Browsing by Subject "Assignment problem"

Now showing 1 - 4 of 4

Open Access
An exact algorithm for the minimum squared load assignment problem
(Elsevier, 2019) Karsu, Özlem; Azizoglu, M.
In this study, we consider an assignment problem with the objective to minimize the sum of squared loads over all agents. We provide mixed integer nonlinear and linear programming formulations of the problem and present a branch and bound algorithm for their solution. The results of our computational experiment have shown the satisfactory behavior of our branch and bound algorithm.
Open Access
A genuinely polynomial primal simplex algorithm for the assignment problem
(Elsevier, 1993) Akgül, M.
We present a primal simplex algorithm that solves the assignment problem in 1 2n(n+3)-4 pivots. Starting with a problem of size 1, we sequentially solve problems of size 2,3,4,...,n. The algorithm utilizes degeneracy by working with strongly feasible trees and employs Dantzig's rule for entering edges for the subproblem. The number of nondegenerate simplex pivots is bounded by n-1. The number of consecutive degenerate simplex pivots is bounded by 1 2(n-2)(n+1). All three bounds are sharp. The algorithm can be implemented to run in O(n3) time for dense graphs. For sparse graphs, using state of the art data structures, it runs in O(n2 log n+nm) time, where the bipartite graph has 2n nodes and m edges. © 1993.
Open Access
The linear assignment problem
(Springer, 1992) Akgül, Mustafa; Akgül, Mustafa; Hamacher, H. W.; Tüfekçi, S.
We present a broad survey of recent polynomial algorithms for the linear assignment problem. They all use essentially alternating trees and/or strongly feasible trees. Most of them employ Dijkstra’s shortest path algorithm directly or indirectly. When properly implemented, each has the same complexity: O (n 3) for dense graphs with simple data structures and O (n 2 log n+nm) for sparse graphs using Fibonacci Heaps.
Open Access
Two new algorithms for the linear assignment problem
(1990) Ekin, Oya
The linear assignment problem (AP) being among the first linear programming problems to be studied extensively,, is a fundamental problem in combinatorial optimization and network flow theory. AP arises in numerous applications of assigning personnel to jobs, assigning facilities to locations, sequencing jobs, scheduling flights, project planning and a variety of other practica.1 problems in logistics planning. In this thesis work, we seek for new approaches for solving the linear assignment problem. The main concern is to develop solution methods that exhibit some sort of parallelism. We present two new approaches for solving the assignment problem : A dual-feasible signature guided forest algorithm and a criss-cross like algorithm.