Question 1

(a)      The table below shows the process times on two machines in a flow shop.

(i)       Apply Johnson’s  rule to schedule the jobs so that the  makespan time  is minimised. What is the makespan?      [20%]

(ii)      Draw up a table showing the time in, time out, and processing time for both machines for each job for the optimal schedule you have derived.         [30%]

(b)      Suppose that there is a third operation which is needed in the process so that the table becomes;

Can Johnson’s rule be applied to the problem of finding the optimal order for the jobs?

Give a full explanation of the reasons for your answer and explain the process of applying the rule to the 3 machine problem. [50%]

Question 2

(a)      Formulate, but do not solve, the following problem as a Linear Programme and

construct the first tableau needed to solve the linear programme using the Simplex method.  (Note that you do not need to go further than the first tableau.)

An investor has up to £250,000 to invest in three types of investments. Type A pays 8% annually and has a risk factor of 0. Type B pays 10% annually and has a risk factor of 0.06. Type C pays 14% annually and has a risk factor of 0.10.

To have a well-balanced portfolio, the investor imposes the following conditions. The average risk factor should be no greater than 0.05. Moreover, at least one-fourth of the total portfolio is to be allocated to type A investments and at least one-fourth of the portfolio is to be allocated to type B investments. How much should be allocated to each type of investment to obtain a maximum return? [60%]

(b)      Find  the  optimal  solution  to  the following  linear  programming  problem  using  a

graphical method.  Graph paper is provided at the end of this paper.

Maximize      4x + 3y

Subject to

2x+3y≥6

3x-2y≤9

x+5y≤20

x, y >=0                                                                                        [40%]

Question 3

(a)      Identify an inspection process to improve the management of maintenance in an organisation using non-contact measurement technology. [25%]

(b)      Compare and contrast the main characteristics, strengths and weaknesses of using Qualitative and Quantitative Methods in the management of maintenance. [75%]

Question 4

(a)      What are the main characteristics of the Scientific Method? (eg rigour etc.)      [50%]

(b)      What is meant by a solution to a problem which is “parsimonious”?  Give a simple example.    [10%]

(c)      Outline  some obstacles to  conducting scientific  research  and  data  collection  in management.                  [40%]