Efficient medication management within healthcare facilities is paramount for ensuring patient well-being. This literature article delves into the intricacies of optimizing medication assignment within automated dispensing systems (ADSs) to enhance patient care and healthcare system efficiency. Consider a typical scenario within healthcare facilities: a patient's prescription includes two medications that require simultaneous administration for effective treatment. In such instances, the accessibility of both medications when needed is imperative. However, in many healthcare settings, these medications are stored in separate, often distant locations within the Automated Dispensing Device (ADD). This physical separation can lead to a time-consuming process for healthcare professionals who must retrieve and administer these drugs. Our research proposes a solution to this issue by advocating for the allocation of both medications in close proximity within the ADD column. Although this allocation strategy appears straightforward, it is subject to specific constraints ensuring optimized medication assignment. By meticulously designing the drug allocation process within ADD machines, we aim to minimize delays in medication retrieval and administration, ultimately leading to improved patient outcomes. Our research introduces the use of synthesized controllers to enhance the drug allocation process. These controllers are founded on mathematical modeling, employing Petri nets as a methodology. Furthermore, we present the concept of place invariants as a supervisory control technique to assign drugs to specific locations efficiently. The essence of our methodology lies in introducing controlled places within the Petri net model. Each controlled place corresponds to a specific constraint related to medication allocation. This innovative approach guarantees the optimal assignment of medications, complying with all relevant constraints. This fusion of mathematical modeling and supervisory control techniques holds the potential to redefine the management of medication assignment in healthcare facilities, particularly within automated systems. Drawing from prior applications of this methodology across various domains, we illustrate how these synthesized controllers can efficiently manage drug allocation within automated systems. By amalgamating the strengths of mathematical modeling with real-world healthcare applications, we bridge the gap between theoretical concepts and practical solutions, offering a tangible response to a critical healthcare challenge. At its core, this paper builds upon existing researches in the field, further advancing the optimization of medication assignment within healthcare facilities. By leveraging advanced control methodologies and innovative techniques, we continue our journey toward a more efficient and dependable way to streamline drug allocation. The ultimate objective remains to elevate the overall performance of automated dispensing systems, enhance patient outcomes, and contribute to the overall well-being of individuals accessing healthcare services.

Automated dispensing system (ADD), Assignment problem, Petri nets, Supervisory control, Place invariant method.