Bipartite matching problems play a crucial role in various software engineering tools, including resource allocation and task assignment. In this paper, we address a specific variant of the bipartite matching problem, called the Double Assignment Problem (DAP), focusing on the allocation of machines to workers in a production environment. The objective is to maximize the number of worker-machine associations, subject to a second, orthogonal matching problem: associating some worker W to a machine M implies that the (ordered) list of servers employed by M are dedicated to the respective programs used by the worker W. Since DAP is, in general, NP-hard, we introduce a heuristic that quickly approximates candidate results. The heuristic is called k-swap stability and has originally been formalized to tackle a specific DAP instance arising in the niche field of anti-unification. We extend the definition to our more general setting and give promising preliminary results obtained by applying our k-swap implementation on a testbed of examples.