OR-Notes

J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.


IMPERIAL COLLEGE PROJECT MANAGEMENT - SAMPLE EXAMINATION QUESTIONS

Below are sample examination questions, adapted from past papers to reflect the course as taught in Spring term 2000.

Sample compulsory questions (40% of the total mark)

Question

A project is specified by the following activities:

Activity Immediate      Duration
         Predecessor(s) (days)
A        -               11
B        A               9
C        A,B             11
D        A               19
E        B               7
F        C,D,E           15
G        E,F             4

Question

The table below defines the activities within a small project.

Activity  Immediate      Normal  Normal   Crash   Crash 
          Predecessor(s) Time    Cost     Time    Cost 
                         (days)  (£000ís) (days)  (£000ís)
A         -              6        24       4       34
B         -              4        12       3       22
C         A              5        20       3       28
D         A              7        29       4       47
E         B              6        26       5       34
F         B              8        34       5       52
G         C,E            10       27       6       47
H         D,F            9        34       7       48


Sample other questions (each 30% of the total mark)

Question

Consider the following project (all times are in days).

Activity   Immediate       Optimistic   Most           Pessimistic
           Predecessor(s)  Time         Likely Time    Time
A          -               1            2              3
B          -               2            3              4
C          -               1            3              5
D          A               1            2              3
E          B               1            1              1
F          B               1            2              3
G          B               2            3              4
H          C               3            5              7
I          C               1            3              5
J          A               2            3              4
K          D,E             2            3              4
L          F,K             2            4              6
M          G,H             3            4              5
N          I               1            3              5
O          J,L,M,N         1            2              3


Question

Consider the following network for a small maintenance project (all times are in days).

Activity   Immediate       Optimistic   Most           Pessimistic
           Predecessor(s)  Time         Likely Time    Time
A          -               2            3              4
B          -               5            6              7
C          -               5            6              7
D          A               3            4              5
E          A               2            3              4
F          C               3            4              5
G          C               8            10             16
H          B,E,F           5            6              7
I          B,E,F           7            11             15
J          B,E,F           2            3              4
K          G,J             3            4              5
L          D,H             7            11             15


Question

The Research and Development (R&D) division of a company has been developing four possible new product lines. The Project Manager must now make a decision as to which of these four products will actually be produced and at what levels. Therefore, he has to formulate a mathematical model to find the most profitable product mix.

The start-up cost associated with beginning the production of each product and the marginal net revenue from each unit produced are shown below.

                      Product 1    Product 2    Product 3    Product 4
Start-up cost (£)     40000        30000        60000        50000
Marginal revenue (£)  80           70           100          90

All product lines require the use of two specific resources R1 and R2. The requirements of each resource per unit produced are shown below. In either case, resource availability is limited to 7000 units.

              Units of Resource Required per Unit of Product Produced
              Product 1    Product 2    Product 3    Product 4
Resource R1   6            4            7            5
Resource R2   5            7            4            6

Only 800 units of product 1 could be sold whereas all units that could be produced of the other three products could be sold.

The following policy constraints have been imposed by management on the production levels of each product.

Formulate the problem of deciding which products to produce, and at what levels, as a linear integer program..