Vaccination Schedule under Conditions of Limited Vaccine Production Rate

The paper is devoted to optimal vaccination scheduling during a pandemic to minimize the probability of infection. The recent COVID-19 pandemic showed that the international community is not properly prepared to manage a crisis of this scale. Just after the vaccines had been approved by medical agencies, the policymakers needed to decide on the distribution strategy. To successfully fight the pandemic, the key is to find the equilibrium between the vaccine distribution schedule and the available supplies caused by limited production capacity. This is why society needs to be divided into stratified groups whose access to vaccines is prioritized. Herein, we present the problem of distributing protective actions (i.e., vaccines) and formulate two mixed-integer programs to solve it. The problem of distributing protective actions (PDPA) aims at finding an optimal schedule for a given set of social groups with a constant probability of infection. The problem of distributing protective actions with a herd immunity threshold (PDPAHIT) also includes a variable probability of infection, i.e., the situation when herd immunity is obtained. The results of computational experiments are reported and the potential of the models is illustrated with examples.

A computational status update for exact rational mixed integer programming

The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe a substantial revision and extension of this framework that integrates symbolic presolving, features an exact repair step for solutions from primal heuristics, employs a faster rational LP solver based on LP iterative refinement, and is able to produce independently verifiable certificates of optimality. We study the significantly improved performance and give insights into the computational behavior of the new algorithmic components. On the MIPLIB 2017 benchmark set, we observe an average speedup of 10.7x over the original framework and 2.9 times as many instances solved within a time limit of two hours.

Automated Calibration of Farm-Sale Mixed Linear Programming Models using Bi-Level Programming

We calibrate Linear and Mixed Integer Programs with a bi-level estimator, minimizing under First-order-conditions (FOC) conditions a penalty function considering the calibration fit and deviations from given parameters. To deal with non-convexity, a heuristic generates restart points from current best-fit parameters and their means. Monte-Carlo analysis assesses the approach by drawing parameters for a model optimizing acreages under maximal crop shares, a land balance and annual plus intra-annual labour constraints; a variant comprises integer based investments. Resulting optimal solutions perturbed by white noise provide calibration targets. The approach recovers the true parameters and thus allows for systematic and automated calibration.

Parallelizing Subgradient Methods for the Lagrangian Dual in Stochastic Mixed-Integer Programming

The dual decomposition of stochastic mixed-integer programs can be solved by the projected subgradient algorithm. We show how to make this algorithm more amenable to parallelization in a master-worker model by describing two approaches, which can be combined in a natural way. The first approach partitions the scenarios into batches and makes separate use of subgradient information for each batch. The second approach drops the requirement that evaluation of function and subgradient information is synchronized across the scenarios. We provide convergence analysis of both methods. We also evaluate their performance on two families of problems from SIPLIB on a single server with 32 single-core worker processes, demonstrating that when the number of workers is high relative to the number of scenarios, these two approaches (and their synthesis) can significantly reduce running time.