The distribution process of multi-dose vaccines

Abstract

The distribution chain of two-dose vaccines by an air carrier (KLM cargo) with its practical features is modelled to study the influence of supply uncertainty. First the goal is to find an efficient solution approach for the model which gives good quality solutions in reasonable computation time. Secondly with the developed solution method the supply uncertainty is taken into account using robust optimization. Solving the model using an exact solution method leads to a too large increase of computation time with increase of the model size for the purpose of robust analysis. Nevertheless, given the high reliability of the model the results of this commercial model are used as a reference. To circumvent the high computation time, two alternative solution methods are developed and implemented. Respectively the genetic algorithm and the rolling horizon method. A basic implementation of the genetic algorithm does not provide adequate results and gets trapped in a local optimum. An analysis shows that measures are needed to increase the flexibility and stimulate the algorithm to find so called “transaction-less” events. To achieve this, a toolbox is developed. The toolbox consists of analysis tools (measurement of convergence rate, sparsity and a diversity measurement) and tools intended to improve the convergence and accuracy of the solution. These latter are an adapted mutation operator that stimulates the number of transaction-less events (sparsity) and an approach for directed mutation. Each measure by itself has a positive effect on the initial convergence rate, but the algorithm still gets trapped at a somewhat improved local optimum at a level of approximately 10% above the optimum solution. A strong improvement is found by combining these measures of the toolbox resulting in solutions that approach the optimal solution within less than 5% for a single destination at a very high convergence rate. The best found combination of measures are implemented to solve a multi-destination problem. The results prove to be not as good as the result for the single destination: the gap to the optimal solution is roughly 10% and the convergence rate is somewhat slower. Probably this is due to the fact that the boundary conditions impose a reduction of flexibility for the multi-destination setting. On the other hand this finding might provide a base for worthwhile future work. Since this is solver is not (yet) suitable to be used in the robustness analysis. Three different implementations of the rolling horizon method were made: (i) the straight forward (myopic) approach, (ii) extending the time window with relaxed periods and (iii) a shifting rolling horizon. The straight forward approach is significantly improved by using the relaxed and shifting methods...