We investigate the allocation of children to childcare facilities and propose solutions to overcome limitations in the current allocation mechanism. We introduce a natural preference domain and a priority structure that address these setbacks, aiming to enhance the allocation process. To achieve this, we present an adaptation of the Deferred Acceptance mechanism to our problem, which ensures strategy-proofness within our preference domain and yields the student-optimal stable matching. Finally, we provide a maximal domain for the existence of stable matchings using the properties that define our natural preference domain. Our results have practical implications for allocating indivisible bundles with complementarities.

翻译：我们研究了儿童在托育机构的分配问题，并提出了克服当前分配机制局限性的解决方案。我们引入了一个自然的偏好域和优先序结构，以解决这些缺陷，旨在优化分配流程。为此，我们针对该问题改进了延迟接受机制，该机制在偏好域内保证策略无关性，并生成学生最优稳定匹配。最后，我们通过定义自然偏好域的特性，给出了稳定匹配存在的最大域。研究结果对存在互补性的不可分割组合分配具有实际应用意义。