Facets of the axial three-index assignment polytope

We revisit the facial structure of the axial 3-index assignment polytope. After reviewing known classes of facet-defining inequalities, we present a new class of valid inequalities, and show that they are facets of this polytope. This answers a question posed by Qi and Sun~\cite{QiSun00}. Moreover, we show that we can separate these inequalities in polynomial time

Understanding electric vehicle charging behaviours

The UK Government has announced its intention to ban the sales of internal combustion cars and vans from 2035. Ofgem's Decarbonisation Action Plan states that GB electricity network operators should have a network that can power 10 million electric vehicles by 2030. It is widely recognized and acknowledged that stress on current electricity networks can be alleviated with smart technologies, which enable smart demand management using advanced predictive analytics, such as accurate forecasting algorithms, and prescriptive analytics, such as advanced load balancing and optimization algorithms. To successfully utilize analytical models for charging electric vehicles at scale it is essential for these models to inherently capture vehicle users' interaction with charging infrastructure, both personal and public. Hence the need for understanding charging behaviours and the factors that influence these behaviours. The aim of this project is to utilize public and home charging data to develop a finer understanding of charging behaviours and influencing factors, and explore algorithmic frameworks that embed these behaviours in realizing large scale smart charging solutions

Approximating the multi-level bottleneck assignment problem.

We consider the multi-level bottleneck assignment problem (MBA). This problem is described in the recent book 'Assignment Problems' by Burkard et al. (2009) on pages 188-189. One of the applications described there concerns bus driver scheduling.We view the problem as a special case of a bottleneck m-dimensional multi-index assignment problem. We give approximation algorithms and inapproximability results, depending upon the completeness of the underlying graph. Keywords: bottleneck problem; multidimensional assignment; approximation; computational complexity; efficient algorithm.Bottleneck problem; Multidimensional assignment; Approximation; Computational complexity; Efficient algorithm;

Facets of the axial three-index assignment polytope

We revisit the facial structure of the axial 3-index assignment polytope. After reviewing known classes of facet-defining inequalities, we present a new class of valid inequalities, and show that they define facets of this polytope. This answers a question posed by Qi and Sun (2000). Moreover, we show that we can separate these inequalities in polynomial time. Finally, we assess the computational relevance of the new inequalities by performing (limited) computational experiments

Revisiting surrogate relaxation for the multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is a classic problem in combinatorial optimisation. Several authors have proposed to use surrogate relaxation to compute upper bounds for the MKP. In their papers, the surrogate dual is solved heuristically. We show that, using a modern dual simplex solver as a subroutine, one can solve the surrogate dual exactly in reasonable computing times. On the other hand, the resulting upper bound tends to be strong only for relatively small MKP instances