Inverse scheduling: applications in shipping

Abstract

Optimisation problems are concerned with finding optimal solutions with respect to some objective functions with given problem parameters. Inverse optimisation refers to the situation where the problem parameters are minimally adjusted so that a given feasible solution becomes an optimal solution with respect to the objective function. In this paper we study inverse optimisation of single-machine scheduling problems to minimise the total weighted completion time, whereby the processing times and the weights are minimally adjusted, respectively, so that a given feasible schedule becomes an optimal schedule, under the constraint that the objective value based on the adjusted parameters is no worse than that based on the original parameters. Three distance measures, namely L1-norm, L2-norm, and L∞-norm, are considered for each of the problems under study. Such scheduling problems are known as inverse scheduling, which has wide applications including berth allocation in quayside in shipping operations.