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Prob_Inventory_Problems

# Prob_Inventory_Problems - IE 251 Production and Inventory...

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Unformatted text preview: IE 251 Production and Inventory Control Exam #2 Fall 2010 2...(56 pts) Demand is Normally distributed E(D) n—n \$.25/s/yr. 6000/ r. 2500/ r. \$30/unit a) Assuming lost sales and Q=EOQ, determine the reorder point. b) Determine ETRC(s) for the policy determined in part (a). m “ “ e) For the reorder point policy found in part (a), determine the ileicit value of B1. (W 1&3 f) For 32 costing of shortages, R = 1/2 month, and var(L) = 1 mo.2 , determine the order-up-to-level. g) ' ' I. l_ ' TQ s\ 7 \$3 a ”P ,m = l—-—~— =_l_:.__<_2.____c = 4___“°me‘ C i u? 32 ‘6 +rQ (“Kwanzaa“) =.oow:. EDA (.2s)(3) ——§I-<= 3.07 , =73‘S‘ S= XLi-Kﬁ = b€¥+(5-°73(35—~°°)= 272g 84;?) ./ Q0.) Emu-33: A’a§+\.U[E +6’ (K+G (1031+B: 55061de = 40(60003 'm 2500 éu(3.os\=.ooom 73;,- + (- 33(2) ~— + W (3.0, town”) g /: 5134']: EH] +E[x] = \$5"? @ AIMIK1= UM(%11‘UM[*1 = 742%: Wis-[3% @ G (amv m2": 01: 250° =71la7 IE 251 ”fr-’2: Production and Inventory Control 3 Exam #2 Fall 2010 (d 3 Q - 3—6 [A+B,_UGLG1(K\] = 3(éooo\ {401- (%o\(z\(7zl.7)(.oooaq7 . __ ﬂ__________. W (.15NC83 = 4‘“ w "max = W: our] a K= 3 01 (353(91771'C3070‘m‘ﬁ / €5.35: 5 2 Sam +(3. 023(72; 73 {/2 2423/) I. \‘sr- '. -,L.. ’u/L_621rc‘r (a BM. .7... e ~ .; ‘L 6-7:: 2'(5'°WZ= (735)(3\(7ll.7)(.151 2 174.231 (boaoTB' B . : (7(332 ' 053475 T A6 ._ I'ZL. .zz_//:’ 5.0%) \ oODS‘Wb (\th _2. (£5 011—: 1:th + D mum—N 7. =.(n(721737’,+("—°—-"°)( 3 7- 77°29 °E+L=li77°m ”‘0‘“7 7' - 25007” “72 .- = 1604!? - ~ (015.5 ”K = (-25% \$70 3o + <- 253(50 = .000347 4%42 3.3/3! ___\ // \ " ‘54 : X12“ + K972“. 2 “go/113390015. 5) ,—. 4142/4 34/63. ‘ _ ém _ (’A-l Quad = ‘20 P121“? [:CQ—tﬂ, 6": Hue ‘k J‘R' “2'4 ~25o l 172. 6-2.“. 2’“: 0.7- .; (.7500) R+L X : 2(.017 (150) S 3co4t7+(2\$b;" =~ 73!.15‘0 75 + .7050) (.qnauasm : .mgosS‘ 5 K: {EL 5 =ﬂe+L +KGE+L =750 «115000153 123444é§9 IE 251 Production and Inventory Control Exam #1 Fall, 2009 3...(27 pts) Given the following data for an inventory control system under periodic review and assuming that demand not met directly from inventory results in “lost sales”, am 0 R ZQOOO/yr 10000/yr 1week Zweeks 1.5 weeks .98 \$3/um‘t/yr a) Determine the optimal order-up-to-level S. b) If 2 =10, determine the “implicit” value of B4 c) Assuming demand not met directly from inventory is now backordered, determine the value of S if the TBS is prescribed to be 6 years. __ 4 1. (0.3 5‘ = X R“ + «6‘9“ “1‘ E(L)a*1+ Emzm (L3 = (amowa’w zoom 1‘”) = 4,042,047 G (KP stoma—m z 52. s:- u ?z rRl-L G“ : (|\(10000§L: (34235074 52 , 40000 _ r—"() .02\ 7' 7— 7. - (52 ‘ ( gm: LN]; : 5,441,134 -9 cm 2442 5921(24423 W3 A = .0621 '-> “=13? = EEWOMH (amuwzif 4234 (H mum -’% +(E—2woatwﬁukﬂw “it; re. Gm WQMWJMMAmﬁmMm-im n8 0‘ . ‘ 2 ‘——/tlu. lithe dwuwﬂai 84/2 LAW [a Bar II R“ m . . . O = __ _-_ Smnﬁ‘f ' “”(0 Rh+thr—>?“"(K\ Emmi/2‘ #2 Bi “‘5‘” M = (IKE/52.3 fl)“ (1.3),.) = .0496 ~——> (.Mqtﬂ.o§77\ +2—1- ’- - 0571 ling/52) + (EN/Io 8y“, = .0571 R _ l/5:. - 4, 1.0031 -—>i<=a.73 '— 3751(2an03 + (2.73) (24¥[email protected] IE 251 Production and Inventory Control Exam #2 Fall 2008 2...(25 pts) demand demand leadtime A v * rate st. dev. ,ﬂﬁOO/yr m \$110 \$.25/\$/yr - a) Using the “sequential” approach, determine the reorder point and the order quantity for a continuous review inventory policy. Assume the demand distribution is Normal. b) Redo part (a) assuming the variance of the leadtime interval is 1. 5 c) Determine the equivalent 82 for the policy determined in part (a) AUwXIawﬁ " £461 1 :) EO “‘7 a Q if??? - 2 62 S = XL+KGL @— (KW 'Eﬁ éwi" "_::::_5.(M3 , U TL(5+.15‘) (zwao)+(: 5+\(1137.+ : 'Ogéol (cf’fjggi-l :/ 3 l S 5—. 6) ::> —% l< : In 54 (b\ W(L)= (.5 144° _ - 7. ,_7_ _ Z Z 01 — £0.76? + ovum ' Ti (35007+ (zoooo) (1.53/11Z 3: 257m :7 6:: 1430+ _ UN 1 45‘ élrm— “0+ 525) 2.0.2074, A K=/.f_5__ __ _ l ‘ 7 /:j;., 5' \ § (loauow + (( (,5) (leo‘éo/LQ 3699.1/ '3. = _ _ r . 4/ ( > +< [.3 may SIB —~> 32:9—L :sz\(.as> Z. IE 425 Resource Allocation and Production Planning Exam 2 Fall 2004 4... Probabilistic Inventory Control. Demand Normally distributed. _—-___— 2000/yr W (a) Determine order-up-to-level S (b) Determine the implied value of B2 (c) If B2 doubles, but the expected time between stockout occasions increases by only 50%, what % change in inventory cost must occur. E(D\K (CL) Guﬂq = T0413 R—H. Z Z. 1. J... 7- 7- ‘ 2. 01 : E(L\<r fE(D\vwz(l-\ = ,;l (40“ +(20w‘ (7713 ('73 : YéﬁLfI-f I; 2 2_ (T = Iaom'f G} ‘ 3‘1 (‘iovwz = 33750 R” Gain. : 347 ' 07005 (£43 (.0057 1‘ < 1 M _- G‘Lud ‘ .omz. »——> K=;2.C,c. 3+7 : A 2 ano 5‘ XR+L + K TR“. '7 + (2440(3er = 1/73 LEW Rgm = R“ ——> B : (RV : imoﬁ - Ba 2 V (l0 ~ 3'2‘ {(9,ch m “5036‘ (a) Vaduz: @.thénmt6uéu [r‘zméﬁa tram—1 T55 2:???" "5T3“ ”131 ——> r1: 432 _ as; M 4 | FL '7' ~ 7—. : ”—1 = ’— .3 ——r -- 7 , .. m_.-_~~_ ['3 as l'5 (—8—???) ['5' 3( )1 . - , x r :'+ “-3570 \ ‘ Mml ‘ 7DW.MW (m re A (l) ‘ £~ —L mud—6) DR “m _ T“ ’> TBS ”mum ItﬁVN'EWﬂIm 3—. ,. ’E_q_._ __ P (k, : UR Emmi“ 215765 ’ 1.§( R \ ' “‘ 3 AWN; IQ: “Mezwzﬂﬂ “Rum 1.3 6‘ .76 y. IE 251 Production Planning and Control Exam 1 Fall 2007 3... Probabilistic Inventory Control. Given the following data and assuming demand is Normally distributed: -______— 5000/yr 3000/yr _-E_ 3/\$/ r u 10/5 short a) Determine (s,Q) for a continuous review control system, assuming shortages are backordered. b) Assuming the variance of the lead-time interval is .75, determine the resulting optimal safety stock. c) Redo part (b), assuming lost sales. d) Determine the implied value of the fill rate for your answer in part (c). e) Assuming shortages are backordered, fixed lead-time of 1 month, and a review period of 1. 5 months, determine an optimal order-up-to-level. cm 6W @— xjr—‘uﬂ Q .253 ”game? 2 _ (345m 7.» .. - ”out: __ i“ S — /“L+KOT_ - 97; + (2.853(5cmﬁ3 2 2334.35‘@ .002l‘i —>K— :2. 35— E82. (Sb-vb» ([03 2. [Z 2_ 2- 7- - 300° u.» q- to; + Wm ~ , + emu-m m 5W 0— = —. — = - -_ L 441s 7% 3 SS KR - (2.353(1‘34151323 IQS‘YCZe’ 6:9”- ! 320+ Gr ((0)6091?) + (5453(5) ' 6 02!? -- Hails? Q.‘Z;zc?z~ ~zaeS~3L§Fz "\ (l): : 365/367.8'5 @ t .00375'—'; ' = 247 5‘: ﬁrm. +i< 0}“ = %(5m7+ (2.67”!sz (5m) =(44qg) 1. Name .5432; MSE 425' . Resource Allocation & Production Planning Quiz 2 — Fall 1990 Specify the reorder point and the order quantity such that the expected time between stockouts is 5 years. Data: A = \$500 L = .15 yr. v = \$2 fL(x) = 56%5 Q 0 < x 5_2000 r = \$.3/\$-yr. XL: [W0 T55: ~QF¢(\$) __ [0'00 ’ ‘5" L -—’—~ =ééé7 4. , D / ' 25% __ 5'00 L7 .. asgm— W -3335 (2)03) Java S Q “IE 32’.) @ g4? 11 ﬂfﬁmﬁg‘f ﬁlgiﬂ‘wad/L )ALZEzmmL ,ﬂa ﬂoaaﬁiﬂémi‘ mi ; 'ﬂﬂdb? jawm‘tg 6/0711 fwrlbrguoaa ﬂung-1r -Poer/gbd ﬂaming fag/g. ‘ .71er xxx/o maliég‘; . 01". M” E .7: Exec/13h. ‘r = .Bl‘blvd/ﬁ. A = 520 L : 1WGf‘C’a. 6-3,: 4O , _ :2- TB’S = EMMA-o ”L’— _ .0 5091’ TKCQ(ZM\ = 2W0 (to) +- »._ ”LI-HO ‘ Triad/cud; £913- (2&4 ~— 194%?“ . . ma . : 429 5: Ram; :. Zr; + 039306,. ' J... .. ﬂ?— = 3' EWING-‘- 'D/qaes) _ (“715770)(5) .933 MSE 4&5— W W m1 Begum»; PJW 62%; @1455 QW= 61M (m) Mrﬁ/lzwk MW 41:“ 783 (Md A P2 WMMW. WWMMDAKQMMkMMM-up- ﬁ-M W11 fauna Mm: R: (wak- ‘L: = ZWLA 6 7- lagoon/1X1. TBS =l439M. mu): 3 (r = 263000 T_’"‘...—,—._ ‘:\_ > K = 4.07 7.) _ DR (l’Pz), :.__ llrva )( m) 3: 003241 EK Z1344- “7m " f“??? __/ g > I i I I 2' ‘ z : 0:: 12,023? = 7M2307 6‘1. 2:0’ + Ema/((1.) ®: U-R’:/Q773 /) d - :(2](?472307)+(Ifﬂ¢§)(33 /' _ _V _ _‘ \ E V/ " - 26+772qo ‘/3 O—R‘H. :"- lQ—E:+G‘:z 7-“7Cq2307 +2L‘l-7ﬁjﬁo l _ 4' . 3 ' I ,S — xw+ M‘R+L (gin-WWW)+(2.3¥\(5g¥4> ’,./" ‘ 3....(30 pts) “sequential” approach. Relevant data: A=\$55 1=\$.3/\$/yr E(D)=50000/yr aD=1000 L=.O9yr v=\$3/unit B1=\$100 B2=\$200/\$ short P2=.99 0- L (a) A! IE 497 / MSE 425 Production Planning and Resource Allocation Exam 1 Fall 2002 Consider the (s,Q) inventory control model that is speciﬁed using a Among the 3 stock out costs and measure, determine which requires the least safety stock. Determine what value B1 must have such that the 2 stock out cost measures provide the same safety stock protection. Let R=.05yr, B3=\$5/\$/yr (ignore the other stock out costs and measure), and var(L)=.1 Specify s and S using the Revised Power Approximation for an (R,s,S) inventory control system. Mud-(39444.4: &..LA EOQ M W Lo» 55 mick, thzi/O "iTz-m KM WWWMWW (a) watt-Jo. MWMWUZM 06K. 8‘ .' K _= 11K 06‘ (5000D7(lobl .» i T‘ W 61'\X/z= (2L W(n471\(3)(3m(33 Y],— =I.+7a7 B '. z ___E : (24mm - "a" 1:1 Exam) 32\$ (Rooﬂfoooo)- .00007+®7‘l ,-~—\ : = 0-9,) __ , --\ \\ :21 Gum 03¢ - (247322: on = [email protected] IE 251 Production and Inventory Control Exam 2 Fall 2005 3... Probabilistic lnventom Models Given that the carrying cost factor is \$0.25 / \$ / yr. and the following data for an item: A v E(D) c L \$90 \$7 10000/ yr. 2000/ yr. 0.15 yr. (a) (12 pts) The item is being managed by a continuous review control system with P2 = .995 and shortages are backordered. Determine the appropriate reorder point and order quantity. (b) (12 pts) Determine the expected time between stock outs for the policy found' In part (a). (c) (13 pts) The safety stock under continuous review for some value of B1= B, is the same as the safety stock under periodic review with a review period of 1 month and B1= B - 50. Determine that value of B. (d) (13 pts) Assume for this part of the problem that lead time for the item is random with the variance of the lead time equal to its mean (=.15 yr). Assuming continuous review, back order, and 32 = \$30 / \$ short, determine the cost savings of reducing the lead time variance to zero (assuming that it can be accomplished for free...). (cm 62 = 506) = “9”!!me (<1) (.25) 01 = \{.Is (gum) - 774.4 3. Gang : Q04?!) - (ION-D .005) as — 77‘1‘41-‘06655 ﬁK: -2095— Q L. .. S= -—X,_+K<l';_= (. 455000») +(3 0353(7?‘ ‘Qw (In) T85= =P7W+= 562 7.000 (loow)( I?) 5:431“: > CR: .2 015'] IE 251 Production and Inventory Control Exam 2 Fall 2005 (CA SSL=SSR+ LLf—ék 7-K g- R+L R+L FR“ “1454.085 (£20007 =9“. l K=l’4h[VP.:&W—} HIM“ [ 003% B} K,“ = 2,0”. LgDRv'Qv—“ﬁjﬂ-z 2,642. 002%"; (B— 403-3 (”my—Wm”; -- («a-«NEMTo‘ozsm-s'o‘ﬁ 549074. ,sz (.ooaa B) = (£33346: A (.00283 (B-S‘oﬂ 1M (.0014 \$3 =1557IM (.omMa-sm [.558 .0024 B = [.oo223(e-so) a a. name“ iguanénﬁdmthwdvnﬁ IE 251 Production and Inventory Control Exam 2 Fall 2005 .. 2- “z (4.) of: ._ a“ + 1: mm '-‘- (”51(1an + ((0m0\(.(5‘\= 15.40:); 01:34 ‘50 Mirna} :.¢S‘ .. LG _ . 15% m 4+3 '? m -( In B: D ( so]( wow) *JW‘ 4%Atuk iA-lunhaL mt = (.7 mumsowﬂo as) + 173;- (345030 o62:)(3o)(7) ‘-‘ 34414.10 «mauve : and m = (714. nummr =s\+—-‘ “’0" (774 LYomXBOYv) '3 773bf3 ..CMW5= BQ‘HL. 204131.53 =314H.47 IE 251 Production and Inventory Control 3... Periodic Review An inventory is controlled by a periodic review system where demand not satisﬁed directly from stock is lost. The following data set is relevant to the s-eciﬁcation of the s stem: “mum-"Emmi:- \$3/\$ short \$.3/\$/ r 3000/ r 2000/ r Demand follows a Normal distribution. a) (10 pts) Determine the order-up-to level, 5. b) (8 pts) Determine the corresponding expected total relevant cost per year. (0-3 <T.L=E(nc-L+émzmm =(-i\(£lwo\2+lsmxz(u\ = (.3 um" G‘ = Nil-0 L. 2. ' 4. Tim ‘ (-05l(&wv\Z-+ muol‘ = Issue) (TR—w: [23? - Rr ,- 15st») 5‘ ~. (u ~ 42—...» ; :91— - 1mm P” 7 RH'Bw (.os7l.3)+?> 3.91:? ‘ '°°‘H3 ’9 K 23’“ 5': (mqeco) + K “72+; =ﬂ§4\$u§ow§ 113.5%) 0.9.25") Diff< \ REG» ,. Us.) Ema ( s»: w[ a + «0&3 wnﬂcmm] + W = (.3305) ['fﬂi‘i’i Z .05 ...
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Prob_Inventory_Problems - IE 251 Production and Inventory...

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