Combined Network Design and Multiperiod Pricing: Modeling, Solution Techniques, and Computation

Abstract

In this paper we describe an efficient algorithm for solving novel optimization models arising in the context of multi-period capacity expansion of optical networks. We assume the network operator must make investment decisions over a multi-period planning horizon while facing rapid changes in transmission technology, as evidenced by a steadily decreasing per-unit cost of capacity. We deviate from traditional, and monopolistic, models in which demands are given as input parameters, and the objective is to minimize capacity deployment costs. Instead, we assume the carrier sets end-to-end prices of bandwidth at each period of the planning horizon. These prices determine the demands that are to be met, using a plausible and explicit price-demand relationship; the resulting demands must then be routed, requiring an investment in capacity. The objective of the optimization is now to simultaneously select end-to-end prices of bandwidth and network capacities at each period of the planning horizon, so as to maximize the overall net present value of expanding and operating the network. In the case of typical large-scale optical networks with protection requirements, the resulting optimization problems pose significant challenges to standard optimization techniques. The complexity of the model, its highly nonlinear nature and the large size of realistic problem instances motivates the development of efficient and scalable solution techniques. We show that while general-purpose non-linear solvers are typically not adequate for the task, a specialized decomposition scheme is able to handle large-scale instances of this problem in reasonable time, producing solutions whose net present value is within a small tolerance of the optimum.

Towards optimizing the deployment of optical access networks

“…During this period of time, parts of the network can possibly be used already and generate profit for a carrier, before construction in other sections has even been started. Similarly as for other infrastructure planning problems, models can be time-expanded and turned into incremental models, see, for instance, Chang and Gavish (1995) and Bienstock et al (2006). As an example, we sketch modifications that can be done to get a multi-period version of the FTTH P2MP model (6), (7), (8), (9), (10), (11) and (12) for T time periods.…”

“…Arulselvan et al (2011). In principle, the model can also be extended to account for replacement or removal of equipment, if this seems appropriate, as done in Bienstock et al (2006).…”

MIP Modeling of Incremental Connected Facility Location

“…Most of the literature on applications in the telecommunications sector consider capacitated problems. Recent contributions are, e.g., [5,11]. Much less literature is available on the Connected Facility Location problem.…”

Joint Design and Pricing on a Network

“…Exploiting those cost savings and handling increased demand involves the optimization of technology acquisition and pricing processes (Lanning et al 2000, Başar andSrikant 2002). A recent paper by Bienstock et al (2006) addresses this issue within a dynamic framework, assuming a demand model involving constant elasticities and null cross elasticities. Several references to network design problems can be found therein, and also in the classic book by Ahuja et al (1993).…”