Note—On “Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms”

Abstract

In the course of the deliberations of the 1977 Lanchester Prize Committee, Alan J. Goldman brought to our attention an error in the proof of Lemma 1 of our paper (Cornuejols, G., M. L. Fisher, G. L. Nemhauser. 1977. Location of bank accounts to optimize float: an analytic study of exact and approximate algorithms. Management Sci. 23 789–810.). The lemma, however, is true and the original correct, but long and intricate, proof was provided to the Committee, see (Cornuejols, G., M. L. Fisher, G. L. Nemhauser. 1977. On the uncapacitated location problem. Ann. Discrete Math. 1 163–178.) for details.

A constrained cluster-based approach for tracking the S&P 500 index

“…Hard constraints of (4) are identified and relaxed by putting these constraints in the objective. The resulting problem is called the Lagrangian relaxation and represents an upper bound on the optimal solution of (4) see (Cornuejols et al, 1977;Fisher, 1981;Geoffrion & Bride, 1978;Geoffrion, 2010). In particular, two constraints in model (4) P jKj k¼1 q k ¼ q and P jKj k¼1 p k γ α , can be put into the objective function by using the Lagrange multipliers λ and μ, respectively.…”

The p-median problem: A survey of metaheuristic approaches

“…(i) Lagrangian heuristics. These heuristics for solving PMP (Cornuejols, et al, 1977) are based on the mathematical programming formulation (5)-(9). Different variants of this approach are suggested in Galvão Type Heuristic References CH Greedy Kuehn & Hamburger (1963), Whitaker (1983.…”

“…Stingy Feldman et al (1966), Moreno-Pérez et al (1991). Dual ascent Galvão (1977Galvão ( , 1980 Cornuejols et al (1977), Mulvey & Crowder (1979), relaxation Galvão (1980), Beasley (1993), Daskin (1995), Senne & Lorena (2000), Barahona & Anbil (2000), Beltran et al (2004). MH Tabu search Mladenovic et al (1995Mladenovic et al ( , 1996, Voss (1996), Rolland et al (1996), Ohlemüller ( Murray & Church (1996), , Annealing Levanova & Loresh (2004).…”

A Discrete Particle Swarm Optimization Algorithm for Uncapacitated Facility Location Problem

“…There are many different titles for the UFL problem in the literature: the problem of a nonrecoverable tools optimal system [3], the standardization and unification problem [4], the location of bank accounts problem [5], warehouse location problem [6], uncapacitated facility location problem [7], and so on. The academic interest to investigate this mathematical model reasoned different interpretations.…”