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Firm

A firm is a business organisation, such as a corporation, partnership or sole proprietorship, that sells goods or services to customers to earn profit, that will increase the wealth of it's owners and grow the business.
The owners and operators of a firm have as one of their main objectives the receipt or generation of a financial return in exchange for their services.
While most firms have just one location, a single firm can consist of one or more establishments, as long as they fall under the same ownership.

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The Intuitive Lowest Cost Method

The Intuitive Lowest Cost Method Or The Minimum Cell Cost Method

The Intuitive Lowest Cost Method is a cost based approach to finding an initial solution to a transportation problem.
It makes allocations starting with the lowest shipping costs and moving in ascending order to satisfy the demands and supplies of all sources and destinations.

This straightforward approach uses the following steps.
Identify the cell with the lowest cost.Allocate as many units as possible to that cell without exceeding the supply or demand.Then cross out the row or column or both that is exhausted by the above assignment.Move on to the next lowest cost cell and allocate the remaining units.Repeat the above steps as long as all the demands and supplies are not satisfied. 
When we use the Intuitive Approach to the Bengal Plumbing problem, we obtain the solution as below.

Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F Warehouse G Factory Capacity Plant A Rs.50
Rs.40 100 Rs.30 100 Plant…

Vogel's Approximation Method (VAM)

The Vogel's Approximation Method

In addition to the North West Corner and Intuitive Lowest Cost Methods for setting an initial solution to transportation problems, we can use another important technique - Vogel's Approximation Method (VAM).
Though VAM is not quite as simple as Northwest Corner approach, but it facilitates a very good initial solution, one that is often the optimal solution.
Vogel's Approximation Method tackles the problem of finding a good initial solution by taking into account the costs associated with each alternative route, which is something that Northwest Corner Rule did not do.

To apply VAM, we must first compute for each row and column the penalty faced if the second best route is selected instead of the least cost route.

To illustrate the same, we will look at the Bengal Plumbing transportation problem.

Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F Warehouse G Factory Capacity Plant A
Rs.50
Rs.40
Rs.30 100 Plant B
Rs.80
Rs.

Modified Distribution (MODI) Method

Modified Distribution (MODI) Method

The MODI method is another way of evaluating the initial solution of a transportation problem and finding a more optimal solution with much less iterations compared to the Stepping Stones method.

It allows us to compute improvement indices much quickly for each unused square without drawing all of the closed paths.
MODI provides new means of finding the unused route with the largest negative improvement index. Once the largest index is identified, we are required to trace only one closed path. We can then decide the maximum number of units that can be shipped along that unused route.

We begin with an initial solution obtained by the Northwest Corner Rule.

Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F Warehouse G Factory Capacity Plant A 100 Rs.50
Rs.40