Optimization Letters

, Volume 11, Issue 1, pp 225–239 | Cite as

A cutting plane approach to combinatorial bandwidth packing problem with queuing delays

  • Sachin Jayaswal
  • Navneet Vidyarthi
  • Sagnik Das
Short Communication


The combinatorial bandwidth packing problem (CBPP), arising in a telecommunication network with limited bandwidth, is defined as follows. Given a set of requests, each with its potential revenue, and each consisting of calls with their bandwidth requirements, decide: (1) a subset of the requests to accept/reject; and (2) a route for each call in accepted requests, so as to maximize the total revenue earned in a telecommunication network with limited bandwidth. However, telecommunication networks are generally characterized by variability in the call (bits) arrival rates and service times, resulting in queuing delays in the network. In this paper, we present a non-linear integer programming model to account for such delays in CBPP. Using simple transformation and piecewise outer-approximation, we reformulate the model as a linear mixed integer program (MIP), but with a large number of constraints. We present an efficient cutting plane approach to solve the resulting linear MIP to \(\epsilon \)-optimality.


OR in telecommunications Bandwidth packing Integer programming Queueing Cutting plane algorithm 



This research was supported by the Research and Publication Grant, Indian Institute of Management Ahmedabad, provided to the first author, and by the Canadian Natural Science and Engineering Research Council Discovery Grant 386501-2010 provided to the second author. This support is gratefully acknowledged. The authors also acknowledge Vikranth B. T. Chetty for his assistance in computational experiments. The authors would like to thank the editor-in-chief as well as the referees for the constructive comments on the earlier version of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Production and Quantitative MethodsIndian Institute of Management AhmedabadAhmedabadIndia
  2. 2.Department of Supply Chain and Business Technology Management, John Molson School of BusinessConcordia UniversityMontrealCanada
  3. 3.Department of Industrial and Enterprise Systems EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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