Applications of Linear Programming

Applications of Linear Programming

Personnel Assignment Problem

Assume that we are given 'n' jobs, 'm' persons and the predictable productivity cij of ith person on the jth job. We need to search an assignment of person's xij ≥ 0 for all i and j, to 'n' jobs so that the average output of person assigned is highest, subject to the conditions


Where ai is the number of persons in personnel class i

            bj is the number of jobs in personnel class j

Transportation Problem

Assume that 'm' factories (sources) provide 'n' warehouses (destinations) with certain product. Factory Fi (i=1, 2 ... m) manufactures ai units and warehouse Wj (j=1, 2, 3 ... n) needs bj units. Assume that the cost of shipping from factory Fi to warehouse Wj is directly related to the amount shipped and that the unit cost is cij. Let the decision variables xij be the quantity shipped from factory Fi to warehouse Wj. The aim is to find out the number of units transported from factory Fi to warehouse Wj in order that the total transportation cost


The supply and demand must be fulfilled accurately.

Mathematically, this problem is to determine xij (i=1, 2 ... m; j=1, 2 ... n) so as to reduce the total transportation cost


Efficiency on Operation of system of Dams

In the above problem, we need to determine variations in water storage of dams which produce power in order to maximize the energy obtained from the whole system. The physical restrictions of storage appear as inequalities.


Optimum Estimation of Executive Compensation

The main aim here is to find out a consistent plan of executive compensation in an business concern. Job ranking, Salary and the amounts of each factor requisite on the ranked job level are taken into concern by the constraints of linear programming.

Agriculture Applications

Linear programming can be applied to agricultural planning for assigning the limited resources like water supply, labour and working capital etc, so as to maximize the net returns.

Military Applications

These applications include the problem of choosing an air weapon system for gurillas so as to keep them pinned down and at the same time minimize the amount of aviation gasoline which is used, a variation of transportation problem that maximize the net tonnage of bomb dropped on a set of targets and the problem of community protection against disaster to determine the number of defense units that should be utilized in the attack so as to provide the required level of protection at the least possible cost.

Production Management

Linear programming can be used in production management to determine product smoothing, product mix and assembly time-balancing.

Marketing Management

Linear programming assists in analyzing the efficiency of advertising campaign and time based on the accessible advertising media. It also assists in travelling salesman in determining the shortest route for his tour.

Manpower Management

Linear programming permits the personnel manager to examine personnel policy combinations in terms of their accurateness for maintaining a steady flow of people into and out of the firm.

Physical distribution

Linear programming finds the most cost-effective and efficient manner of establishing manufacturing plants and distribution centers for physical distribution.

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