The two-flight low risk helicopter transportation problem under the split pickup scenario

The paper considers a special class of routing problems with the objective of minimizing the passengers risk. A major area of application of the low risk models is helicopter transportation widely used in the petroleum industry. In general, the total risk is considered to be proportional to the number of passengers exposed to landings and takeoffs during several multi-leg flights. We give a review of most of the studied models and demonstrate their links with the known problems of combinatorial optimization, such as the minimum latency problem, the multiple deliverymen problem, single machine and parallel machine scheduling, etc. In this paper, we focus on the problem of minimizing total risk, provided that the pickup from a number of locations is performed by two flights, and it is allowed that a location is visited by both flights, splitting the pickup demand. We show that the problem in NP-hard and admits a pseudopolynomial-time dynamic programming algorithm. We also develop a fully polynomial-time approximation scheme and a fast 5/4-approximation algorithm. The results of computational experiments with our algorithms are reported.