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1、运筹学实验课程试题(09信管)要求：1、翻译；2、建模；3、利用集合建模；4、从外部输入输出数据。试题 1(L10914001)6-2.The Otto Maddick Machine Tool Company produces two products,muffler bearings andtorque amplifiers.One muffler beating requires 1/8 hour of assembly labor,0.25 hours in thestamping department,and 9 square feet of sheet steel.Each tor
2、que amplifier requires 1/3 hour inboth assembly and stamping and uses 6 square feet of sheet steel.Current weekly capacities in thetwo departments are 400 hours of assembly labor and 350 hours of stamping capacity.Sheet steelcosts 15 cents per square foot.Muffler bearings can be sold for$8 each.Torq
3、ue amplifiers can besold fbr$7 each.Unused capacity in either department cannot be laid off or otherwise fruitfullyused.a)Formulate the LP useful in maximizing the weekly profit contribution.b)It has just been discovered that two important considerations were not included.i.Up to 100 hours of overti
4、me assembly labor can be scheduled at a cost of$5 per hour.ii.The sheet metal supplier only charges 12 cents per square foot fbr weekly usage inexcess of 5000 square feet.Which of the above considerations could easily be incorporated in the LP model and how?Ifone or both cannot be easily incorporate
5、d,indicate how you might nevertheless solve the problem.试题2(L10914002)6-4.The Aviston Electronics Company manufactures motors fbr toys and small appliances.Themarketing department is predicting sales of 6,100 units of the Dynamonster motor in the nextquarter.This is a new high and meeting this deman
6、d will test Avistons production capacities.ADynamonster is assembled from three components:a shaft,base,and cage.It is clear that some ofthese components will have to be purchased from outside suppliers because of limited in-housecapacity.The variable in-house production cost per unit is compared wi
7、th the outside purchase costin the following table.ComponentOutside CostInside CostShaft1.210.81Base2.502.30Cage1.951.45Avistons plant consists of three departments.The time requirements in hours of eachcomponent in each department if manufactured in-house are summarized in the following table.The h
8、ours available for Dynamonster production are listed in the last row.ComponentCuttingDepartmentShapingDepartmentFabricationDepartmentShaft0.040.060.04Base0.080.020.05Cage0.070.090.06Capacity820820820a)What are the decision variables?b)Formulate the appropriate LP.c)How many units of each component s
9、hould be purchased outside?试题3(L10914003)6-5.Buster Sods younger brother,Marky Dee,operates three ranches in Texas.The acreageand irrigation water available for the three farms are shown below:Water AvailableFarmAcreage(acre feet)14001500260020003300900Three crops can be grown.However,the maximum ac
10、reage that can be grown of each crop islimited by the amount of appropriate harvesting equipment available.The three crops are describedbelow:TotalWaterExpectedHarvestingCapacityRequirementsProfitCrop(in acres)(in acre-feet/acre)(in S/acre)Milo 7006400Cotton 8004300Wheat 3002100Any combination of cr
11、ops may be grown on aa)What are the decision variables?b)Formulate the LP.farm.试题4(L10914004)7-1.Certain types of facilities operate seven days each week and face the problem ofallocating person power during the week as staffing requirements change as a function of the day ofthe week.This kind of pr
12、oblem is commonly encountered in public service and transportationorganizations.Perhaps the most fundamental staffing problem involves the assignment of days offto full-time employees.In particular,it is regularly the case that each employee is entitled to twoconsecutive days off per week.If the num
13、ber of employees required on each of the seven days ofthe week is given,then the problem is to find the minimum workforce size that will allow thesedemands to be met and then to determine the days off for the people in this workforce.To be specific,let us study the problem faced by the Festus City B
14、us Company.The number ofdrivers required fbr each day of the week is as follows:Mon Tues Wed Thurs Fri Sat Sun18 16 15 16 19 14 12How many drivers should be scheduled to start a five-day stint on each day of the week?Fonnulate this problem as a linear program.What is the optimal solution?试题5(L109140
15、05)7-3.A political organization,Uncommon Result,wants to make a mass mailing to solicit funds.It has identified six audiences0 it wishes to reach.There are eight mailing lists it can purchase inorder to get the names of the people in each audience.Each mailing list covers only a portion of theaudien
16、ces.This coverage is indicated in the table below:AudiencesMailingBusiness BrickListM.D.LL.D.D.D.S.ExecutiveLaversPlumbersCost1YNNYNN$50002NYYNNN$40003NYNNNY$60004YNNNNY$47505NNNYNY$55006NNYNNN$30007NYNNYN$57508YNNNYN$5250A HY indicates the mailing list contains essentially all the names in the audi
17、ence.An”N“indicates that essentially no names in the audience are contained in the mailing list.The costsassociated with purchasing and processing a mailing list are given in the far right column.Nochange in total costs is incurred if an audience is contained in several mailing lists.Formulate a mod
18、el that will minimize total costs while ensuring all audiences are reached.Which mailing lists should be purchased?试题6(L10914006)7-5.Postal Optimality Analysis(Due to Gene Moore).As part of a modernization effort,theU.S.Postal Service decided to improve the handling and distribution of bulk mail(sec
19、ond-,third-and fourth-class non-preferential)in the Chicago area.As part of this goal,a new processingfacility was proposed for the Chicago area.One part of this proposal was development of alow-cost operational plan for the staffing of this facility.The plan would recognize the widelyfluctuating ho
20、urly volume characteristic of such a facility and would suggest a staffing pattern orpatterns that would accomplish the dual objectives of processing all mail received in a day*s timewhile having no idle time.A bulk mail processing facility,as the name implies,performs the function of receiving,unpa
21、cking,weighing,sorting by destination,and shipping of mail designated as non-preferential,including second class(bulk rate),third class(parcel post),and fourth class(books).It is frequentlydesigned as a single purpose structure and is typically located in or adjacent to the largemetropolitan areas t
22、hat produce this type of mail in significant volume.Although the trend in suchfacilities has been increased utilization of automated equipment(including highly sophisticatedhandling and sorting devices),paid manpower continues to account fbr a substantial portion of totaloperating expense.Mail is re
23、ceived by the facility in mailbags and in containers.Both of which are shipped intrucks.It is also received in tied and wrapped packages,which are sent directly to the facility onrailroad flatcars.Receipts of mail by the facility tend to be cyclical on a predictable basisthroughout the 24-hour worki
24、ng day,resulting in the build-up of an inventory of mail during busyhours,which must be processed during less busy hours.A policy decision to have nno idle time”imposes a constraint on the optimal level of staffing.Once the facility is ready for operations,it will be necessary to implement an operat
25、ing planthat includes staffing requirements.A number of assumptions regarding such a plan are necessary atthe outset.Some of them are based upon existing Postal Service policy;whereas,others evolvefrom functional constraints.These assumptions are as follows:i.Pieces of mail are homogeneous in terms
26、of processing effort.ii.Each employee can process 1800 pieces per hour.iii.Only full shifts are worked(i.e.,it is impossible to introduce additional labor inputsor reduce existing labor inputs at times other than shift changes).iv.Shift changes occur at midnight,8:00 A.M.and 4:00 P.M.(i.e.,at the en
27、ds of thefirst,second and third shifts,respectively).v.All mail arrivals occur on the hour.vi.All mail must be processed the same day it is received(i.e.,there may be no*inventory carryover from the third shift to the following days fiirst shift).vii.Labor rates,including shift differential,are give
28、n in the following table:DailyShiftS/HourRate1 st(Midnight-8 A.M.)7.8062.402nd(8 A.M.-4 P.M).7.2057.603rd(4 P.M.-Midnight)7.6060.80viii.Hourly mail arrival is predictable and is given in the following table.Cumulative Mail Arrival1st Shift 2nd Shift 3rd ShiftHour Pieces Hour Pieces Hour Pieces010056
29、,3500900242,5501700578,100020083,3001000245,0001800592,8000300147,0001100249,9001900597,7000400171,5001200259,7002000901,5000500188,6501300323,4002100908,8500600193,5501400369,9502200928,4500700210,7001500421,4002300950,5000800220,5001600485,1002400974,000a)Formulate the appropriate LP under the no
30、idle time requirement.Can you predictbeforehand the number to staff on the first shift?Will there always be a feasible solution to thisproblem for arbitrary arrival patterns?b)Suppose we allow idle time to occur.What is the appropriate formulation?Do you expectthis solution to incur higher cost beca
31、use it has idle time?试题7(L10914007)7-8.The St.Libory Quarry Company(SLQC)sells the rock that it quarries in four grades:limestone,chat,Rcdi-Mix-Grade,and coarse.A situation it regularly encounters is one in which ithas large inventories of the grades it does not need and very little inventory in the
32、 grades needed atthe moment.Large rocks removed from the earth are processed through a crusher to produce thefour grades.For example,this week it appears the demand is fbr 50 tons of limestone,60 tons ofchat,70 tons of Redi-Mix and 30 tons of coarse.Its on-hand inventories fbr these same grades arer
33、espectively:5,40,30 and 40 tons.For practical purposes,one can think of the crusher as havingthree operating modes:close,medium and coarse.SLQC has gathered some data and hasconcluded one ton of quarried rock gets convened into the following output grades according to thecrusher setting as follows:T
34、ons Output per Ton InputCrusherRedi-MixCoarseOperatingCost/TonOperatingModeLimestoneChatClose0.500.300.200.00$8Medium0.200.400.300.10$5Coarse 0.05 0.20 0.35 0.40$3SLQC would like to know how to operate its crusher,so as to bring inventories up to theequivalent of at least two weeks worth of demand.P
35、rovide whatever help your currentcircumstances permit.试题8(L10914008)7-9.A certain optical instrument is being designed to selectively provide radiation over thespectrum from about 3500 to 6400 Angstrom units.To cover this optical range,a range ofchemicals must be incorporated into the design.Each ch
36、emical provides coverage of a certain range.A list of the available chemicals,the range each covers,and its relative cost is provided below.Range Covered in AngstromsRelativeChemicalLower LimitUpper LimitCostPBD350036554PPO352039053PPF360036581PBO365040754PPD366039151POPOP390044496A-NPO391040952NASA
37、L395041603AMINOB399540651BBO400041952D-STILB400042002D-POPOP421044052A-NOPON432044512D-ANTH4350450024-METHYL-V4420540097-D-4-M445048003ESCULIN445045701NA-FLUOR520060009RH0DAMINE-6G 560062008RHODAMINE-B 6010 6400 8ACRIDINE-RED 6015 6250 2What subset of the available chemicals should be chosen to prov
38、ide uninterrupted coveragefrom 3500 to 6400 Angstroms?试题9(L10914009)7-12.Acie Knielson runs a small survey research company out of a little office on theNorthwest side.He has recently been contracted to do a telephone survey of the head-ofhouseholdof at least 220 households.The demographics of the s
39、urvey must satisfy the following profile:Aee of headpf household 1825 2635 366。=61Households in survey(min):30 50 100 40When Acie makes a phone call,he knows only on average what kind of head-ofhousehold hewill find(if any).Acie can make either daytime or nighttime phone calls.Calls at night have ah
40、igher probability of success.However,they cost more because a higher wage must be paid.Beinga surveyor,Acie has good statistics on all this.Specifically,from past experience,he knows he canexpect:Call Type18-2526-3536-6061 ormoreNot athomeCost/callDay2%2%8%15%73%S2.50Night4%14%28%18%36%S5.50In words
41、,what are the decision variables?What are the constraints?What is yourrecommendation?How much do you estimate this project will cost Acie?试题 10(L10914010)7-14.Your agency provides telephone consultation to the public from 7 a.m.to 8 p.m.,fivedays a week.The telephone load on your agency is heaviest
42、in the months around April 15 of eachyear.You would like to set up staffing procedures for handling this load during these busy months.Each telephone consultant you hire starts work each day at either 7,8,9,10,or 11 a.m.,works fbrfour hours,is off fbr one hour,and then works for another four hours.A
43、 complication that hasbecome more noteworthy in recent years is that an increasing fraction of the calls handled by youragency is from Spanish-speaking clients.Therefore,you must have some consultants who speakSpanish.You are able to hire two kinds of consultants:English-speaking only,and bilingual(
44、i.e.,both English-and Spanish-speaking).A bilingual consultant can handle English and Spanish callsequally well.It should not be surprising that a bilingual consultant costs 1.1 times as much as anEnglish-only consultant.You have collected some data on the call load by hour of the day andlanguage ty
45、pe,measured in consultants required,fbr one of your more important offices.Thesedata are summarized below:Hour of the day:7 8 9 10 1112 1 2 3 4 5 6 7English load:4 4 5 6 6 8Spanish load:5 5 4 3 25 4 4 5 5 5 334 3 2 1 3 4 4For example,during the hour from 10 a.m.to 11 a.m.,you must have working at le
46、ast threeSpanish-speaking consultants plus at least six more who can speak English.How many consultants of each type would you start at each hour of the day?试题 11(L10914011)8-1.The Slick Oil Company is preparing to make next months pipeline shipment decisions.The Los Angeles terminal will require 20
47、0,000 barrels of oil.This oil can be supplied from eitherHouston or Casper,Wyoming.Houston can supply oil to L.A.at a transportation cost of$.25 perbarrel.Casper can supply L.A.at a transportation cost of$.28 per barrel.The St.Louis terminalwill require 120,000 barrels.St.Louis can be supplied from
48、Houston at a cost of$.18 per barreland from Casper at a cost of$.22 per barrel.The terminal at Fresh air,Indiana requires 230,000barrels.Oil can be shipped to Fresh air from Casper at a cost of$.21 per barrel,from Houston at acost of$.19 per barrel,and from Titusville,Pa.at a cost of$.17 per barrel.
49、Casper will have a totalof 250,000 barrels available to be shipped.Houston will have 350,000 barrels available to beshipped.Because of limited pipeline capacity,no more than 180,000 barrels can be shipped fromCasper to L.A.next month and no more than 150,000 barrels from Houston to L.A.The Newark,N.
50、J.terminal will require 190,000 barrels next month.It can be supplied only from Titusville at atransportation cost of$.14 per barrel.The Atlanta terminal will require 150,000 barrels next mouth.Atlanta can be supplied from Titusville at a transportation cost of$.16 per barrel or from Houstonat a cos