Improving service quality in a congested network with random breakdowns

Abstract

This paper employs some strategies for improving service quality in a congested network consisting of facilities and customers. The quality is measured considering both customers’ travel distances and congestion delays. The strategies include opening new facilities, increasing the service capacities, and incorporating multiple backup services for customers, empowering the network to distribute the facilities’ workload smoothly. The goal is to optimally configure the congested network while improving the service quality. Each facility is modeled as an M/M/1 queuing system and might be broken down frequently during its serving process. The recovery starts immediately, which is a multi-step process, and each step takes an exponentially-distributed random time. The problem is first modeled as a mixed-integer nonlinear program; then, reformulated as a mixed-integer second-order cone program and can be optimally solved. An efficient solution algorithm based on Lagrangian decomposition is also developed. The numerical experiments illustrate the high efficiency of the solution methodology. Several managerial implications, including determining the best backup service level, are provided. Last, an example in distributed computing system design is presented to demonstrate the applicability of the model.