  Opioid Use Disorder (OUD) has reached an epidemic level in the US. Diversion
of unused prescription opioids to secondary users and black market
significantly contributes to the abuse and misuse of these highly addictive
drugs, leading to the increased risk of OUD and accidental opioid overdose
within communities. Hence, it is critical to design effective strategies to
reduce the non-medical use of opioids that can occur via diversion at the
patient level. In this paper, we aim to address this critical public health
problem by designing strategies for the return and safe disposal of unused
prescription opioids. We propose a data-driven optimization framework to
determine the optimal incentive disbursement plans and locations of easily
accessible opioid disposal kiosks to motivate prescription opioid users of
diverse profiles in returning their unused opioids. We develop a Mixed-Integer
Non-Linear Programming (MINLP) model to solve the decision problem, followed by
a reformulation scheme using Benders Decomposition that results in a
computationally efficient solution. We present a case study to show the
benefits and usability of the model using a dataset created from Massachusetts
All Payer Claims Data (MA APCD). Our proposed model allows the policymakers to
estimate and include a penalty cost considering the economic and healthcare
burden associated with prescription opioid diversion. Our numerical experiments
demonstrate the ability of model and usefulness in determining optimal
locations of opioid disposal kiosks and incentive disbursement plans for
maximizing the disposal of unused opioids. The proposed optimization framework
offers various trade-off strategies that can help government agencies design
pragmatic policies for reducing the diversion of unused prescription opioids.
