We study last-mile delivery with the option of crowd shipping, where a company makes use of occasional drivers to complement its vehicle’s fleet in the activity of delivering products to its customers. We model it as a data-driven distributionally robust optimization approach to the capacitated vehicle routing problem. We assume the marginals of the defined uncertainty vector are known, but the joint distribution is difficult to estimate. The presence of customers and available occasional drivers can be random. We adopt a strategic planning perspective, where an optimal a priori solution is calculated before the uncertainty is revealed. Therefore, without the need for online resolution performance, we can experiment with exact solutions. Solving the problem defined above is challenging: not only the first-stage problem is already NP-Hard, but also the uncertainty and potentially the second-stage decisions are binary of high dimension, leading to non-convex optimization formulations that are complex to solve. We propose a branch-price-and-cut algorithm taking into consideration measures that exploit the intrinsic characteristics of our problem and reduce the complexity to solve it.

Scope and Mission

Recent advances in high-throughput technologies have given rise to collecting large amounts of multidimensional heterogeneous data that provide diverse information on the same biological samples. Integrative analysis of such multisource datasets may reveal new biological insights into complex biological mechanisms and therefore remains an important research field in systems biology. Most of the modern integrative clustering approaches rely on independent analysis of each dataset and consensus clustering, probabilistic or statistical modeling, while flexible distance-based integrative clustering techniques are sparsely covered. We propose two distance-based integrative clustering frameworks based on bi-level and bi-objective extensions of the p-median problem. A hybrid branch-and-cut method is developed to find global optimal solutions to the bi-level p-median model. As to the bi-objective problem, an -constraint algorithm is proposed to generate an approximation to the Pareto optimal set. Every solution found by any of the frameworks corresponds to an integrative clustering. We present an application of our approaches to integrative analysis of NCI-60 human tumor cell lines characterized by gene expression and drug activity profiles. We demonstrate that the proposed mathematical optimization-based approaches outperform some state-of-the-art and traditional distance-based integrative and non-integrative clustering techniques.