##### AM-42 - The Classic Transportation Problem

The classic transportation problem concerns minimizing the cost of transporting a single product from sources to destinations. It is a network-flow problem that arises in industrial logistics and is considered as a special case of linear programming. The total number of units produced at each source, the total number of units required at each destination and the cost to transport one unit from each source to each destination are the basic inputs. The objective is to minimize the total cost of transporting the units produced at sources to meet the demands at destinations. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and 3) improving the current solution through iteration. Modeling and solving the classic transportation problem rely strongly on network models, least-cost path algorithms, and location-allocation analysis in the field of geographic information science (GIScience). Thus, it represents a key component in the network analytics and modeling area of GIS&T.

## PD-01 - Linear Programming and GIS

Linear programming is a set of methods for finding optimal solutions to mathematical models composed of a set of linear functions. Many spatial location problems can be structured as linear programs. However, even modest-sized problem instances can be very difficult to solve due to the combinatorial complexity of the problems and the associated computational expense that they incur. Geographic Information Systems software does not typically incorporate formal linear programming functionality, and instead commonly uses heuristic solution procedures to generate near-optimal solutions quickly. There is growing interest in integrating the spatial analytic tools incorporated in Geographic Information Systems with the solution power of linear programming software to generate guaranteed optimal solutions to spatial location problems.