Collaborative Vehicle Routing Problem in the Urban Ring Logistics Network under the COVID-19 Epidemic

This paper explored the problem of collaborative vehicle routing in the urban ring logistics network (Co-VRP-URLN) during the COVID-19 epidemic. According to the characteristics of urban distribution and the restriction of traffic all over China during this period, this study mainly considers a common distribution mode of order exchange through the outer ring of the city and then solves the vehicle routing problem of distribution, which belongs to a special multidepot vehicle routing problem with time windows. According to the definition of the problem, the corresponding mixed-integer programming problem of multicommodity flow is established, and the variable neighborhood search algorithm is designed in detail to solve it. The effectiveness of the algorithm is verified by a standard example, and the benefits of joint distribution are revealed through the improved standard example. At last, the influence of different distribution centers is compared. The results show that this model can significantly improve the distribution efficiency within the city under the restriction of traffic.

Integrated Optimization of Port Rotation Direction and Fleet Deployment for Container Liner Shipping Routes

This paper provides an integrated planning methodology for the optimization of port rotation direction and fleet deployment for container liner shipping routes with consideration of demand uncertainty. We first consider a special case that demand is deterministic. A multicommodity flow network model is developed via minimizing the total network-wide cost. Its decisions are the selection of port rotation direction and fleet deployment and container routings in the shipping network. Afterward, we address the generic case that uncertain demand is considered, which is represented by potentially realizable demand scenarios. We develop a minimax regret model to procure the least maximum regret across all the demand scenarios. The proposed models are applied to an Asia-Europe-Oceania liner shipping network with 46 ports and 12 ship routes. Results could provide the liner company with a comprehensive decision tool to simultaneously determine port rotation direction and fleet deployment when tackling uncertain demand.

Maximum Multicommodity Flow with Intermediate Storage

The multicommodity flow problem deals with the transshipment of more than one commodity from respective sources to corresponding sinks without violating the capacity constraints. Due to the capacity constraints, flows out from the sources may not reach their sinks, and so, the storage of excess flows at intermediate nodes plays an important role in the maximization of flow values. In this paper, we introduce the maximum static as well as maximum dynamic multicommodity flow problems with intermediate storage. We present polynomial and pseudopolynomial time algorithms for the former and latter problems, respectively. We also present the solution procedures to these problems in contraflow network having symmetric as well as asymmetric arc transit times. We transform the solutions in continuous-time settings by using natural transformation.

An analytical solution to the multicommodity network flow problem with weighted random routing

We derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the non-uniform multicommodity flow problem under weighted random routing. We show the mean load at each node, net of its demand and normalized by its (weighted) degree, is a constant equal to the trace of the product of two matrices: the Laplacian of the demand matrix and the generalized inverse of the graph Laplacian. For the case of uniform demand, this constant reduces to the sum of the inverses of the non-zero eigenvalues of the graph Laplacian. We note that such a closed-form expression for the network capacity for the general multicommodity network flow problem has not been reported before, and even though (weighted) random routing is not a practical procedure, it enables us to derive a (tight) upper bound for the capacity of the network under more standard routing policies. Using this new expression, we compute network capacity for a sample of demand matrices for some prototypical networks, including uniform demand (one unit between all node pairs) and broadcast demand (one unit between a source node and each other node as destination), and finally derive estimates of the mean load in some asymptotic cases.

Cost-effective joint optimisation of BBU placement and fronthaul deployment in brown-field scenarios

In this work, one proposes a model to evaluate the optimal deployment of Centralised Radio Access Network (C-RAN) architecture elements, i.e. Base Band processing Units (BBUs) and fronthaul links, in a brown-field scenario, in which traditional base stations are already deployed and a physical network is present. The proposed optimisation framework jointly optimises BBU placement and accesses network infrastructures deployment. It clusterises the Remote Radio Heads in the scenario through a Multicommodity Flow approach and solves the minimum cost fronthaul network deployment through a Rooted Delay-Constrained Minimum Spanning Tree approach. Optical fibre and microwave links are considered as fronthaul infrastructures. The proposed optimisation framework is validated through a comparison with a theoretical output for a canonical scenario, being afterwards applied to a real scenario. A cost analysis for different scenario configurations is presented, and trade-offs and guidelines for a cost optimal deployment of C-RAN are provided. The analysis of results for the real scenario of the city of Lisbon and its surrounding areas shows that the delay budget in the fronthaul network highly impacts on capital expenditures as well as on operational ones. It is shown that a larger delay budget enables an annual cost reduction up to 72% in urban areas and 54% in rural ones.

Efficient Algorithms on Multicommodity Flow over Time Problems with Partial Lane Reversals

The multicommodity flow problem arises when several different commodities are transshipped from specific supply nodes to the corresponding demand nodes through the arcs of an underlying capacity network. The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow problem if it maximizes the flow at each time step. The earliest arrival transshipment problem is the one that satisfies specified supplies and demands. These flow over time problems are computationally hard. By reverting the orientation of lanes towards the demand nodes, the outbound lane capacities can be increased. We introduce a partial lane reversal approach in the class of multicommodity flow problems. Moreover, a polynomial-time algorithm for the maximum static flow problem and pseudopolynomial algorithms for the earliest arrival transshipment and maximum dynamic flow problems are presented. Also, an approximation solution to the latter problem is obtained in polynomial-time.

Cost-effective joint Optimisation of BBU Placement and Fronthaul Deployment in Brown-field Scenarios

In this work , one proposes a model to evaluate the optimal deployment of Centralised Radio Access Network (C- RAN ) architecture elements , i.e. Base Band processing Units ( BBUs ) and fronthaul links , in a brown- field scenario, in which traditional base stations are already deployed and a physical network is present. The proposed optimisation framework jointly optimises BBU placement and access network infrastructures deployment . It clusterises the Remote Radio Heads in the scenario through a Multicommodity Flow approach , and solves the minimum cost fronthaul network deployment through a Rooted Delay - Constrained Minimum Spanning Tree approach . Optical fibre and microwave links are considered as fronthaul infrastructures . The proposed optimisation framework is validated through a comparison with a theoretical output for a canonical scenario, being afterwards applied to a real scenario. A cost analysis for different scenario configurations is presented , and trade - offs and guidelines for a cost optimal deployment of C- RAN are provided . The analysis of results for the real scenario of the city of Lisbon and its surrounding areas shows that the delay budget in the fronthaul network highly impacts on capital expenditures as well as on operational ones . It is shown that a larger delay budget enables an annual cost reduction up to 72 % in urban areas and 54 % in rural ones .

Cost-effective joint Optimisation of BBU Placement and Fronthaul Deployment in Brown-field Scenarios

In this work , one proposes a model to evaluate the optimal deployment of Centralised Radio Access Network (C- RAN ) architecture elements , i.e. Base Band processing Units ( BBUs ) and fronthaul links , in a brown- field scenario, in which traditional base stations are already deployed and a physical network is present. The proposed optimisation framework jointly optimises BBU placement and access network infrastructures deployment . It clusterises the Remote Radio Heads in the scenario through a Multicommodity Flow approach , and solves the minimum cost fronthaul network deployment through a Rooted Delay - Constrained Minimum Spanning Tree approach . Optical fibre and microwave links are considered as fronthaul infrastructures . The proposed optimisation framework is validated through a comparison with a theoretical output for a canonical scenario, being afterwards applied to a real scenario. A cost analysis for different scenario configurations is presented , and trade - offs and guidelines for a cost optimal deployment of C- RAN are provided . The analysis of results for the real scenario of the city of Lisbon and its surrounding areas shows that the delay budget in the fronthaul network highly impacts on capital expenditures as well as on operational ones . It is shown that a larger delay budget enables an annual cost reduction up to 72 % in urban areas and 54 % in rural ones .