Kernelized sorting is a method for aligning objects across two domains by considering within-domain similarity, without need to specify cross-domain similarity measure. In this paper we present the Convex Sorting where, unlike in previous approaches, object matching formulated as convex optimization problem, leading simpler and global optimum solution. Our outputs soft alignments between object...

There are n graduate students and n faculty members. Each student will be assigned a scholarship by the joint faculty. The socially optimal outcome is tbat the best studcnt should get the most prestigious scholarship, the second-best student should get the second most prcstigious scholarship, and so on. The socially optimal outcome is common knowledge among all faculty members. Each professor w...

The hypergraph assignment problem (HAP) is the generalization of assignments from directed graphs to directed hypergraphs. It serves, in particular, as a universal tool to model several train composition rules in vehicle rotation planning for long distance passenger railways. We prove that even for problems with a small hyperarc size and hypergraphs with a special partitioned structure the HAP ...

There has been considerable recent interest in the dynamic vehicle routing problem, but the complexities of this problem class have generally restricted research to myopic models. In this paper, we address the simpler dynamic assignment problem, where a resource (container, vehicle or driver) can only serve one task at a time. We propose a very general class of dynamic assignment models, and pr...

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadra...

In a supply chain, cross-docking is one of the most innovative systems for ameliorating the operational performance at distribution centers. Cross-docking is a logistics strategy in which freight is unloaded from inbound trucks and (almost) directly loaded into outbound trucks, with little or no storage in between, thus no inventory remains at the distribution center. In this study, we consider...

A branch and bound algorithm for finding the minimal cost symmetric assignment is discussed. The matching problem in graph theory and the Chinese postman puzzle are all special cases of the symmetric assignment problem, and hence this algorithm can be applied to solve them.