A hybrid algorithm for large-scale non-separable nonlinear multicommodity flow problems

We propose an approach for large-scale non-separable nonlinear multicommodity flow problems by solving a sequence of subproblems which can be addressed by commercial solvers. Using a combination of solution methods such as modified gradient projection, shortest path algorithm and golden section search, the approach can handle general problem instances, including those with (i) non-separable cost, (ii) objective function not available analytically as polynomial but are evaluated using black-boxes, and (iii) additional side constraints not of network flow types. Implemented as a toolbox in commercial solvers, it allows researchers and practitioners, currently conversant with linear instances, to easily manage large-scale convex instances as well. In this article, we compared the proposed algorithm with alternative approaches in the literature, covering both theory and large test cases. New test cases with non-separable convex costs and non-network flow side constraints are also presented and evaluated. The toolbox is available free for academic use upon request

The scope for pavement porters: addressing the challenges of last-mile parcel delivery in London

The UK parcel sector generated almost £9 billion in revenue in 2015, with growth expected to increase by 15.6% in 2019 and is characterized by many independent players competing in an ‘everyone-delivers-everywhere’ culture leading to much replication of vehicle activity. With road space in urban centers being increasingly reallocated to pavement widening, bus and cycle lanes, there is growing interest in alternative solutions to the last-mile delivery problem. We make three contributions in this paper: firstly, through empirical analysis using carrier operational datasets, we quantify the characteristics of last-mile parcel operations and demonstrate the reliance placed on walking which can make up over 60% of the round time; secondly we introduce the concept of ‘portering’ where vans rendezvous with porters who operate within specific ‘patches’ to service consignees on-foot, potentially saving 86% in driving distance on some rounds; finally, we highlight the wider practical issues and optimization challenges associated with operating driving and portering rounds in inner urban areas