A column generation heuristic for congested facility location problem with clearing functions

Nonlinear clearing functions, an idea initially suggested to reflect congestion effects in production planning, are used to express throughput of facilities prone to congestion in a facility location problem where each demand site is served by exactly one facility. The traditional constant capacity constraint for a facility is replaced with the nonlinear clearing function. The resulting nonlinear integer problem is solved by a column generation heuristic in which initial columns for the restricted master problem are generated by known existing algorithms and additional columns by a previously developed dynamic programming algorithm. Computational experimentation in terms of dual gap and CPU time based on both randomly generated and published data sets show not only clear dominance of the column generation over a Lagrangian heuristic previously developed, but also the high quality of results from the suggested heuristic for large problems.