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There has been an unexpected increase in the amount of healthcare waste during the COVID-19 pandemic. Managing healthcare waste is vital, as improper practices in the waste system can lead to the further spread of the virus. To develop effective and sustainable waste management systems, decisions in all processes from the source of the waste to its disposal should be evaluated together. Strategic decisions involve locating waste processing centers, while operational decisions deal with waste collection. Although the periodic collection of waste is used in practice, it has not been studied in the relevant literature. This paper integrates the periodic inventory routing problem with location decisions for designing healthcare waste management systems and presents a bi-objective mixed-integer nonlinear programming model that minimizes operating costs and risk simultaneously. Due to the complexity of the problem, a two-step approach is proposed. The first stage provides a mixed-integer linear model that generates visiting schedules to source nodes. The second stage offers a Bi-Objective Adaptive Large Neighborhood Search Algorithm (BOALNS) that processes the remaining decisions considered in the problem. The performance of the algorithm is tested on several hypothetical problem instances. Computational analyses are conducted by comparing BOALNS with its other two versions, Adaptive Large Neighborhood Search Algorithm and Bi-Objective Large Neighborhood Search Algorithm (BOLNS). The computational experiments demonstrate that our proposed algorithm is superior to these algorithms in several performance evaluation metrics. Also, it is observed that the adaptive search engine increases the capability of BOALNS to achieve high-quality Pareto-optimal solutions.