It is often difficult to verify the solutions of computationally intensive mathematical optimization problems. Metamorphic testing is a technique to verify software test output even when a complete testing oracle is not present. We apply metamorphic testing to a classic optimization problem, the quadratic assignment problem (QAP). A number of metamorphic relations for the QAP are described in d...

one of the questions that has been ignored in letter of credit is a problem of assignment of proceeds in letter of credit that has been discussed generally below the transfer of lc subject, but has differed with it. so in this article, the author has tried to use the words assignment and transfer exactly in their place to clear the existent differences. at first, the writer’s hypothesis was tha...

In this paper we present an algorithm for generating quadratic assignment problem (QAP) instances with known provably optimal solution. The flow matrix of such instances is constructed from the matrices corresponding to special graphs whose size may reach the dimension of the problem. In this respect, the algorithm generalizes some existing algorithms based on the iterative selection of triangl...

The multilevel generalized assignment problem (MGAP) is a variation of the generalized assignment problem, in which agents can execute tasks at different efficiency levels with different costs. We present a branch-and-price algorithm that is the first exact algorithm for the MGAP. It is based on a decomposition into a master problem with set-partitioning constraints and a pricing subproblem tha...

Page 55 line 6: replace " among the matched " with " among the unmatched " ; 229 line 13: replace " Palubeckis [544] " with the following (missing) reference: G. Palubeckis. The use of special graphs for obtaining lower bounds in the geometric quadratic assignment problem. 289 eqn (9.27): replace " s ∈ F " with " S ∈ F " ; 308 line 14: replace " approximation algorithms which yield a feasible s...

We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (aminimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases. For the mo...

A number of effective solution methods for the classical Generalised Assignment Problem (GAP) have been proposed during the last thirty years. Exact branch and bound approaches to solving GAP have been proposed by (Ross, Soland 1975, Martello, Toth 1990). More recently however heuristics have been utilised in order to reduce the size of the branch and bound tree by seeking good feasible solutio...

We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and its running time is O(f (N)), our algorithm guarantees a (1 + α)-approximation ratio, and it runs...

This paper describes what is termed the "generalized assignment problem". It is a generalization of the ordinary assignment problem of linear programming in which multiple assignments of tasks to agents are limited by some resource available to the agents. A branch and bound algorithm is developed that solves the generalized assignment problem by solving a series of binary knapsack problems to ...