Model for Network Assignment Problem of Capacitated Freight with Disruptions Integer Multicommodity Flow with Recourse

mends the use of travel time values for congested periods that are 2.5 times the value of time estimates during uncongested periods (7). Kawamura investigated differences in value of time among operators and trucking industry segments; findings from Kawamura’s research show that freight carriers have a value of time that is several times higher than that of passenger vehicles and that there is significant heterogeneity among carriers (8). Therefore, for accurate modeling of the impact of disruptions, a freight network assignment model must account for the variation in time value and associated costs under disruptions. Disruptions can provoke delays that result in longer travel times, higher fuel consumption, and loss of a driver’s productivity. Delays and congestion at bottlenecks not only affect a company’s bottom line but also increase greenhouse gas emissions and pollution levels (9). There is also heterogeneity in vehicle–driver costs. A recent study by the American Transportation Research Institute found that specialized carrier types have the highest cost per mile, followed by less-than-truckload and truckload carrier types (10). Hence, an assignment framework for freight networks must account for this variation in disruption and travel costs by commodity and carrier types. Transportation costs can be up to 10% of the final product costs (11). Supply chain costs can greatly exceed transportation-related disruption costs if companies rely heavily on lean practices, such as just-in-time deliveries, as well as increasingly long international transportation chains. Companies use sophisticated logistics systems to meet customer requirements without an overall increase in operating costs (12). Continuous real-time monitoring of shipment cost and delivery time is being used by companies to reduce transportation costs while avoiding costly delays or disruptions, high levels of safety stocks, and system redundancies (13). Continuous tracking and monitoring of vehicles and containers from origin to destination can increase shipment efficiency and profitability. Realtime information and adaptive routing can help companies maintain high levels of customer service with less cost than comparable assetor capital-intensive strategies that rely on redundant vehicles or capacity. This paper develops an integer multicommodity flow with recourse formulation to capture the adaptive routing behavior of freight decision makers (FDM), shippers, and carriers and that incorporates heterogeneity in response to disruptions and valuations of time cost by commodity type. This presents a new modeling framework that builds on the work of Unnikrishnan and Figliozzi (14). The essential difference between this paper and that earlier work is that capacity constraints are applied to every link of the network noticeably; the addition of capacity constraints makes the problem A modeling framework is proposed for the freight network assignment problem with recourse, network travel time and cost disruptions, and link flow capacity constraints. “Recourse” is defined as the ability of a user to reconsider and adapt his or her routing decisions in response to newly acquired information about network disruption. When real-time tracking and monitoring of network shipments allow companies a routing recourse, network capacity must be simultaneously considered. If a disruption significantly alters network flows, the capacity of alternative or secondary routes may be quickly reached. A new freight mathematical model with a capacitated network and adaptive routing was developed and solved. Results showed that simultaneous consideration of recourse and capacity constraints was superior to benchmark results obtained with nonadaptive deterministic behavior.