Solution methods for the p‐median problem: An annotated bibliography

  title={Solution methods for the p‐median problem: An annotated bibliography},
  author={J. Reese},
  • J. Reese
  • Published 1 October 2006
  • Business
  • Networks
The p‐median problem is a network problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p‐median problem on a network. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 48(3), 125–142 2006 

Median Problems in Networks

The P-median problem is a classical location model “par excellence”. In this paper we, first examine the early origins of the problem, formulated independently by Louis Hakimi and Charles ReVelle,

Solving Large p-Median Problems with a Radius Formulation

By means of a model based on a set covering formulation, it is shown how the p-median problem can be solved with just a column generation approach that is embedded in a branch-and-bound framework

A tighter formulation of the p-median problem

It is shown that the efficiency of the standard branch-and-cut algorithm has been significantly improved and the structure of the new formulation of the p-median problem is explored in order to derive reduction rules and to accelerate the LP-relaxation resolution.

The minimum information approach to the uncapacitated p-median facility location problem

The minimum information theory is applied to the uncapacitated p-median facility location problem to determine the most probable allocation solution and investigates the bi-levelling problem.

An efficient Benders decomposition for the p-median problem

A branch-and-Benders-cut approach is implemented that outperforms state-of-the-art methods on benchmark instances by an order of magnitude and leads to a new compact formulation for the p-median problem.

A three‐stage p‐median based exact method for the optimal diversity management problem

A known decomposition approach is improved where smaller PMPs, related to the network components, can be solved instead of the initial large problem.

The most probable allocation solution for the p-median problem

A minimum information approach is applied to the capacitated p-median problem to estimate the most likely allo cation solution based on some prior probabilities, and the most probable solution is achieved through minimizing a log-based objective function.



A Dual-Bounded Algorithm for the p-Median Problem

A dual bound, based on the dual of the LP relaxation of the integer programming formulation of the p-median problem, is developed and tested in a branch-and-bound algorithm.

A graph theoretical bound for the p-median problem

The Robustness of Two Common Heuristics for the p-Median Problem

Optimal p-median solutions were computed for six test problems on a network of forty-nine demand nodes and compared with solutions from two heuristic algorithms. Comparison of the optimal solutions

An Algorithm for the M-Median Plant Location Problem

The problem is to locate a given number of plants along a road network so as to minimize the total distance between plants and warehouses assigned to them. It is modeled as an integer programming

A branch‐and‐price algorithm for the capacitated p‐median problem

A branch‐and‐price algorithm is presented, that exploits column generation, heuristics and branch‐ and‐bound to compute optimal solutions for the capacitated p‐median problem.

A Comparison of Two Heuristic Methods for the p‐Median Problem with and without Maximum Distance Constraints

The performance of Ardalan′s heuristic is compared with that of Teitz and Bart for the location of service facilities, where performance is assessed in terms of the accuracy of solutions. The

Two exact algorithms for the capacitated p-median problem

A branch and price algorithm is proposed for the p-median problem, comparing it with a standard MIP solver and a branch and bound algorithm based on Lagrangean relaxation, which shows very good performances and computational time robustness.

A column generation approach to capacitated p-median problems