MODULE CODE : MN2032
MODULE TITLE : MANAGEMENT SCIENCE METHODS
DATE OF EXAM : 6 March 2024
1. You are working for a company whose Chief Executive Officer (CEO) is concerned that the company is making inconsistent decisions. She has examined her own judgement as to three objectives for choosing certain courses of actions and has produced the pairwise comparison matrix for these objectives:
Here, for example, her judgement as to objective 1 as compared with objective 3 is rated 7.
(a) The CEO has asked you to decide whether the judgements she has made with respect to these objectives are reasonably consistent or not (assume the value of RI for n=3 is 0.58). (14 marks)
(b) Currently the CEO judgement (pairwise comparison matrices) of the relative worth of two possible courses of action (Aand B) for the company with respect to the above three objectives is:
Assuming that the judgements made with respect to the three objectives are reasonably consistent which course of action (A orB) should the CEO chose? (5 marks)
(c) The CEO has heard at a recent conference she attended that the procedure you applied in deciding your answer to part (a) above involves an approximation. Is this true or not and (if so) clearly indicate the key numeric values in your answer that are an approximation. (6 marks)
2. (a) Clearly explain the Strategic Choice methodology, in particular with regard
to the role played by UE, UV and UR. (13 marks)
(b) Apply the methodology to two problems with which you are familiar. (12 marks)
Your answer to this question should be limited to at most 8 pages.
3. Briefly explain each of the following topics from the viewpoint of Operational Research/Management Science:
(a) SCM (9 marks)
(b) PERT (9 marks)
(c) Utilities, with reference to a risk-seeking decision maker (7 marks)
Your answer to this question should be limited to 2 pages for each of the three parts (so at most 6 pages in total).
4. A company requires a supplier to deliver to it 600 units per week of a component that is needed for production. Each component that the company purchases from its supplier costs £51. The company estimate that their internal costs associated with making an order to the supplier are £77 and that the storage costs associated with keeping one component in stock before it is used in production are £2.20 per month. The current interest rate is 6% per year and the company operates 52 weeks a year.
(a) If the company currently orders every four weeks from its supplier what is the associated total cost per week? (7 marks)
(b) Is there a better order policy that the company can adopt - if so what is it and what would be the associated cost per week? (8 marks)
(c) If the supplier is prepared to give the company a 10% reduction in the cost of a component provided that there is at least six weeks between successive orders then what order policy would you now recommend and what would be the associated cost per week? (10 marks)
5. A company is planning a small project and the following table gives the various activities in that project, as well as their associated completion times.
Here, for example, activity F takes 10 days to be completed.
The immediate precedence relationships are:
In addition, 4 days must elapse between the end of activity D and the start of activity C.
(a) Draw the network diagram and calculate the overall project completion time. State the critical path(s). (12 marks)
(b) Copy the following table and fill in the latest start times and float (slack) times.
(4 marks)
(c) If the completion time for activity C increases to become 12 days whilst simultaneously the completion time for activity E decreases to become 6 days what effect would this have on the overall project completion time?
Copy the following table and fill in the new latest start times and new float (slack) times.
(9 marks)
6. A company is using Markov theory to analyse teenagers switching between four different smartphone applications (“apps”) for instant messaging. These instant messaging apps enable teenagers to conduct group chats, both text and video, as well as exchange pictures.
Teenagers only switch the app they use once every six months (on average). An analysis of data has estimated that the transition matrix shown below applies for the probability of switching every six months between these apps.
Here, for example, there is a probability of 0.13 that a teenager switches from app 2 to app 1. The current market share for these apps is 10%, 20%, 25% and 45% for apps 1,2,3,4 respectively.
(a) Copy the following table and fill in the long-run prediction for the market shares for these apps. (18 marks)
(b) A colleague has remarked that she is only slightly familiar with the approach you have used to calculate these long-run predictions and would like you to list for her the advantages and disadvantages of Markov theory. What would you say to her? (7 marks)
7. A company has formulated a linear program relating to the quantities of two products (X and Y) to produce. Each unit of product X gives a contribution to total profit of £2, each unit of product Y gives a contribution to total profit of £4. Production of the two products is constrained by available working time on two machines (A and B). In the forthcoming week there are 37 hours available on machine A, 30 hours available on machine B. In addition there is one constraint that arises from other considerations (constraint C1, as seen below). The linear program that the company have formulated is:
(a) Solve this linear program graphically using an iso-cost/iso-profit line. The vertices (corners) of the feasible region should be clearly labelled A, B, C etc.
Copy the tables shown below and fill in the values required. (19 marks)
(b) Discuss three areas where large linear programs arise. (6 marks)
8. A company operates as a “pop-up” business whereby it opens a branch for just one full financial year and then closes. This strategy, it believes, enables it to generate new interest in the products it sells by exposing them to customers in busy city centres, and then after closure this business transforms into online sales. In the last full financial year the company operated six branches (Ato F below). The data they have collected for these branches over the last full financial year is shown below.
For example in the last full financial year branch E generated a profit of £32200 and employed 12.4 people (on average over the year). The non-employee cost for branch E,i.e. the cost of operating the branch excluding the cost of employees, was £10300.
(a) Apply data envelopment analysis (DEA) to compare the relative performance of these branches. Copy the table shown below and fill in the efficiencies and reference sets (where appropriate). (14 marks)
(b) Formulate the linear program associated with determining the efficiency of branch A. (6 marks)
(c) A new chief executive officer for the company has been appointed who has some familiarity with Operational Research/Management Science. She wishes to gain further insight into the use of DEA and has asked you to outline the steps associated with starting a DEA study. What would you say to her? (5 marks)