A MULTI ECHELON QUEUING THEORETIC APPROACH TO TIME SENSITIVE SERVICE LEVEL OPTIMIZATION FOR MEDICAL SUPPLY CHAIN DISTRIBUTION DURING PANDEMIC OUTBREAKS

Abstract

During a pandemic, the distribution of time-sensitive medical supplies, such as vaccines, poses a critical public health challenge characterized by stochastic demand and stringent response time constraints. This study presents a novel multi echelon queuing theoretic model for the integrated optimization of facility location, inventory allocation, and distribution logistics. We model the supply network as a system of interconnected facilities where demand follows a Poisson process and incorporate two key flexibilities: lateral trans-shipments between distribution centers and pipeline stock management from central depots. The objective is to minimize total system costs including fixed facility, inventory holding, pipeline, and lateral transportation costs while ensuring that a target demand fraction is fulfilled within a maximum allowable response time. The problem is formulated as a Mixed Integer Linear Program MILP and solved using a Lagrangian relaxation scheme coupled with a sub gradient optimization algorithm. Numerical simulations, based on a case study of 40 demand locations in Delta State, Nigeria, demonstrate the model’s efficacy. The results show that the optimized network consistently achieves high Time Based service levels > 0.7 for all locations, with many exceeding 0.  95 by effectively balancing inventory across echelons and leveraging lateral trans-shipments to mitigate local shortages. This approach provides a quantifiable decision support tool for designing resilient, responsive, and cost effective medical supply chains for future public health emergencies.