DCSN 200 Final, Spring 2003

ycSh 2 90 ip & y AMERICAN UNIVE School of Business OPIM 205: Computer Modeling for Management Spring 2002-2003 Final exam Version A: Date, June 7th, 2003; Time: 11:00am-1:00 pm. (Question 1, 25 marks) Oi] Company is planning to operate pipelines for transporting oil from its source in the Gulf to storage facilities in the mainland. Before reaching the storage facilities, the oil must pass through one or more pumping stations. The network below gives the maximum amount that can be transported in the pipes between sites in thousands of gallons per hour. Assuming a 24 hour per day operation, what is the maximum volume of oil that can be pumped from the source to the storage facility per day? [10] Acverding to the “Mas Flow Min Cut Theorem’. Phe max How alone the network Is the sum of max Hows along the ares of the mun. cut Phe min. cur alone the netvork ts the vreen cut above which has capacity 300 This can he found by idenutving all cuts ir wh re Sapoorihy MIternatis chy. one can tse the Fa Putkerson gig dM also as show on the petecark above Where are the bottlenecks in the network? Pat Patt capacity of the are irom PUMP STA {2] ayortho gs at tleneeks are en cub of Tie vel ark othe Ene VAP ACTED € (nother that can be Gansidered to be a Pottieneek ts the sf to PLUMP SE ANCL C. Assuming that the numbers on the arcs represent distance in miles, and a fire brigade station is located at the source site (GULF) with responsibility to provide emergency cover to all sites in the network. The chief officer wants to draw an emergency plan showing the list of minimum cost routes to reach each PUMP/STORAGE station from the main office located at the source site. List those routes and their associated distances. [15 This shortest path problem with source the GULP node Dihstras algorithm eenerates ihe shortest paths From the GULP nade to Hie rest of the nodes Node Tentative dist. d() Tentative Predecessor __| predecessor _ _ Pimp STA #1 1? GULF Pumo STA #2 15 GULF Ip STA #2 He GULF mp STA #4 [70 LS Puip STA #5 1 P Ho STORAGE 10 Pump STA #4 Fup STA HS According to the tree the shortest i fo PO Ow rump STA #i is are Pump STA #2 Pump 3 Pump STA #4 Pump STA #S STORAGE ans \ IS path from GU cily from GUL i$ through though Pump STA #4 Q i ty F ior a cistance is directly from GULF for a distance ctiy from GULF tor a aisiance is through Pump STA #3 and GULF Pump STA #2 and GULF for a aistance or of TZ of 15 of iG fora distance of 43 for Me Vir a (Question 2, 30 Marks) Consider the following information about activities for the design of a new laptop. The times are in weeks and the costs are in ‘000s. Activity | Immediate | Normal | Crashed | Variance | Normal | Crashed Predecessors | Duration | Duration Cost Cost A 4 2 2 10 60 B 6 3 3 20 110 Cc A 5 4 2 15 50 D B,C 4 3 1 25 70 |E_ B 3 ! \ 15 55 F E 5 1 2 25 65 G D,F 10 4 5 20 50 A. Determine the critical path and the expected completion time for this project using normal times? [8] 4 5 4 10 5 LS Nrario og eoetirr cretec pe GaP choeareyyy fi cred oat ft SUT ods ch GREY CHIN RS Or GRUPO 8) GE CONE ieNeStarly 0 PSCAP Gf bebo Ny tr ESB) GL ERIBy oes PN ERP Yy 4 bes PS) omanth bey bbe maxes Gb 8 bby 8 4 GS PSiR PEiBG ob bai 3 PSery bbcby 8 bbba Sb paeGa) omaxihbeby bbcbab oman; is d4) G4 bbttrp fd ge 24 Phe completion ting ab the proycer under normal tines } CMBy cain hSiDLbSibat ominiio; Go ESB? 4 bie \r bse r S ENEAD 4 LiaStartic mim ht Ad ESeBae mins loo tL bsiseame ft SlackiStamty LStStamy) fS¢Starmy Sachi Ad ESCA PNeAP bo Sigchti3) UNC) ESC) Ge Slacht@y) ESE} ESSEC) S StackiDy PSE) ESiDpy 3) Siacktha LSeer bSGor oe - 60 8 ce fat eget Nici NET} poi Pout - voka gy nen Sitay ft Loy SlackiG) ESeGE PSG la. i Vis critical math is Start i 1 { f Pho crHical Palin Stare eG Aa B. What is the simultaneous effect of a 1-week delay to activity C and a 1-week delay to activity D on the completion time of the projects? [2] Vhe slack of aetinnsa fois bo and thar af actin fdas f alse Phe combined effect of Phe slack of activin Cis land that af activity Dis } also. The combined eltect 6: delaying both aclivities O\ one tune UME is to delay fe propech OV i UATE C. What would be the net expected gain or loss if the design department will get a bonus of $30,000 if the project takes less than 22 weeks, $0 if the project is completed within 22 and 25 weeks, and a penalty of US$10,000 if it takes longer than 25 weeks? [8] ENpected net gain 34000" PEN 22) HE PCDT NTS PEGUEPON 2S) VoaapeN yoo variy ys eStartit osartrs cRal vardesy rbal ovue dry dbhab var de yeaa ii a4 ber Therefore. assutiog Mois Norma: witli sigdii 24 aii Vicia Nb 0 D4 ds COHN pRA RG Calis rere PE boage n GPEANEE Pe WE UT baxpected er gain ven Normdiste 2 shit) T4osqite bia deer bo mgcei-Normdist(28. 24 sqrtetiay Traen pip D732 Hep eieeds SN ERG Sb AN? 0 D. Can you suggest a minimum crash cost schedule in order to complete the projects within 16 weeks? [4] hin cases ave need ta shuse off we savecks from the Le ak yphenion v peechian wile Sotige THiat acusdhy Cr on The erliicai Path cai Be Fedtleed Tom Pty 4 Weeks tor a savings of © weeks Sifaidariv. acinities A and 8 can be seduced by 2 weeks cach without affecting the slackness of any of the activities. fora total savings of S weeks E. Write a linear programming model to find the optimal crash cost schedule, which determines the amount by which an activity is to be crashed to complete the project within 16 weeks. [8] Vsstume that the acu ities dtu ditions can be reduced ab a Constant Cost ieee Viti) be Tie vost of reduce activiiv bby Poweebk. Fo Start G Then NUStariy | NEENY Oth ety e428 NB CL dee coesy 3a Lae SHAG NtD} Nith) Nitin MIG) The LP to find the optimal crash ditrations for the activities tora praect compleion time of is ds li iber of weeks the proivet is to be reduced bs and be thy start ime of acuyas boi G Mlin ZS VOX 3G NB) FS VEC) AS YD) TSE ENC SNUG {cost function) YoXr 2 YB 2 Yer 48 NUDE LE Vea 2G Yuba te VEG & (iia ita rcduciiGis ave upper bowinds) (precedcnd “ rehitionships nist be respecied) (the project must be finished within £6 weeks} (Question 3, Marks 20) A Lebanese food company has decided to produce fruit yogurt for which the annual demand potential is an estimated 1.2 million boxes. A box contains six pieces of 250 grams each. The company has a choice of two machines to lease for producing the fruit yogurt. The annual lease costs of machines are $40,000 and $45,000 whereas the daily production capacities are 2750 and 11,000 boxes, respectively. The factory is open 365 days a year. The production setup cost is estimated at $4000, while the holding cost is estimated at $0.10 per box per year. The company estimates that it will earn $1.20 on each box produced. A. Determine which machine should be Jeased in order to minimize the annual total cost. [10] fer D be the annual demand The total annua ONEOFS COSL Ue SeTUPY COSES aNd Tle iedse Costs. PA LIVEN SeLD Cost Is Co. Steer and tae holdie cost per bos is ¢ sf Option | ber]. bethe lease cost of the machine the vearly machine capacs hs JPM SO Py SE boses wWitheh ix less than the vearly demand, |herefore. nbealfy. there is ne inventors tdealhy. there §s fe setup cost over the lone run ether. becaiise once the machine is setup. i meyer needs ta Ae setup vain Pho oaks ait bon bo pbs dec ceva Phe munimum annual tori sd hoon Option 2 bet is be the ease Cost ob ine machine [he vearfy machine capasiiy BO LEGG 308 0 40 fs Ao boxes whieh ts greater than the vearly demand Therefore. usine the optimal production lot sive (section & 3 heretore, using the optimal production lot sive (sect S eye SUITED | JOE LOO baci Led } 200 4 tit recon Phe annual minum dotalcospis dQ Tiei - PD Ra iy eyeae P. Svi saa 7H Cicely, Opin bis teas Costly SO HIRT 1 a Ue aaa Remark: Note that in pructes. one souk want to maximize s rather than MME 7e COs TE revenue Were COMSTAL HT OLA cases. Te TW OPyectbves would Nave been equivalent, But. iso happens that here they are not because the vearly capacity of machine [as tess than the vearly demand An analysis that is: nore World fees cammared nrodins not cost. This can he dane usine the wien earnings per boy B. What would be the decision (with regards to the order quantity and the associated annual cost) if the fruit yogurt boxes couldn’t be kept in storage for more than three weeks after production? [10] Option | da Unis cause. the analysts does not ¢ Makise The machine eapaerky is fess chain the demand by oF 1) Tb because the produc ing pertad Po should be equal to the COMSUUDPUOD durlmy period 4 yt ; i and that by i; KT) D since the s orders per vear wil be Pt is) Ps) dfenee. tne variable Cost ts PVeiy (R-Dp EO, 2 , © bea The problem is Vin ENV GE Pe DED OK-Di and 1, Note than PVET i OK-Da PC DCR TD: Without the upper bound on Ts. the : wor hay : Wate oat vepheiteis Se Sd Vera a a tL Vedas sy 1 iu BIereratel Vtrh G GPPeT a poo Bo ys af PET OY occurs: Qos . ai 1 } at * } i wey Vari aa Vat REN S emma : + Vuh iy =! days and EVEt p> S49 420 ° 4.000 oO. : 4 i herglore. factoring 1 the lease. the annual cost of this option is SUT LET ed Clearly. option PE with an annual cost of S40.000 is sal better. ve OF Note that the same remark as in the first question sib applies. In practice. Ho is more retevant tO compare maximum proints rather TAO MAME COSTS. In practice also. the machine in option 2 may be used to produce different hinds of products daring the idle days of the yogurt evele, So its lense cast could be shared among the different products on a time proportional basis. The analysis of that rol ; fut eT Heated though: Powe wsoi i perishable (in which ¢: : called Economie Lot S Propiem). (Question 4, Marks 25) Suppose that a cell phone operator offers customers a choice of three monthly leasing plans: Plan I: $30 per month with 20 free minutes and $.30 per minute for additional! minutes Plan II: $40 per month with 30 free minutes and $.20 per minute for additional minutes Plan III: $60 per month with 100 free minutes and $.10 per minute for additional minutes An AUB student wanted to lease a line. He/she estimates that the total amount of talk time can be approximated by the following distribution: Time Probability 30 minutes 30 60 minutes 40 100 minutes .20 150 minutes 10 A. Construct the payoff cost matrix of leasing the phone under the three plan. Usage 3G mins | tT sage oO mins. | Csage foe Wns sie |e ayes Jy Ss ols fp ve Jesby i | as B. Ifhe/she were an optimistic student, which plan would he/she chooses? [5] chy rege aay i re ai 4 tof totes the minin Sopris on , att Hpi PE GEFOUSS CaS POSS ae Sie SVOREG CMGI GEE WoT n i herton trot i teri mie CLROTIONL Ge aihit ier Across Wie MaMa Taal were Oblaned fhab choice Would correspond to Pian i aid the Usaue SGamins state or ature C. If he/she bases the leasing decision on the expected value criterion, which leasing plan would be chosen? [7] VEVREN EP TR SESE Le CELE TL Gap tet VePlan 2) 3 ote ed tor Desde i tod 4 EN ¢Plin 3) fi 8 oti OE fon TEOthy Fp eaSe Ot The jeast expected value is associated with Plan i Pherefore Phin boas chosen in this D. If the student were able to seek an advice from an expert consultant on the amount of perfect talk time, how much the student should pay the consultant for the advice. [8] EVPE PRPE PRES Swe dibedusy Computed t Riv n Pale SSy dtd be tse bob $3 Preretore PVPE tS and the pas neotere than