运筹学实验课程试题(英文试题).docx

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1、运筹学试验课程试题(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1L109140016-2. The Otto Maddick Machine Tool Company produces two products, muffler bearings and torque amplifiers. One muffler beating requires 1/8 hour of assembly labor, 0.25 hours in the stamping department, and 9 square feet of sheet steel. Ea

2、ch torque amplifier requires 1/3 hour in both assembly and stamping and uses 6 square feet of sheet steel. Current weekly capacities in the two departments are 400 hours of assembly labor and 350 hours of stamping capacity. Sheet steel costs 15 cents per square foot. Muffler bearings can be sold for

3、 $8 each. Torque amplifiers can be sold for $7 each. Unused capacity in either departmentcannot be laid off or otherwise fruitfully used.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

4、 100 hours of overtime assembly labor can be scheduled at a cost of $5 per hour.ii. The sheet metal supplier only charges 12 cents per square foot for weekly usage in excess of 5000 square feet.Which of the above considerations could easily be incorporated in the LP model and how? If one or both can

5、not be easily incorporated, indicate how you might nevertheless solve the problem.试题2L109140026-4.The Aviston Electronics Company manufactures motors for toys and small appliances. The marketing department is predicting sales of 6,100 units of the Dynamonster motor in the next quarter. This is a new

6、 high and meeting this demand will test Aviston”s production capacities. A Dynamonster is assembled from three components: a shaft, base, and cage. It is clear that some of these components will have to be purchased from outside suppliers because of limited in-house capacity. The variable in-house p

7、roduction cost per unit is compared with the outside purchase cost in the following table.ComponentOutside CostInside CostShaft1.210.81Base2.502.30Cage1.951.45Aviston”s plant consists of three departments. The time requirements in hours of each component in each department if manufactured in-house a

8、re summarized in the following table. The hours 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 approp

9、riate LP.c) How many units of each component should be purchased outside?试题3L109140036-5. Buster Sod”s younger brother, Marky Dee, operates three ranches in Texas. The acreage and irrigation water available for the three farms are shown below:Water AvailableFarmAcreage(acre feet)14001500260020233300

10、900Three crops can be grown. However, the maximum acreage that can be grown of each crop is limited by the amount of appropriate harvesting equipment available. The three crops are described below:TotalWaterExpectedHarvestingCapacityRequirementsProfitCrop(in acres)(in acre-feet/acre)(in S/acre)Milo7

11、006400Cotton8004300Wheat3002100Any combination of crops may be grown on a farm.a) What are the decision variables?b) Formulate the LP.试题4L109140047-1. Certain types of facilities operate seven days each week and face the problem of allocating person power during the week as staffing requirements cha

12、nge as a function of the day of the week. This kind of problem is commonly encountered in public service and transportation organizations. Perhaps the most fundamental staffing problem involves the assignment of days off to full-time employees. In particular, it is regularly the case that each emplo

13、yee is entitled to two consecutive days off per week. If the number of employees required on each of the seven days of the week is given, then the problem is to find the minimum workforce size that will allow these demands to be met and then to determine the days off for the people in this workforce

14、.To be specific, let us study the problem faced by the Festus City Bus Company. The number of drivers required for each day of the week is as follows:MonTuesWedThursFriSatSun18161516191412How many drivers should be scheduled to start a five-day stint on each day of the week? Formulate this problem a

15、s a linear program. What is the optimal solution?试题5L109140057-3. A political organization, Uncommon Result, wants to make a mass mailing to solicit funds.It has identified six “audiences“ it wishes to reach. There are eight mailing lists it can purchase in order to get the names of the people in ea

16、ch audience. Each mailing list covers only a portion of the audiences. This coverage is indicated in the table below: Audiences MailingBusinessBrickListM.D.LL.D.D.D.S.ExecutiveLayersPlumbersCost1YNNYNN$50002NYYNNN$40003NYNNNY$60004YNNNNY$47505NNNYNY$55006NNYNNN$30007NYNNYN$57508YNNNYN$5250A “Y“ indi

17、cates the mailing list contains essentially all the names in the audience. An “N“ indicates that essentially no names in the audience are contained in the mailing list. The costs associated with purchasing and processing a mailing list are given in the far right column. No change in total costs is i

18、ncurred if an audience is contained in several mailing lists.Formulate a model that will minimize total costs while ensuring all audiences are reached.Which mailing lists should be purchased?试题6L109140067-5. Postal Optimality Analy(Dsiuse to Gene Moore). As part of a modernization effort, theU.S. Po

19、stal Service decided to improve the handling and distribution of bulk mail (second-, third- and fourth-class non-preferential) in the Chicago area. As part of this goal, a new processing facility was proposed for the Chicago area. One part of this proposal was development of a low-cost operational p

20、lan for the staffing of this facility. The plan would recognize the widely fluctuating hourly volume characteristic of such a facility and would suggest a staffing pattern or patterns that would accomplish the dual objectives of processing all mail received in a day”s time while having no idle time.

21、A bulk mail processing facility, as the name implies, performs the function of receiving, unpacking, 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 frequently design

22、ed as a single purpose structure and is typically located in or adjacent to the large metropolitan areas that produce this type of mail in significant volume. Although the trend in such facilities has been increased utilization of automated equipment (including highly sophisticatedhandling and sorti

23、ng devices), paid manpower continues to account for a substantial portion of total operating expense.Mail is received by the facility in mailbags and in containers. Both of which are shipped in trucks. It is also received in tied and wrapped packages, which are sent directly to the facility on railr

24、oad flatcars. Receipts of mail by the facility tend to be cyclical on a predictable basis throughout the 24-hour working day, resulting in the build-up of an “inventory“ of mail during busy hours, which must be processed during less busy hours. A policy decision to have “no idle time“ imposes a cons

25、traint on the optimal level of staffing.Once the facility is ready for operations, it will be necessary to implement an operating plan that includes staffing requirements. A number of assumptions regarding such a plan are necessary at the outset. Some of them are based upon existing Postal Service p

26、olicy; whereas, others evolve from functional constraints. These assumptions are as follows:i. Pieces of mail are homogeneous in terms 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 inputs

27、or 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 ends of the first, 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

28、.e., there may be no“inventory“ carryover from the third shift to the following day”s furst shift).vii. Labor rates, including shift differential, are given in the following table:DailyShiftS/HourRate1st (Midnight-8 A.M.)7.8062.402nd (8 A.M. -4 P.M).7.2057.603rd (4 P.M. -Midnight)7.6060.80viii. Hour

29、ly mail arrival is predictable and is given in the following table. Cumulative Mail Arrival 1st Shift2nd Shift3rd ShiftHourPiecesHourPiecesHourPieces010056,3500900242,5501700578,100020083,3001000245,0001800592,8000300147,0001100249,9001900597,7000400171,5001200259,7002023901,5000500188,6501300323,40

30、02100908,8500600193,5501400369,9502200928,4500700210,7001500421,4002300950,5000800220,5001600485,1002400974,000a) Formulate the appropriate LP under the no idle time requirement. Can you predict beforehand the number to staff on the first shift? Will there always be a feasible solution to this probl

31、em for arbitrary arrival patterns?b) Suppose we allow idle time to occur. What is the appropriate formulation? Do you expect this solution to incur higher cost because it has idle time?试题7L109140077-8. The St. Libory Quarry Company (SLQC) sells the rock that it quarries in four grades: limestone, ch

32、at, Redi-Mix-Grade, and coarse. A situation it regularly encounters is one in which it has large inventories of the grades it does not need and very little inventory in the grades needed at the moment. Large rocks removed from the earth are processed through a crusher to produce the four grades. For

33、 example, this week it appears the demand is for 50 tons of limestone, 60 tons of chat,70 tons of Redi-Mix and 30 tons of coarse. Its on-hand inventories for these same grades are respectively: 5, 40, 30 and 40 tons. For practical purposes, one can think of the crusher as having three operating mode

34、s: close, medium and coarse. SLQC has gathered some data and has concluded one ton of quarried rock gets convened into the following output grades according to the crusher setting as follows: Tons Output per Ton InputCrusherOperatingModeLimestoneChatRedi-MixCoarseOperatingCost/TonClose0.500.300.200.

35、00$8Medium0.200.400.300.10$5Coarse0.050.200.350.40$3SLQC would like to know how to operate its crusher, so as to bring inventories up to the equivalent of at least two weeks worth of demand. Provide whatever help your current circumstances permit.试题8L109140087-9. A certain optical instrument is bein

36、g designed to selectively provide radiation over the spectrum from about 3500 to 6400 Angstrom units. To cover this optical range, a range of chemicals must be incorporated into the design. Each chemical provides coverage of a certain range. A list of the available chemicals, the range each covers,

37、and its relative cost is provided below.Range Covered in AngstromsRelativeChemicalLower LimitUpper LimitCostPBD350036554PPO352039053PPF360036581PBO365040754PPD366039151POPOP390044496A-NPO391040952NASAL395041603AMINOB399540651BBO400041952D-STILB400042002D-POPOP421044052A-NOPON432044512D-ANTH435045002

38、4-METHYL-V4420540097-D-4-M445048003ESCULIN445045701NA-FLUOR520060009RHODAMINE-6G560062008RHODAMINE-B601064008ACRIDINE-RED601562502What subset of the available chemicals should be chosen to provide uninterrupted coverage from 3500 to 6400 Angstroms?试题9L109140097-12. Acie Knielson runs a small survey

39、research company out of a little office on the Northwest side. He has recently been contracted to do a telephone survey of the head-of-household of at least 220 households. The demographics of the survey must satisfy the following profile:Age of head-of-household18-2526-3536-60= 61Households in surv

40、ey (min):305010040When Acie makes a phone call, he knows only on average what kind of head-of-household he will find (if any). Acie can make either daytime or nighttime phone calls. Calls at night have a higher probability of success. However, they cost more because a higher wage must be paid. Being

41、 a surveyor, Acie has good statistics on all this. Specifically, from past experience, he knows he can expect:Percent of calls finding head-of-household of given typeCall Type18-2526-3536-6061 ormoreNot athomeCost/callDay2%2%8%15%73%$2.50Night4%14%28%18%36%$5.50In words, what are the decision variab

42、les? What are the constraints? What is your recommendation? How much do you estimate this project will cost Acie?试题10L109140107-14. Your agency provides telephone consultation to the public from 7 a.m. to 8 p.m., five days a week. The telephone load on your agency is heaviest in the months around Ap

43、ril 15 of each year. 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 forfour hours, is off for one hour, and then works for another four hours. A complicatio

44、n that has become more noteworthy in recent years is that an increasing fraction of the calls handled by your agency is from Spanish-speaking clients. Therefore, you must have some consultants who speak Spanish. You are able to hire two kinds of consultants: English-speaking only, and bilingual (i.e

45、., both English- and Spanish-speaking). A bilingual consultant can handle English and Spanish calls equally well. It should not be surprising that a bilingual consultant costs 1.1 times as much as an English-only consultant. You have collected some data on the call load by hour of the day and langua

46、ge type, measured in consultants required, for one of your more important offices. These data are summarized below:Hour of the day:7891011121234567English load:4456685445553Spanish load:5543234321344For example, during the hour from 10 a.m. to 1l a.m., you must have working at least three Spanish-speaking consultants plus at least six more who can speak English.How many consultants of each type would y