Authors are listed alphabetically. Both authors contributed equally.
A Dynamic Disaggregation Approach to Approximate Linear Programs for Network Revenue Management†
Article first published online: 7 JUL 2014
© 2014 Production and Operations Management Society
Production and Operations Management
Volume 24, Issue 3, pages 469–487, March 2015
How to Cite
A Dynamic Disaggregation Approach to Approximate Linear Programs for Network Revenue Management. Production and Operations Management (2014), doi 10.1111/poms.12239, .
- Issue published online: 12 MAR 2015
- Article first published online: 7 JUL 2014
- Accepted manuscript online: 23 APR 2014 08:35AM EST
- Manuscript Accepted: MAR 2014
- Manuscript Received: SEP 2012
- network revenue management;
- choice behavior;
- dynamic programming;
- linear programming
The linear programming approach to approximate dynamic programming has received considerable attention in the recent network revenue management (RM) literature. A major challenge of the approach lies in solving the resulting approximate linear programs (ALPs), which often have a huge number of constraints and/or variables. Starting from a recently developed compact affine ALP for network RM, we develop a novel dynamic disaggregation algorithm to solve the problem, which combines column and constraint generation and exploits the structure of the underlying problem. We show that the formulation can be further tightened by considering structural properties satisfied by an optimal solution. We prove that the sum of dynamic bid-prices across resources is concave over time. We also give a counterexample to demonstrate that the dynamic bid-prices of individual resources are not concave in general. Numerical experiments demonstrate that dynamic disaggregation is often orders of magnitude faster than existing algorithms in the literature for problem instances with and without choice. In addition, adding the concavity constraints can further speed up the algorithm, often by an order of magnitude, for problem instances with choice.