Linear programming can be used in construction management to solve many problems such as:
The problem to be solved using linear linear programming is to minimize or maximize some particular feature. This can be maximizing profit or minimizing loss.
Example 1) A ready-mix concrete firm has to supply
concrete to three different projects A, B, and C. The projects
require 200, 350, and 400 cubic meters of concrete in a
particular week.
The firm has three plants P1, P2, and P3
which can produce 250, 400 and 350 respectively.
The cost is different from each Pant to each project since
distance will vary.
It is required to determine the
quantity to be supplied from each plant to each project such
that cost to be incurred is a minimum.
Example 2) A Contractor is organizing the supply of ready-mix
concrete to four sites. He estimates that the total daily requirements of the
four sites amount to twenty four lorry loads and he finds three suppliers who
are able to meet this demand between them. The separate amounts available from
the suppliers are (in lorry loads) are shown below:
S1: 4; S2: 8; S3:12 and
the quantities needed for the four sites are A: 5 , B: 2, C:10, D:7
In the
price negotiation it was agreed that transport costs will be charged to the
contractor in proportion to mileage incurred. The distances involved are:
A | B | C | D | |
---|---|---|---|---|
S1 | 6 | 12 | 2 | 5 |
S2 | 18 | 21 | 13 | 12 |
S3 | 11 | 16 | 5 | 6 |
It is required for the contractor to determine the
minimum total distance to be traveled and corresponding supply
arrangement from each supplier to each site.
Example 3) Five managers who differ in ability and experience are to
be placed in charge of five projects which are different in type and value. The
suitability of each manager for each project is assessed on a numerical scale
with a maximum of twenty points. The results are shown below:
1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|
A | 18 | 16 | 11 | 19 | 5 |
B | 14 | 10 | 15 | 8 | 6 |
C | 9 | 13 | 8 | 8 | 6 |
D | 15 | 14 | 10 | 12 | 10 |
E | 11 | 11 | 14 | 10 | 8 |
To which project should each manager be assigned in order to obtain the
highest total points score for the firm? This is a typical assignment problem.
see [Example 1] provided with Our On-line Program which is based on the assignment matrix.
The problem here is to maximize output that is to allocate
construction managers such that the overall output for the all
construction projects is the best possible. This can be converted to a
minimization problem by considering the points below the maximum that
each construction manager's suitability was assessed for each
construction project. In other words, if the construction manager A was
assessed at 18 points out of twenty for project 1, the new scale to be
used for the minimization problem is (20-18) that is 2. The table below
represents the mark down figures for each construction manager in each
project.
1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|
A | 2 | 4 | 9 | 1 | 15 |
B | 6 | 10 | 15 | 12 | 14 |
C | 11 | 7 | 12 | 12 | 14 |
D | 5 | 6 | 10 | 8 | 10 |
E | 9 | 9 | 6 | 10 | 12 |
See [Example 2] provided with Our On-line Program
Notes:
The free layer of Our Assignment Module is now available for testing and evaluation. The full version will follow.
Reference: