Question

Discuss how your organization could use an operations management linear programming application to solve a problem or improve a business process.

Answer 1

Definition: Linear programming is a simple technique where we depict complex relationships through linear functions and then find the optimum points.

In this definition what does "optimum points" mean? It simply means best result, no other way to make it more efficient. The maximum value we can get from that event. Now Linear Programming can be used in businesses to make it more efficient, reduce cost, reduce wastage, which in turn will increase its market value and goodwill. In the field of business and management,
linear programming is a method for solving complex problems in the two main areas of product mix (where the technique may be
used where it is difficult to decide just how much of each variable to use in order to satisfy certain criteria such as maximizing profits or minimizing costs, subject to certain constraints) and distribution of goods.

Now let us discuss some specific areas where Linear Programming can be used.

1. 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.

2. Production Management: 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.

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. Human Resource 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.

5. Marketing: 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.

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.

Formulating a linear Programming in business and management:

This is a simplified example will illustrates the way in which a problem relating to business is formulated.
A large sub-contractor machines special parts to order. For one order he has two machines, X and Y
available. Unfortunately, the machines perform more effectively on some jobs than others. Machine Y can do
10 units per hour on contracts from Alpha Ltd., 12 per hour on components from Beater & Co. and 26 per
hour on those from Chester Inc., while Machine X can produce 16, 9 and 10 units per hour respectively.
However, this is complicated by certain constraints which are:
Maximum number of units per month of units from Alpha, Beater and Chester are 6,500, 4,440 and 800 per
month respectively
the machines X and Y are restricted to working a maximum of 260 and 350 hours per month respectively.
The problem is to find how many hours should each machine work to maximise profits. This is answered by
plotting machine Y's hours against machine X's hours using mathematical models for the three suppliers and
then solving these using linear programming.

1. Define the variables
Let the number of hours for machine X be x
Let the number of hours for machine Y be y

2. Define the constraints
The model for Alpha can be found by using the above data as follows:
Machine X can produce 16 units per hour so if it works x hours the total is 16x hours.
Machine Y can produce 10 units per hour, so if it works y hours the total is 10y hours.

So the model for Alpha, which cannot exceed 6,500 is: 10y + 16x ≤ 6500
and the model for Beater which cannot exceed 4,400 is: 12y + 9x ≤ 4400.
and the model for Chester which cannot exceed 8,000 is: 26y + 10x ≤ 8000.

3. Define the objective function
A profit model is necessary in order to find the conditions for maximum profit i.e. the optimum number of
hours for X and for Y. In this case, the profits on each machine's output are: X = £40 per hour and Y = £24,
so the total profit is P = 40x + 24y.

Because of the existence of only two variables (x and y) this can be solved by plotting the models on a graph
for the three suppliers and moving the profit model until it reaches the highest point of intersection of the
three supplier lines.