Handling Transportation Problems & Special Cases

Instructor: Lucinda Stanley

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

In this lesson we'll discuss how to handle transportation problems such as unequal supply and demand, unacceptable routes, and how solving transportation problems can maximize the objectives of a business.

Transportation

Transportation is all about getting a product from one place to another, simple, right? Put the product on a truck or railcar and you're good to go. Well, not exactly. There's a bit more that goes into it. It becomes particularly complicated when there are multiple places the product is coming from, and multiple places the product is going to. Transportation managers must crunch some serious numbers (do some math) to find the optimum path for getting their product to the customer. Let's look at some common problems a transportation manager might encounter.

Unequal Supply and Demand

One common transportation issue has to do with supply and demand. Supply is how much of a product a producer has to sell and demand is how much of a product customers want to buy.

We can use a matrix to help us solve transportation problems. Let's say we have two warehouses that can supply our product and two places that need the product. We have an equal demand to supply. The matrix would look like this:

Basic Transportation Matrix
Basic Transportation Matrix

In this scenario, we just send the product from the warehouse closest to the facility. This way costs are reduced, product gets to where it can be sold, and revenue is earned. Simple. But not always the case.

If there is more supply than demand it doesn't really pose a transportation problem because the extra product doesn't have to be shipped. Therefore there aren't any transportation costs. Warehouse costs, yes, but transportation costs, no. There is also no revenue from products sitting in the warehouse.

If we have a higher demand than we do supply, we have an unbalanced transportation problem that needs to be solved. We have to figure out the most cost-effective and revenue-producing solution to meet as much demand as possible with the supply we have.

We can use the matrix structure again to visualize the problem:

Unequal Supply and Demand Matrix
Unequal supply and demand matrix

We see that each warehouse can supply 250 pieces, but there is a demand for 800. We are short 300 pieces. The shortage is represented by including another supply row called dummy. We will also add some information about costs (in red) to help us as we work through the problem.

We can solve this problem using one of two methods:

Northwest Corner Rule

The northwest corner rule which fills in the cells starting in the upper left corner:

Northwest Corner Rule Matrix
Northwest Corner Rule

We start in the upper left corner and assign (in blue) as much supply to the first destination as we can. Destination 1 has a need for 400 pieces. Our Supply 1 has 250 pieces so we assign all of those to Destination 1. We still need 150 pieces for Destination 1 so we assign those from Supply 2. The remaining 100 from Supply 2 are assigned to Destination 2. When we get more supply, it is applied to the shortage in Destination 2. This method basically fills orders for destinations based on where they are in the matrix. We can figure the total cost like this:

Total Cost: 15(250) + 45 (150) + 40 (100) = $14,500.

Minimum Cell Cost

If cost is the primary factor, we're going to solve it using the minimum cell cost method:

Minimum Cell Cost Matrix
Minimum cell cost matrix

We find the cell that has the least cost. That would be $15 for Supply 1 going to Destination 1, and we assign as much supply as possible, which is 250.

The next lowest cost is Supply 1 to Destination 2 ($30), but there isn't any supply left in Supply 1 so we turn to Supply 2 with a $40 cost to Destination 2 and assign all 250 there.

Our total cost would be: 15(250) + 40(250) = $13,750. Notice that using the minimum cell cost method results in a lower cost than the Northwest Corner rule.

Unacceptable Routes

What if the transportation manager knows that Destination 1 prefers not to receive product from Supply 1? For example, perhaps the destination feels that the product from Supply 1 is inferior. Whether this is true or not isn't relevant because we want to make Destination 1 happy. This becomes an unacceptable route, meaning, the transportation manager will want to avoid this route if possible. That makes sense, but how can a transportation manager include this unacceptable route in their calculations? If they are using the minimum cell cost method, they can increase the cost for the route from Supply 1 to Destination 1, thereby taking it out of the loop.

Let's see how this would look by using the data we've already been looking at. We increase the cost for the route from Supply 1 to Destination 1 from 15 to 60, essentially wiping out that route in favor of other more favorable routes for Destination 1:

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