# Project of linear programming

P In general we use the following two methods for the solution if a linear programming problem.

### Linear programming applications

This means, more than one optimum solution is possible. The sequence of activities to meet the final objective of constructing the road should be scheduled in a realistic way to avoid chances of scheduling failures. Time-cost optimization of construction projects with generalized activity constraints. Optimal solution An optimal solution of a linear programming problem is the set of real values of the decision variables which satisfy the constraints including the non-negativity conditions, if any and at the same time optimize the objective function. Yamin, R. Now, to setup the objective function. General form of L. Depending on the cause, a construction company may be required to accept the extra cost associated with deadline issues, and sometimes the customer may wish to pay extra to have a job finished earlier. The firm is planning to utilize this spare capacity by increasing the production of the remaining one or more of the existing three products. Charnce, who also did some important theoretical work, and W. You look for running an activity in its normal time or the crash time.

The problem is that the project is already fast-tracked so the schedule needs to be crashed. P Standard form of L.

## Linear programming examples in project management

The proposed exact method provides the optimal solution by considering all the possible time-cost alternatives for each activity thus minimizing the project cost. Problem of the linear- programming type had been formulated and solved before the pioneering work of Dantzig. The total crash time needed can be adjusted in both models. The objective here is to minimize the total production and inventory cost. Simplex method : This is the most powerful tool of the linear programming as any problem can be solved by this method. All constraints are expressed in the function of equality form except the restrictions. Zhou, J. The project is to construct a road scheduled in two phases with a total of days. In such a case, if you justify the costs involved, you can consider further crashing the activities of the new critical path too. Wood worked on allocating problems for the United States Air Force. Big-M-method and Two phase method. The procedure is straight forward and requires only time and patience to execute manually. These resources may be capital, production capacity, manpower, time etc.

Table-4 shows different additional cost associated with the crashing times to give an idea of crash-cost to make a proper schedule management decision. However, one of the most important aspects of the project you need to consider is if crashing an activity reduces the overall time of the project.

In such cases, one method is to design its dual which invariably will have less number of constraints. To formulate a linear programming problem and solve in simplex method and dual problem.

Determination of the solution space that defines all feasible solutions of the model.

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