# Linear Programming In Construction

## Linear Programming In Construction

Linear Programming can be used in Construction Management to optimize the use of available resources, as well as many other optimization problems.
Linear Programming problems fall into two Categories:
• ## Transport Optimization Problems

This is concerned with scheduling of goods and services from various starting points (called sources) to a number of destinations.
• ## Mixture Optimization problems

The mixture problems are when resources have to be shared among two or more products or activities

### Linear Programming in Construction Management

Linear programming can be used in construction management to solve many problems such as:

• #### Location of new production plants, offices and warehouses

Note: (The assignment or HR module is covered by On-line Program)

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.

### Examples of use of linear programming in construction

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:

• When you "minimize output" of Example 2, you get same allocation as that obtained when you maximize output in example 1.
• The sum of the outputs in the two cases will equal to (5 being number of managers multiplied by 20 the maximum score that could be given to a construction manager at a specific project or location; i.e. 100)
• Though Manager 5 score at project 5 is the lowest but from an overall company performance perspective it is feasible to assign him this to this project!
• The best output at a single location will not necessarily contribute to the best overall output.

The free layer of Our Assignment Module is now available for testing and evaluation. The full version will follow.

Reference:

• Fellows R.et.al, Construction management in practice
• R. O and J. P, Management techniques applied to the construction industry