Ann Oper Res (2014) 222:45–71 DOI 10.1007/s10479-012-1221-3 Location and allocation based branch and bound algorithms for the capacitated multi-facility Weber problem M. Hakan Akyüz · ˙ I. Kuban Altınel · Temel Öncan Published online: 18 September 2012 © Springer Science+Business Media, LLC 2012 Abstract Given the locations of J customers, their demands and I capacitated facilities, the Capacitated Multi-facility Weber Problem (CMWP) is concerned with locating I facilities in the plane to satisfy the demand of J customers with the minimum total transportation cost which is proportional to the distance between them. We propose two types of branch and bound algorithms for the ℓ r distance CMWP with 1 ≤ r< ∞. One of them is an alloca- tion space based branch and bound algorithm for which a new branching variable selection strategy and new lower bounding procedures have been proposed. The other one is new and partitions the location space. Based on extensive computational experiments we can say that the proposed algorithms are promising and perform better than the existing ones. Keywords Branch and bound · Discrete approximation · Facility location–allocation · Transportation 1 Introduction Given the locations of J customers and their demands, the Capacitated Multi-facility Weber Problem (CMWP) is concerned with locating I capacitated facilities in the plane and satisfy- ing the demands of J customers at minimum total transportation cost, which is proportional This research is supported by the Turkish Scientific and Technological Research Council (TÜB ˙ ITAK) Research Grant No: 107M462, and Galatasaray University Scientific Research Projects Grant Nos: 07.402.014, 10.402.001 and 10.402.019. The first author acknowledges the partial support of National Graduate Scholarship Program for PhD Students awarded by TÜB ˙ ITAK. M.H. Akyüz ( ) · T. Öncan Department of Industrial Engineering Ortaköy, Galatasaray University, ˙ Istanbul 34357, Turkey e-mail: mhakyuz@gsu.edu.tr T. Öncan e-mail: ytoncan@gsu.edu.tr ˙ I.K. Altınel Department of Industrial Engineering Bebek, Bo˘ gaziçi University, ˙ Istanbul 34342, Turkey e-mail: altinel@boun.edu.tr