Signal transduction is a process of transmitting signals for controlling biological responses. The protein-protein interaction (PPI) data, containing signal transduction proteins, can be considered as a bi-directional, weighted network with the proteins as nodes, the interactions between them as edges, and the confidence score of the interaction as weights on edges. If the edges of this network are given a capacity of one, and if the starting and ending proteins are the supply and demand nodes, then this problem can be modeled as a capacitated transshipment model with pathways as the solutions. Our application concerns finding the signaling pathways for yeast’s mitogen-activated protein-kinase (MAPK) pheromone response and filamentation growth using the model created in the SAS OPTMODEL. The results demonstrate that the proposed model is easier to understand and interpret, and is applicable to the PPI network to discover signaling pathways efficiently and accurately.