exam2last - Name ‘24’ Exam 2 — ISyE 4803 Spring 2006...

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Unformatted text preview: Name ‘24’ Exam 2 — ISyE 4803 Spring 2006 M“ ‘ +1” Show all work for partial credit. 1. (20 points) Given the following flight network with four airports: Writethe standard linear prograni to maximize tevenue where the number. of tickets for flight i. Assume that the plane for A-B holds 200 passengers, the plane for B-C holds 802'and the plane for B—D holds 150. The demand data is as follows: ' 443/ ~‘vggr‘ny—rr‘wl.,.-.M~.W,..~~._w-r 5- . 6::“294 2. (10 points) For problem 1, suppose the solution of the‘dual gives the following values for the dual variables: for A-B=$300, B-C=$190, and B-D=$O. What classes should remain open and why? 3. (20 points) For problem 1, suppose the demand is normally distributed (with means and standard deviation given). For the flight from A—C, use the expected .. marginal seat revenue (EMSR) heuristic to compute the protection levels; . ~ M 6 l> c 9 E? w gm (A095 I” 2- L\IL- .1 - — 2 2 fl = zXYVtfilv’l éw’<‘>"7’o s 7’ a 2 ’- m m «.,.w~““,w~.,.,...m,_1 .mirwww .‘wmw-u---—~—«gs-aurrv-w-w—q‘y:- ; wwr— - < ~ ~ , * ~~ ~—w~~ m'r1;--v~'~.:~ >~ ~rv~7wx~~~ A: s ‘w -. v . - v_ 7 ~ ~ ‘_ — - r 4. (12 points) Suppose we find the initial booking limits for a flight with capacity of 50 to be 50 for class 1, 40 for class 2, and 10 for class 3. In addition, the requests for tickets come in as follows: 10 tickets in class 2, 5 tickets in class 3, 30 tickets for class 1, and 15 tickets for class 2. Fill out the following table. Use the method where booking limits are updated first (i.e., the first method in the homework). ‘59 “Wm la 40 5‘0 .- .- 5. (10 points) Why is the so-called “winner’s curse” more severe in first-price sealed bid auctions than in English auctions? We? NW“ ‘a 7””? "t labs »% IN)” 2 Vion 7t» wa/extht/T "fl em,qu Oiyflw/{7u7-L16V‘h7 W‘I‘a ng'lA OW/ {uw/ (mt/Wm W .zm7z‘0/mx7ly‘l/5 Vs revue/o In 6/71.”, 6. (10 points) Find the Nash equilibria (if any) from the following payoff matrix: ‘ — - As ' Mayan .‘ 9, -‘ DD 00 00 N —-.v .....--...~.._«1‘. wt...”,-......;...‘—‘..,.._..‘-.-—~’M.~.«.m»~. -. .-- u. .. »- t N. _._,..T- . W: ‘3, yaw—flywqw—rgmm ~..—.__V....W,~.‘.._.....,_,, ...,, g. j. . 7. (18 points) You are in an auction with 5 bidders. The private valuations of the bidders are uniformly distributed on [300,400], and your valuation is $369. Answer the following: a. If the auction were an English auction and the other valuations were $310, $338, $353, and $363 and the minimum bid increment were $1, what would the outcome be? b. Suppose instead the auction were a Dutch auction with the same information (though you don’t know the valuations of the other bidders). What should your bid be, and what would the outcome be in this case? 0. Are the auctions in a and b efficient? Why or why nOt? J) T 0/on Gena—k Ova” (AW 0/ (“W sizes“ 5/ 9' 2w ‘7) Km la, (7:) KW 17 \yc 3001’ f 3 135‘” ei’W/S If WSV‘J W'A J {'1 Dim/5 f wDW’; ' o) —’ ( {S 6%7; 4/7 S.:, ((2 I [WW WV} \/.,\\/43 W WC} ng' Tsfl_+ 9%»: ’V’ / MM/vk/ gtné/ aIIIIIIII-IIIIIIIIIIIIIIIIIIIIIIIIIIII- ...L Soc. Soc. 5°C.. 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(20 points) Given the following flight network with four airports: " the: standard line-af- program to InaXinlize rei/ende where 5a,. is the number Vof ' tickets for flight i. Assume that the plane for A-B holds 150 passengers, the plane for B-C holds 70, and the plane for B-D holds l6Q.__Ihe_demand data is as follows: A Standard Fare mand Deviation ><f+ x2 +7zg+ xi1 w; “50 fixza‘X's-TXL} +XE+X1 Flo )(Sv‘i’ é lb? Xs “l3 5(5 570 ' 4 'sllslg XV“ g 7 \L‘ x .5 ~10 5 ’0 ‘ x3, ":4 7 ‘ )(Ltfi Kg {‘17, 2. (10 points) For problem 1, suppose the solution of the dual gives the following values for the dual variables: for A-B=$300, B-C=$190, and B—D=$100. What classes should remain open and why? z 99 9 C A ~—-‘ 5 \ 0 O \ D $~:’L4 fwtr —;(/’S 0+ l‘W} e) l/lf—jh 3. (20 points) For problem 1, suppose the demand is normally distributed (with means and standard deviation given). For the flight from A-C, use the expected . marginal seat revenue (EMSR) heuristic to compute the protection levels, - M 6 f’ g lg lg- 0‘90 1 3°“ 7’0 £90 3 «we 7,; 12/9 ‘(ls/ class L “W W}: “)7 L i s %g 13/qu \ _ \80 (aeyoW‘f) 7-9 Sim“ «A; :3 ‘°)5‘°‘}9) valet—Mt. w. “a. 3:... NWT-“"1" qua-H“? W- .(_\T......_,.fi_...~. -vvw..~w‘.m._ w— an... » "r. w..- ...: V ,. . 4. (12 points) Suppose we find the initial booking limits for a flight with capacity of 60 to be 60 for class 1, 45 for class 2, and 12 for class 3. In addition, the requests for tickets come in as follows: 15 tickets in class 2, 5 tickets in class 3, 30 tickets for class 1, and 15 tickets for class 2. Fill out the following table. Use the method where booking limits are updated first (i.e., the first metho in the homework). 0 4S \7- '42 (go Asset?( In) El 15 tickets in class 2 fl ‘15 \l 5 tickets in class 3 N a 30 tickets in class 1 15 tickets in class 2 5. (10 points) Why is the so-called “winner’s curse” more severe in first-price sealed . bid auctions than in English auctions? Max/US! don}, Wc aww] Diva/we ‘Liyoe/i‘ am M W Wee/Ms ;- m); i} Acme OVA») {we F643“ +0 OW/OSlTI/V‘L?(/ W Vc\\1( / [A “L9, bf lavif’ A 6. (10 points) Find the Nash equilibria (if any) from the following payoff matrix: "3-,....wswwwwwe“,.mw..yy.n..y~wwmmmwwwww.7...— -—_v . , ~ . n. ,m.v.mu.~_.,.—w«»-v;~.~~--~ ~'.1' ~ " ‘ - ' ‘ " r " 7 ' y-‘v\.~r..__....,m—~W._ .7—........w,r.,.‘.‘.._.\......_.h.-,,v.‘fi......m_,,.._,VH.-.,. ,- . r 7. (18 points) You are in an auction with 5 bidders. The private valuations of the bidders are uniformly distributed on [300,400], and your valuation is $369. Answer the following: a. If the auction were an English auction and the other valuations ‘were $310, $338, $353,, and $363 and the minimum bid increment were $1, 'what would the outcome be? b. 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exam2last - Name ‘24’ Exam 2 — ISyE 4803 Spring 2006...

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