11.2 Transportation Models

Transportation models represent a specialized class of linear programming problems designed to optimize the allocation and movement of goods or resources from multiple supply locations to multiple demand destinations. In the context of distribution logistics, these models are instrumental in determining the most cost-effective way to transport products from Distribution Centers (DCs) to market locations, while satisfying both supply and demand constraints.

The primary objective of a transportation model is to minimize the total transportation cost across the network, ensuring that:

• The supply capacity at each DC is not exceeded,
• The demand requirements at each market are fully met, and
• The cost of shipping along each route is taken into account.

Key Components of a Transportation Model:

• Supply Points (DCs): Each DC has a defined capacity, representing the maximum quantity of goods it can supply.
• Demand Points (Markets): Each market has a specific demand that must be fulfilled.
• Transportation Costs: These are the per-unit costs associated with shipping goods from each DC to each market.
• Decision Variables: These represent the quantity of goods to be transported along each route (i.e., from a specific DC to a specific market).

By formulating these elements into a linear programming framework, transportation models enable firms to make data-driven, cost-efficient decisions in complex distribution networks.

The basic structure can be represented in a transportation tableau: