APPLICATIONS OF LINEAR PROGRAMMING FOR SOLVING BUSINESS PROBLEMS
A mathematical optimization model consists of an
objective function and a set of constraints in the form of a system of
equations or inequalities. Optimization models are used extensively in almost
all areas of decision-making, such as engineering design and financial
portfolio selection. This site presents a focused and structured process for
optimization problem formulation, design of optimal strategy, and
quality-control tools that include validation, verification, and post-solution
activities.
Applications of linear programming for solving business
problems;
1. Production Management: LP is applied
for determining the optimal allocation of such resources as materials,
machines, manpower, etc. by a firm. It is used to determine the optimal
product- mix of the firm to maximize its revenue. It is also used for product
smoothing and assembly line balancing.
2. Personnel Management: LP technique
enables the personnel manager to solve problems relating to recruitment,
selection, training, and deployment of manpower to different departments of the
firm. It is also used to determine the minimum number of employees required in
various shifts to meet production schedule within a time schedule.
3. Inventory Management: A firm is faced with the
problem of inventory management of raw materials and finished products. The
objective function in inventory management is to minimize inventory cost and
the constraints are space and demand for the product. LP technique is used to
solve this problem.
4. Marketing Management: LP technique enables the
marketing manager in analyzing the audience coverage of advertising based on
the available media, given the advertising budget as the constraint. It also
helps the sales executive of a firm in finding the shortest route for his tour.
With its use, the marketing manager determines the optimal distribution
schedule for transporting the product from different warehouses to various
market locations in such a manner that the total transport cost is the minimum.
5. Financial Management: The financial manager of a
firm, mutual fund, insurance company, bank, etc. uses the LP technique for the
selection of investment portfolio of shares, bonds, etc. so as to maximize
return on investment.
6. Blending Problem: LP technique is also applicable
to blending problem when a final product is produced by mixing a variety of raw
materials. The blending problems arise in animal feed, diet problems, petroleum
products, chemical products, etc. In all such cases, with raw materials and
other inputs as constraints, the objective function is to minimize the cost of
final product.
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