The Capacitated p-facility Location Problem on the Real Line

Jack Brimberg, Ephraim Korach, Moshe Eben-Chaim, Abraham Mehrez

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The problem we address involves locating p new facilities to service a set of customers or fixed points on the real line such that a measure of total cost will be minimized. A basic form of this problem was investigated by Love (1976), who observed that the fixed points must be allocated in sequence to the new facilities in an optimal solution, and thus, the problem can be solved by a dynamic programming algorithm. Since then, other forms of the model have been investigated; however, in all cases it is assumed that the new facilities have unlimited capacity so that customer flows are always allocated to the nearest facility. The objective of this paper is to analyze the effect of capacity constraints on the optimal locations of the new facilities. A general fixed-cost function is also included to account for practical considerations such as zoning regulations, and to permit the facilities to be located anywhere on the line instead of only at the fixed vertices. A dynamic programming method is formulated to solve the problem when the variable cost components are increasing convex functions of travel distance. The problem is shown to be NP-hard under more general cost structures. International Federation of Operational Research Societies 2001.

Original languageEnglish
Pages (from-to)727-738
Number of pages12
JournalInternational Transactions in Operational Research
Issue number6
StatePublished - 1 Jan 2001


  • Complexity
  • Dynamic programming
  • Location-allocation

ASJC Scopus subject areas

  • Business and International Management
  • Computer Science Applications
  • Strategy and Management
  • Management Science and Operations Research
  • Management of Technology and Innovation


Dive into the research topics of 'The Capacitated p-facility Location Problem on the Real Line'. Together they form a unique fingerprint.

Cite this