Exact models for selection problems: from clinical trials to network design

Discrete optimization is becoming an increasingly important tool for solving problems in the real world. The matching problem and the network design problem are two well studied selection problems in this area. They can be considered as modelling relations between nodes of a bi-graph or a graph, respectively.<br><br>Using acute stroke trials as a context, the assignment algorithm is utilized to investigate a complex relationship between the overall degree of individual matching, the size of samples, and the quality of matching on variables. It is concluded that the post-hoc individual matching in parallel group randomized clinical trials cannot be recommended as a technique for treatment effect estimation.<br><br>Based on the concept of the transshipment problem we proposed a mixed integer programming model to solve the asymmetric traveling salesman problems. The formulation is extendable to other transportation scheduling problems which are related to the traveling salesman problem (TSP) such as the Multiple TSP (m-TSP) and the Selective TSP (STSP). In addition to avoiding any cycles and being easy to implement, the model has a reasonable order of space complexity. It can be built on either a directed graph or an undirected graph.<br><br>The reserve network design problem is a variation of the STSP which maximizes some utilities subject to various constraints. These constraints include a budget limitation and spatial attributes such as connectivity and compactness. The proposed model achieves the contiguity and to some extent compactness attributes. It does this without incurring the problem of sub-tours and requiring any regular shape assumptions. Furthermore, where full connectivity is not required, the model enables the trade-off between the number of contiguous areas and utility to be determined easily.<br><br>The combinatorial structure of the reserve network design problem places it in the category of NP-hard problems which have exponential time complexity. We explored approaches to reduce the computational effort and introduced an approach with improved efficiency. Using this approach, the experimental results show the solution time significantly reduced on average.<br>