The Pollyanna Problem: Assignment of Participants in a Gift Exchange

The Pollyanna Problem: Assignment of Participants in a Gift Exchange

Virginia M. Miori (Saint Joseph's University, Philadelphia, PA, USA)
Copyright: © 2014 |Pages: 12
DOI: 10.4018/ijbir.2014010101


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.
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The holiday season brings many complications to family and workplace dynamics. One of these complications is the assignment of participants in a Pollyanna gift exchange. Over the years, it has become clear that this assignment can never please all participants, but offering a fair assignment can help to mitigate the flurry of complaints. The assignment problem provides an initial approach to this problem, a bijective mapping of a set of alternatives onto itself. Though gift exchanges do require a bijective assignment, a mapping of this type will not fulfill the complex constraints imposed by family or group dynamics. The rules of the exchange are found in Figure 1.

Figure 1.

Rules of the exchange

For small families (organizations), this problem may be most easily solved through constraint relaxation and simple heuristics. Certain family (group) configurations also present problems for which this approach has no solution. Again, constraint relaxation must be considered along with heuristics. As families (groups) increase in number, more complex and standardized heuristics are required to generate solutions. This paper presents one such approach in addition to a multidimensional assignment formulation for multi-year assignments.

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