Enhanced model representations for an intra-ring synchronous optical network design problem allowing demand splitting

In this paper, we consider a network design problem arising in the context of deploying synchronous optical networks (SONET) using a unidirectional path switched ring architecture, a standard of transmission using optical fiber technology. Given several rings of this type, the problem is to find an assignment of nodes to possibly multiple rings, and to determine what portion of demand traffic between node pairs spanned by each ring should be allocated to that ring. The constraints require that the demand traffic between each node pair should be satisfiable given the ring capacities, and that no more than a specified maximum number of nodes should be assigned to each ring. The objective function is to minimize the total number of node-to-ring assignments, and hence, the capital investment in add-drop multiplexer equipments. We formulate the problem as a mixed-integer programming model, and propose several alternative modeling techniques designed to improve the mathematical representation of this problem. We then develop various classes of valid inequalities for the problem along with suitable separation procedures for tightening the representation of the model, and accordingly, prescribe an algorithmic approach that coordinates tailored routines with a commercial solver (CPLEX). We also propose a heuristic procedure which enhances the solvability of the problem and provides bounds within 5-13% of the optimal solution. Promising computational results are presented that exhibit the viability of the overall approach and that lend insights into various modeling and algorithmic constructs.