A 0--1 LP Model for the Integration and Consolidation of Air Cargo Shipments

This paper addresses the problem of determining the optimal integrations and consolidations of air cargo shipments. A freight forwarder arranges for the execution of many jobs (shipments) on behalf of several clients. Each job consists of a number of sequential activities, such as pickup, truck transportation, warehousing, and air transportation. Each activity can be performed by a number of processing units, such as trucking companies, warehouses, and airlines. If a number of consecutive activities of a job are integrated, i.e., performed by the same processing unit, then it typically costs less. If a number of similar activities of different jobs are consolidated, i.e., performed by the same processing unit, then it also typically costs less. Given a number of jobs and processing units, the sets of activities that can be integrated and consolidated, and the associated costs, the decision problem is to determine which processing unit should perform each activity of each job to minimize the total cost. This problem of assigning shipment activities to processing units is formulated as a linear 0--1 program. Principal properties of the model are established. Exploiting the special structure of this model, we design a solution procedure that includes heuristics and a branch-and-bound algorithm.