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## Applications of Linear Programming

Applications of Linear Programming

Personnel Assignment ProblemAssume that we are given 'n' jobs, 'm' persons and the predictable productivity c

_{ij}of i^{th}person on the j^{th}job. We need to search an assignment of person's x_{ij}≥ 0 for all i and j, to 'n' jobs so that the average output of person assigned is highest, subject to the conditionsWhere a

_{i}is the number of persons in personnel class ib

_{j}is the number of jobs in personnel class jTransportation ProblemAssume that 'm' factories (sources) provide 'n' warehouses (destinations) with certain product. Factory F

_{i}(i=1, 2 ... m) manufactures a_{i}units and warehouse W_{j}(j=1, 2, 3 ... n) needs b_{j}units. Assume that the cost of shipping from factory F_{i}to warehouse W_{j}is directly related to the amount shipped and that the unit cost is c_{ij}. Let the decision variables x_{ij}be the quantity shipped from factory F_{i}to warehouse W_{j}. The aim is to find out the number of units transported from factory F_{i}to warehouse W_{j }in order that the total transportation costThe supply and demand must be fulfilled accurately.

Mathematically, this problem is to determine x

_{ij}(i=1, 2 ... m; j=1, 2 ... n) so as to reduce the total transportation costEfficiency on Operation of system of DamsIn 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 CompensationThe 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 ApplicationsLinear 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 ApplicationsThese 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 ManagementLinear programming can be used in production management to determine product smoothing, product mix and assembly time-balancing.

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

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