Solving a tri-objective convergent product network using the Steiner tree

Considering convergent product as an important manufacturing technology for digital products, we integrate functions and sub-functions using a comprehensive fuzzy mathematical optimization process. To form the convergent product, a web-based fuzzy network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is to be a link between two nodes. The aim is to find an optimal tree of functionalities in the network adding value to the product in the web environment. First, a purification process is performed in the product network to assign the links among bases and sub-functions. Then, numerical values as benefits and costs are determined for the arc and the node, respectively. Also, a fuzzy customers’ value corresponding to the arcs is considered. Next, the Steiner tree methodology is adapted to a multi-objective model of the network to find the optimal tree. A fuzzy multi-objective solution methodology is developed for solving the proposed problem. Finally, an example is worked out to illustrate the proposed approach.