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Transportation Modelling

Transportation Modelling
Transportation is the most important part of Logistics & Supply Chain Management. All costs associated with movement of products from one location to another constitute of transportation cost. The average transport costs ranges from 5 to 6 percent of the recommended retail price of the product.

Why Transportation Models are required ?
Companies produce products at locations called Origins and ships these products to customer locations called Destinations.
Each Origin has a limited amount that it can ship, and each Destination must receive a required quantity of the product. 
The Transportation Models prove useful when considering alternative facility locations within the framework of existing distribution system.
Each potential plant, warehouse, or distribution centre will require a different allocation of shipments, depending upon its own production or shipping costs and its strategic position in the network.

Transportation Modelling finds the least cost means of shipping supplies from several Origins to several Destinations.

Origin points (Sources) can be facilities, warehouse or any other points from which the goods are shipped.
Destinations are any points that receive the goods.

 To use a Transportation Model, we need to know the following.
  1. The origin points and the capacity or supply per period at each.
  2. The destination points and the demand per period at each.
  3. The cost of shipping one unit from each origin to each destination.
To illustrate one transportation problem, let's look at a company called Bengal Plumbing, which makes among other products, a full line of bathtubs. The company has many factories and warehouses spread along the length and breadth of the country.
In our example the firm must decide which of its factories should supply which of its warehouses.

Relevant data of Bengal Plumbing are presented in the table below :

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.40

Rs.30
300
Plant C

Rs.90

Rs.70

Rs.50
300
Warehouse Requirement
300
200
200
700









The Table shown above can be explained as following.

Plant (A) Capacity Constraint - 100 Units
Cost of shipping 1 Unit from Plant (A) to Warehouse (E) - Rs. 50
Cost of shipping 1 Unit from Plant (A) to Warehouse (F) - Rs. 40
Cost of shipping 1 Unit from Plant (A) to Warehouse (G) - Rs. 30
Total Demand of Warehouse (E) - 300 Units

Now we know that the 300 Units required by Bengal Plumbing's Warehouse (E) can be shipped in various combinations from its Plants (A), (B) & (C).
The first step in Modelling Process is to set up a Transportation Matrix as shown above. Its purpose is to summarize all relevant data and to keep track of algorithm computations.

Once the data is arranged in tabular form, we must establish a feasible solution to the problem. A number of methods have been developed for this step.
  1. The Northwest Corner Rule
  2. The Intuitive Lowest Cost Method
  3. The Stepping Stone Method
  4. The MODI (Modified Distribution) Method
  5. Vogel's Approximation Method
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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 Warehou
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The Stepping Stone Method

The Stepping Stone Method Once an initial feasible solution to a transportation problem is determined by any of the previous methods, the next step is to solve the model for the optimal solution. The Stepping Stone Method is an iterative technique used to evaluate the cost effectiveness of  the shipping routes not currently in the solution. When applying it, we test each unused cell, or square, in the transportation table by asking : What would happen to the total shipping cost if one unit of product was tentatively shipped to an unused route? To illustrate the same, let us look at the initial solution of the Bengal Plumbing Problem derived by the Northwest Corner Rule. Transportation Matrix for Bengal Plumbing From \ To Warehouse E Warehouse F Warehouse G Factory Capacity Plant A 100 Rs. 5 0 Rs. 4 0 Rs. 3 0 100 Plant B 200 Rs. 8 0 100 Rs. 4 0 Rs. 3 0 300 Plant C Rs. 9 0 100 Rs. 7 0 200 Rs. 5 0 300 Warehous
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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
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