Optimising Vaccine Logistics in Epidemic Situations: An Exact Benders Approach

This paper addresses the problem of optimising the spatial and temporal distribution and allocation of vaccines among different groups in an epidemic situation that minimizes the sourcing and shipping costs and epidemiological impacts (e.g., infections or deaths). The problem combines a combinatorial distribution model with a discrete-time, continuous-state Susceptible-Exposed-Infected-Removed (SEIR) compartmental model that governs the disease dynamics, resulting in an intractable mixed-integer bilinear program. We propose a novel exact logic-based Benders decomposition algorithm to solve the problem. Furthermore, a simulation procedure is developed to solve the special case of uniform mixing. Our numerical analysis demonstrates the effectiveness of the proposed model and solution algorithm.