Abstract:
The effective and optimum decision making in modern business environment is critical due
to the competition and complexity. When considering a manufacturing organization, the most
critical decision would be to identify the product mix that will maximize the profit while
maintaining the required quality standards. This study is focused on optimizing the profit of a
concrete yard of a government corporation in Sri Lanka using linear programming.
The organization considered produces Beams, Poles, Pipes and Bridge components
and has available expenditure, skilled-labour and demand as the main constraints. Per unit
selling price or non-labour costs do not vary based on the level of production. However the
labour cost varies significantly according to the type of labour (skilled or non-skilled)
allocated to different products. Therefore labour allocation becomes a sub-problem in the
study. The data from March 2014 to July 2014 (150 days) was collected for the study.
This study reveals that the organization is capable of improving its profits if they
produce at the optimum level. In most of the months that have been considered, the total
profits can be improved over Rs.150,000 based on optimum production. The criticality of
labour allocation has been proven by the results of the study. Because based on the optimum
labour allocation, the organization is capable of improving its profits even if they are
committed for a product mix other than the optimum product mix. This can be done by
minimizing the total labour costs. Based on the optimum labour allocation for the actual
production the profit can be improved over Rs.75,000 for the considered months. The
sensitivity analysis indicates the sensitivity of the coefficients of the objective function and
the constraints. The sensitivity of the variables as well as constraints vary based on
considering time duration. The constraints have positive as well as negative shadow prices.
This model can be used to identify the future product mixes that will maximize the
profit while maintaining the quality standards based on the resource availability. Even if the
coefficients of the variables subjected to change, still the model can be used with little
amendments to improve the profits.
