This lecture explains the assignment problem, where resources need to be assigned to tasks, and how it can be modeled as a transhipment problem using an artificial network. Through an example involving selling masterpieces to children, the instructor demonstrates how to represent the problem as a network, define nodes and arcs, and calculate costs to maximize revenue. The lecture then delves into the optimization problem, constraints, and capacity constraints associated with the transhipment problem, emphasizing the integral nature of the optimal solution.