Another application of linear optimization is shipping goods from multiple sources to multiple destinations in a way that minimizes costs while satisfying all supply and demand needs. A related task is assigning entities to tasks in a way that minimizes cost or maximizes utility. While these may be modeled as linear optimization problems, we also discuss some algorithms which computes these solutions in a less unweildy manner.
In Section 6.1, we discuss the general transportation problem and an algorithm which heuristically produces a “good” feasible solution. Then in Section 6.2 we explore an algorithm which improves a feasible solution and produces an optimal solution. Then in Section 6.3, we examine a specific type of transportation problem, the assignment problem, and study an algorithm partiular to this class of problem.
