The truckload industry faces a serious and chronic problem of high driver turnover rate—typically more than 100%—with staggering associated costs. Among the major causes of this problem are extended on-the-road times where drivers handle several truckload pickup and deliveries successively; nonregular schedules and get-home rates; and low utilization, i.e., less mileage/unit-time per driver, which leads to low pay. We consider the strategic design of a relay network that may potentially help to alleviate this problem by providing an efficient underlying network that facilitates an assignment of drivers to home bases (domiciles to which they stay close) and generation of more predictable schedules with continuity and higher get-home rates. In relay network design, we are interested in determining a number of relay point locations, assigning network nodes to these relay points (i.e., defining domiciles), and determining the actual route (from the origin to the destination) for each truckload on the network. In doing so, we explicitly consider driver tour lengths, load imbalance at relay points, and the percentage circuity constraints. We develop an efficient Benders' decomposition-based algorithm that is significantly enhanced via strengthened Benders' cuts, cut disaggregation schemes, heuristics for improved upper bounds, and surrogate constraints. Our approach provides the ability to solve large size instances within reasonable solution times and very small optimality gaps. We also examine the effects of changes in the problem parameters on the performance of solution algorithms. Furthermore, in our computational experiments, we provide an analysis of the conditions for which relay network presents most benefits as well as incorporation of direct shipments within relay network operations.
This paper develops a mathematical model for intermodal freight transportation. It focuses on determining the flow of goods, the number of vehicles, and the transferred volume of goods transported from origin points to destination points. The model of this article is to minimize the total cost, which consists of fixed costs, transportation costs, intermodal transfer costs, and CO2 emission costs. It presents a mixed integer linear programming (MILP) model that minimizes total costs, and a fuzzy mixed integer linear programming (FMILP) model that minimizes imprecise total costs under conditions of uncertain data. In the models, node capacity, detour, and vehicle utilization are incorporated to estimate the performance impact. Additionally, a computational experiment is carried out to evaluate the impact of each constraint and to analyze the characteristics of the models under different scenarios. Developed models are tested using real data from a case study in Southern Vietnam in order to demonstrate their effectiveness. The results indicate that, although the objective function (total cost) increased by 20%, the problem became more realistic to address when the model was utilized to solve the constraints of node capacity, detour, and vehicle utilization. In addition, on the basis of the FMILP model, fuzziness is considered in order to investigate the impact of uncertainty in important model parameters. The optimal robust solution shows that the total cost of the FMILP model is enhanced by 4% compared with the total cost of the deterministic model. Another key measurement related to the achievement of global sustainable development goals is considered, reducing the additional intermodal transfer cost and the cost of CO2 emissions in the objective function.
High driver turnover and driver shortage are costly problems in the truckload trucking industry. Extended on-the-road times and low quality of life with irregular schedules and low get-home rates for drivers are commonly attributed as the main culprits in both academic and industry literature. The use of a relay network on which the truckloads switch drivers during their transportation can potentially help reduce drivers’ away-from-home times and regularize their schedule without sacrificing the mileage accumulation on which their pay is determined. Relay network design involves the determination of the relay point (RP) locations, their interconnections, assignment of non-RP nodes to RPs, and the routes for truckloads. Recognizing the importance of considering operational realities such as empty mileage and driver availability along with limited resources, we introduce link capacity constraints and the concept of link imbalance in strategic relay network design. The use of link imbalance is motivated by the need to improve operational efficiency via increased ability to return drivers to their home bases and reduce empty backhauls. To solve our mixed-integer programming design model, we develop an efficient Lagrangean decomposition algorithm that can provide solutions to large-size problems with small optimality gaps within reasonable runtimes. We also present computational experiments on the algorithmic performance, trade-offs between imbalance and cost components, effects of capacity, and the relationship between link- and node-imbalance concepts. The online appendix is available at https://doi.org/10.1287/trsc.2016.0704 .
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