# Using the Minimum-Cost Method to Solve Transportation Problems

Instructor: Lucinda Stanley

Lucinda has taught business and information technology and has a PhD in Education.

This lesson will introduce you to the minimum cost method to solve transportation problems. We will explore why it is used, constraints and data needed to use the method and how the method is used to solve a real problem.

## Cost As A Priority

Jocelyn would like to apply at MGM Manufacturing to become their transportation manager. She's heard that they prefer to use the minimum cost method for solving their transportation problems, but she hasn't had an opportunity to use that method at her current position. She seeks help from Bill a former colleague who she knows has used it. Let's listen in:

Bill says: Well, Jocelyn, the minimum cost method, sometimes called the minimum cell cost method or least cost method is used when the priority is to reduce costs for distribution of materials. As you know, you can use other methods if the priority is time savings rather than cost savings. But it looks like MGM Manufacturing wants to distribute their product for as little cost as possible, thus reducing the overall cost of the product. Let's look at a problem I had just last week.

## Constraints

In the case of the recent problem I had, there were six constraints, three from the supplier and three from the destination. Constraints are the limitations of the distribution such as how much a factory can supply and how much of the product a given facility needs. Let's take a look at the constraints for my transportation problem:

### Supply constraints:

• Orlando supplier can produce fifteen truckloads of the product.
• Baltimore supplier can produce thirty truckloads of the product.
• Boston supplier can produce twenty truckloads of the product.

### Destination constraints:

• Las Vegas needs five truckloads
• St. Louis needs forty truckloads

I created a transportation matrix which is just a simple table that shows all constraints:

## Cost Information

Once I knew my constraints, I gathered information on the cost for delivery from each supplier to each destination and added that to my matrix (in red):

Now that I have all the information in my matrix, I can solve the transportation problem using the least cost or minimum cost method.

## Solve the Problem

I start out by looking for the cell with the lowest cost for transportation. In this case, it's the route from Orlando to Las Vegas at a cost of fifteen, so I want to fill as much of the Las Vegas demand with my supply from Orlando. Orlando can supply fifteen but Las Vegas only needs five, so I fill that in (in blue) and cross out the demand for Las Vegas:

Now I go on to the next lowest cost which is the Boston to St. Louis route for a cost of twenty. Boston can supply twenty but St. Louis needs forty, so I will assign all of Boston's supply to St. Louis which crosses out Boston's supply:

I continue in the same manner, looking for each cell that is the least expensive and assign as much as I can from the supplier to meet the demand of the destination.

Both the Boston to Las Vegas and the Baltimore to Seattle routes have a cost of thirty, but the Las Vegas demand has already been filled, so I can move directly to the Baltimore/Seattle route. Seattle needs twenty and Baltimore has thirty so I fill the Seattle demand from Baltimore and cross out the Seattle demand:

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