriday, March 6, 201543Supply Chain Management By:- Muhammad Shakeel43