Shipment Consolidation in Hub Location Modelling

Abstract

This thesis examines the integration of shipment consolidation and inventory holding decisions with the design of hub networks, where a heterogeneous fleet is used for inter-hub transportation. These problems aim to determine the optimal locations of hubs, allocate demand nodes to them, decide the quantity of inventory to be held at hubs, and assign vehicles from the heterogeneous fleet to operate on hub arcs. This is done while considering inventory storage space at hubs and vehicle capacities. These decisions are made to fulfill a set of demands for flows between origin-destination pairs, distributed across a multi-period planning horizon. Prospective applications of this work include air cargo, less-than-truckload transportation, express shipments, and postal delivery systems.

The first problem studies shipment consolidation and inventory holding in a single allocation hub location problem, which considers a promised delivery time for goods. The goal is to jointly determine the optimal hub locations, allocation of demand nodes to hubs, inventory levels to be held at hubs in each time period, and the type and number of vehicles to be dispatched on inter-hub links in different periods. The objective is to minimize the total cost of infrastructure, transportation, and inventory holding. This problem is formulated as a mixed-integer programming model. To solve larger instances, we propose a variable neighborhood search-based algorithm that incorporates a shipment consolidation sub-problem. Computational experiments with varying parameter values, conducted on a realistically created dataset, demonstrate the comparative effectiveness of the networks generated by both the model and algorithm.

The second problem in this thesis explores the integration of operational decisions regarding shipment consolidation and inventory holding within a hub arc location model for a freight network. In contrast to the first problem, the focus is on locating hub arcs rather than hub nodes. The allocation of demand nodes to multiple hub arcs is allowed in this setting for greater flexibility in routing and consolidation, and the optimal frequency and types of vehicles operating on those hub arcs are also to be determined. A mixed-integer programming model is proposed to minimize the total cost of hub arcs, transportation, and inventory. It determines the optimal location of hub arcs, allocation of demand nodes to these arcs, inventory levels at the origin nodes of hub arcs in each time period, and the type and frequency of vehicles from a heterogeneous fleet to operate on the hub arcs. To solve the problem efficiently, a Benders decomposition-based methodology is developed and further enhanced with Pareto-optimal cuts and two variable fixing techniques. Computational experiments compare the effectiveness of the proposed solution algorithm against a commercial solver and provide insights into the factors influencing these decisions.

The third problem addresses demand uncertainty in the hub arc location problem, integrated with decisions on shipment consolidation and inventory holding. The aim is to minimize total expected costs of infrastructure, transportation, and inventory, modelling the problem as a two-stage stochastic program. The first-stage decisions involve selecting hub arcs and determining the types and frequencies of vehicles. In the second stage, nodes are assigned to hub arcs, and decisions are made on inventory holding and the optimal routing of flows. To solve this, a Sample Average Approximation methodology is employed. Computational experiments assess the algorithm’s convergence, explore the impact of varying costs and frequencies, and estimate the value of considering uncertainty on the decision-making process.