InventoryManagementIVSafetyStock

1、inventory management iv safety stockinventory management iv safety stocklecture 7esd.260 fall 2003 capliceassumptions: basic eoq model demand? constant vs variable? known vs random? continuous vs discrete lead time instantaneous? constant or variable (deterministic/stochastic) dependence of items ?

2、independent correlated? indentured ? review time continuous vs periodic number of echelons? one vs many capacity / resources? unlimited vs limited discounts? none? all units or incremental excess demand? none? all orders are backordered? lost orders? substitution perishability? none? uniform with ti

3、me planning horizon? single period? finite period? infinite number of items? one? many mit center for transportation & logistics - esd.260 2 ? chris caplice, mitfundamental purpose of inventoryto buffer uncertainties in: -supply, -demand, and/or -transportationthe firm carries safety stocks.

4、to capture scale economies in: -purchasing, -production, and/or -transportationthe firm carries cycle stocks.mit center for transportation & logistics - esd.260 3 ? chris caplice, mitcycle stock and safety stockmit center for transportation & logistics - esd.260 4 ? chris caplice, mi

5、tcyclestockcyclestockcyclestocksafety stockon handwhat should my inventory policy be? (how much to order when)what should my safety stock be?what are my relevant costs?timepreview: safety stock logic mit center for transportation & logistics - esd.260 5 ? chris caplice, mitpsocbslknkeustcrrf

6、rdetermining the reorder pointmit center for transportation &amp; logistics - esd.260 6 ? chris caplice, mitr = 9><>d&#039; + kreorder pointestimated demand over the lead time (ft) safety stock k = ss factor= rmsenotewe usually pick k for desired stock out probability 2. safety stoc

7、k = r <>ddefine some termsmit center for transportation &amp; logistics - esd.260 7 ? chris caplice, mit safety stock factor (k) amount of inventory required in terms of standard deviations worth of forecast error stockout probability = p<>d&gt; r the probability of running out o

8、f inventory during lead time service level = p<>dr = 1-pso the probability of not running out of inventory during lead timeservice level and stockout probabilitymit center for transportation &amp; logistics - esd.260 8 ? chris caplice, mitwhere <>d iidn(<>d=10,=25)ss = kprobabi

9、lity of stockoutservice leveldemandforecasted demand (<>d)reorder pointprob (x)cumulative normal distributionmit center for transportation &amp; logistics - esd.260 9 ? chris caplice, mitwhere <>d iidn(<>d=10,=25)prob (x)demandprobability of stockout = 1-slservice levelreorder

10、pointfinding sl from a given kmit center for transportation &amp; logistics - esd.260 10 ? chris caplice, mitusing a table of cumulative normal probabilities . . .0.82640.82380.82120.81860.81590.90.73890.73570.73240.72910.72570.60.77040.76730.76420.76110.75800.70.67000.66640.66280.65910.65540.40

11、.70540.70190.698><#004699'>850.69500.69150.50.51600.51200.50800.50400.50000.00.55570.55170.54780.54380.53980.10.59480.59100.58710.58320.57930.20.63310.62930.62550.62170.61790.31.00.8k0.<#004699'>85080.84<#004699'>850.84610.84380.84130.79950.79670.79390.79100.78810.04

12、0.030.020.010.00if i select a k = 0.42. . . then my service level is this value.or, in excel, use the function: sl=normdist(k+<>d, <>d, , true)k factor versus service levelmit center for transportation &amp; logistics - esd.260 11 ? chris caplice, mitk factor versus service levelserv

13、ice level %k factor safety stock and service level mit center for transportation &amp; logistics - esd.260 12 ? chris caplice, mitexample: if <>d iidnormal (<>d=100,=10) what should my ss &amp; r be? reorder point safety stockkslpso123232.33.99.01117171.65.95.05113 131.28.90.1010

14、0 00.50.50service level what is exactly is service level?mit center for transportation &amp; logistics - esd.260 13 ? chris caplice, mitis notisservice level . . . . probability that a stockout does not occur during lead timethe fraction of demand satisfied from stockprobability that stock is av

15、ailablefill rate for or availability of an item fraction of time that stock is available in the systemprobability that all demand will be satisfied from on hand stock w/in any given replenishment cyclefraction of order cycles during which no sosoccurso, how do i find item fill rate?mit center for tr

16、ansportation &amp; logistics - esd.260 14 ? chris caplice, mitfill rate fraction of demand met with on-hand inventory based on each replenishment cycleorderquantity e unitsshortfillrateorderquantity=but, how do i find expected units short? more difficult need to calculate a partial expectation:e

17、xpected units shortconsider both continuous and discrete casesmit center for transportation &amp; logistics - esd.260 15 ? chris caplice, mitlooking for expected units short per replenishment cycle. 1 2 3 4 5 6 7 8 xwhat is eus if r=5?1/8 pxfor normal distribution wehave a nice result:eus = nkwh

18、ere nk = normal unit loss function found in tables or formulathe nk tablemit center for transportation &amp; logistics - esd.260 16 ? chris caplice, mita table of unit normal loss integrals .09328.09503.09680.09860.10040.9.1334 .1358.1381.1405.14290.7.1580 .1606.1633.1659.16870.6.1120 .1140.1160.1181.12020.81.00.50.40.30.20.10.0k.3328 .3373.3418.3464.3509.2904 .2944.2986.3027.3069.2518 .2555.2592.2630.2668.2169.2203.2236.2270.2304.1<#004699'>857 .1887.1917.1947.1978.07716.07866.08019.08174.08332.3793 .3841.3890.3940.3989.04.03 .02.01.00item fill ratemit center for transportation