The Pollyanna Problem

Abstract

The assignment problem serves as the basis for a novel formulation and initial approach to assigning participants in holiday “Pollyanna” gift exchanges. This research presents the formalization of a typical heuristic assignment with constraints as commonly imposed by family and work dynamics. The constraints include restrictions on exchanging within the same nuclear family, restrictions on repeating that same exchanges as the previous year, balancing “good” gifts with “bad” gifts and restricting direct exchanges. A multidimensional assignment problem is formulated and reformulated employing Lagrangian Relaxation.

Heuristic Approach to Temporal Assignments of Spatial Grid Points for Vegetation Monitoring

“…ThemultidimensionalassignmentproblemwasintroducedbyPierskalla(1968)andabibliography ofmultidimensionalassignmentproblemswaspreparedbyGilbert&Hofstra (1988). Miori(2011,2014)usedassignmentproblemstomodeltruckloadroutingproblemsandthePollyannagift exchangeproblem.SchedulingmedicalresidentswiththetemporalcomponentwasaddressedbyFranz &Miller(1993).Bandeltetal. (1994addressedmulti-dimensionalassignmentproblemswith decomposablecosts.Thethree-dimensionalassignmentproblemwasappliedtoteachingschedules byFriezeandYadegar ( )andBalasandSaltman(1991.Multidimensionalapproximationwas appliedtocapacityexpansionproblemsbyTroungandRoundy (2011).LagrangianRelaxationwas appliedtoamulti-dimensionalassignmentproblemarisingfrommulti-targettrackingbyPooreand Rijavec (1993).…”