Capacity management of forwarder with multiple carriers under uncertain flight travel time and stochastic shipment demand
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Abstract
Abstract Consider a freight forwarder who obtains cargo space from multiple carriers. Some capacities are reserved long term in advance through allotment contracts, while some are booked on short‐term daily basis. A unified mathematical program for both short‐ and long‐term problems under uncertainties is proposed. Demands are modeled using a probability distribution as in the stochastic program, whereas flight travel times belong to an uncertainty set as in robust optimization. In the first stage, the allotments are determined. In the second stage, the shipment demand materializes but the travel time is still unknown, the forwarder determines the daily allocation among flights, given the first‐stage allotment. The objective is to minimize the expected total cost in the two stages. We derive a closed‐form solution for a special case, propose a heuristic for a general case, and evaluate its performance via numerical experiments, whose historical records came from one of the largest Thai forwarders.
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