© University of London 2017UL17/0267 Page 1 of 6 D0~~MN3032_ZB_2016_d0This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDONMN3032 ZB BSc degrees and Diplomas for Graduates in Economics, Management, Financeand the Social Sciences, the Diplomas in Economics and Social SciencesManagement Science MethodsFriday, 12 May 2017: 10:00 to 13:00Candidates should answer FOUR of the following EIGHT questions. All questions carryequal marks.Graph paper is provided at the end of this question paper. If used, it must be detachedand fastened securely inside the answer book.A calculator may be used when answering questions on this paper and it must complyin all respects with the specification given with your Admission Notice. The make andtype of machine must be clearly stated on the front cover of the answer book.PLEASE TURN OVER© University of London 2017UL17/0267 Page 2 of 6 D0 1.(a) Discuss the similarities between Journey Making, Soft Systems Methodology andStrategic Choice.(b) Clearly explain the Journey Making methodology.(c) Apply Journey Making to any problem with which you are familiar.(10 marks)(9 marks)(6 marks) 2.Briefly explain each of the following topics from the viewpoint of OperationalResearch/Management Science:(a) MRP(b) Kendall’s notational system for classifying queueing systems(c) Value judgements in DEA(9 marks)(9 marks)(7 marks) 3. (a) The payoff table below shows for a company the final year end profits expected (£m)from four possible choices (A, B, C and D) with respect to three possible scenarios(S1 to S3 respectively) for the forthcoming year. S1S2S3A211-5B41314C5-513D1218-10 Here, for example, if the company makes choice D (and it can only choose one of A,B, C or D) and the scenario for the forthcoming year turns out to be S3 then it makesa loss of £10m.Copy the following table into your answer book and fill in the choice that should bemade under each criterion and the associated value. CriteriaChoiceAssociated valueOptimisticConservativeRegretEqually likely Based on your analysis which choice would you recommend the company makes?(10 marks)(b) What is the minimum value for the payoff associated with B and scenario S1 such thatunder the Regret criterion you choose B? Clearly explain the steps you take in arrivingat your answer (but without enumerating different values for this payoff).(11 marks)Question continues on next page© University of London 2017UL17/0267 Page 3 of 6 D0(c) For the situation as described in (a) above discuss the use you might make of sensitivityanalysis to generate further insight into the decision as to the choice the company shouldmake. (4 marks)4. (a) A company is using Markov theory to analyse consumers switching between fourdifferent brands of gaming console. An analysis of data has estimated that thetransition matrix shown below applies for the probability of switching between brands. To brandABCDFrom brandA1000B0100C0.120.270.160.45D0.190.140.070.60 Here, for example, there is a probability of 0.27 that a consumer switches from brandC to brand B. The current market shares for brands A,B,C,D are 10%, 20%, 25% and45% respectively.What is the long-run prediction for the market shares for each brand? (17 marks)(b) In a single server queueing system with an exponential service time distribution and aPoisson arrival distribution customers arrive at an (average) rate of 150 per hour. Theserver takes (on average) 20 seconds to serve a customer.Copy the following table into your answer book and fill in the corresponding numericvalues. FactorValue (four decimal places)Average number of customers inthe queueAverage time that a customerspends in the system (in minutes)Probability that there are threecustomers in the system (5 marks)A colleague has argued that values for the factors you have tabulated would be bettercalculated by using discrete-event simulation. Would you agree or not and why?(3 marks)© University of London 2017UL17/0267 Page 4 of 6 D05. A company is planning a small project and the following table gives the variousactivities in that project, as well as their associated completion times. ActivityCompletion time (days)A4B4C3D5E1F3G3 Here, for example, activity G takes 3 days to be completed.The immediate precedence relationships are: ActivityActivityAmust be finished beforeBcan startAmust be finished beforeGcan startBmust be finished beforeGcan startCmust be finished beforeDcan startCmust be finished beforeEcan startFmust be finished beforeAcan startFmust be finished beforeCcan start In addition two other conditions (X1 and X2) must apply• Condition X1: 4 days must elapse between the end of activity C and the start ofactivity B •Condition X2: 2 days must elapse between the end of activity A and the start ofactivity E(a) Draw the network diagram and calculate the overall project completion time. Statethe critical path(s).(9 marks) (b) Copy the following table into your answer book and fill in the latest start times andfloat (slack) times. ActivityLatest start time (days)Float (slack) time (days)ABCDEFG (6 marks)Question continues on next page© University of London 2017UL17/0267 Page 5 of 6 D0(c) A colleague has asked you to clearly explain to them what is meant by thefollowing terms in relation to project planning:• earliest start time• latest start time• float (slack) time• beta distribution• resource smoothingWhat would you say to them? (10 marks)6. A company makes three products (X, Y and Z) and has a number of options available as tohow these products can be produced on the three machines (A, B and C) it has available.These options are tabulated below. ProductOptionTime required (minutes)ABCXA→B→C1067C→B415A→C125YC→B→A987B→C142ZA→B→C1079C→A215 This table shows for each option the machines used (and their order), as well as theprocessing time in minutes required on each machine. For example the option B→C forproducing Y requires 14 minutes of processing on machine B followed by 2 minutes ofprocessing on machine C to produce one unit of product Y. The company can adopt morethan one option for production of any product.The company is planning its production for the next week. Available time in minutes onmachines A, B and C is 2400, 2350 and 2000 respectively. By moving workers betweenmachines it is possible to increase working time at any machine, but at the expense ofreducing working time at another machine. Each minute gained on one machine reducesthe time available on the machine from which it is taken by 2 minutes.Products X, Y and Z sell to customers for £95, £80 and £75 per unit (respectively).(a) Formulate the problem of deciding the number of units of each product to make as an integer program with linear constraints.(20 marks)(b) What might be the principal difficulty in implementing the numeric solution from thisinteger program? Illustrate this difficulty by example using the data provided in thequestion.(5 marks) © University of London 2017UL17/0267 Page 6 of 6 D07. (a) One methodological issue that arises in Operational Research work relates tooptimisation. What do you understand by optimisation within the context of OperationalResearch/Management Science? In particular your answer should make clear what theassumptions behind optimisation are. (17 marks)(b) Illustrate your answer by reference to TWO relevant problems of which you are aware.(8 marks)8. You are working for one company and have been approached by a rival company who wishyou to come and work for them. You have three objectives in choosing whether to stay withyour current company or not:• Objective 1 – salary – the larger the salary the better• Objective 2 – earnings potential – the more you can earn over time the better• Objective 3 – vacation time – the more vacation time you are allowed the betterYour pairwise comparison matrix for these objectives is: Objective123Objective11452–133––1 Here, for example, your judgement as to objective 1 as compared with objective 3 is rated5.(a) Are the judgements made with respect to these objectives reasonably consistent or not(assume the value of RI for n=3 is 0.58)? (13 marks)Currently your judgement (pairwise comparison matrices) of the relative worth of yourcurrent employer (company A) as compared to your potential new employer (company B)with respect to the above three objectives is: ABObjective 1A17B–1 ABObjective 2A1–B51 ABObjective 3A13B–1 (b) Assuming that the judgements made with respect to the three objectives are reasonably consistent which company should you choose to work for?(5 marks)(c) Discuss how you might apply MAUA/MAVA to the situation considered above relating tochoosing which company to work for.END OF PAPER(7 marks)

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