TRANSPORTATION MODELS

Transportation models are special algorithms of linear programming problems in which the objective of the decision maker or the distributor of goods (services) is to prepare a schedule of shipment from different sources to different destinations such that the total cost of transportation is to be minimized.  There are a number of sources (factories, warehouses, or distribution centers) from where the supply of goods can be obtained and there are a number of destinations (customer outlets, depots, or dealerships) which require these products.  The transportation model should be able to determine how many units of the products should be allocated along each route so as to minimize the total cost of such allocations.

The following assumptions are to be considered in any transportation models:
1.  The decision maker is expected to make the best possible match of sources to destinations in allocating goods that will yield the minimum cost of transportation.
2.  The cost per unit of transportation from every source to every destination is givem.
3.  The products are homegenous in the sense that items allocated from different sources can be freely interchanged.  Only the total cost of transportation might vary from one route to another.
4.  All routes are acceptatble except a dummy source or  a dummy destination if injected.
5.  The total cost along any route is the number of items allocated to that route multiplied by its cost per unit.
6.  Total supply equals total demand, i.e., the distribution or transportation table is balanced.

Kinds of Transportation Table
1.  Balanced table .  The table is said to be balanced if the total supply is equal to the total demand which is a standard table.
2. Unbalanced table.  The table is said to be unbalanced if the total supply is not equal to the total demand. 
3. Non-degenerate table.  A table is said to be non-degenerate if the number of occupied cells is equal to the number of rows plus number of columns minus one which is also a standard table.
4.  Degenerate table.  A table is said to be degenerate if the number of rows plus the number of columns minus one is not equal to the number of occupied cells.

Four Different Ways of Allocating Goods
1.  The Northwest Corner Rule
2.  The Minimum Cost Method
3.  The Vogel's Approximation Method
4.  The Stepping Stone Method of Transportation