Most earth observation satellites are equipped with optical sensors, which cannot see through clouds. Hence, many observations will be useless due to the presence of clouds. In this paper, we study the scheduling problem of multiple EOSs under uncertainties of clouds. In order to improve the possibility of completing tasks, we take the scheduling of each task to multiple resources (orbits) into account and establish a novel nonlinear mathematical model. To solve the problem efficiently, an exact algorithm based on enumeration is proposed, in which each subproblem is solved by path programming, and all the feasible solutions of subproblems are combined to solve the master problem. Furthermore, three heuristics are designed to solve the large-scale problems. From the experimental results on random samples, it is observed that the solutions of our model perform better than those of the previous studies. Besides, both our exact algorithm and a mixed-integer nonlinear programming solver-Couenne can solve our model optimally for small problems, but our algorithm is more efficient than Couenne. For large-scale problems, we reveal the strengths and weaknesses of the proposed heuristic algorithms while solving different instances of various sizes.

Resource allocation is one of the core issues in project scheduling to ensure the effective use of scare renewable resources, and has been regularly encountered in production systems in the manufacturing and service industries. The transfers of renewable resources between activities generally incur certain scheduling costs and affect the robustness of a certain schedule in an uncertain environment. To address this issue, a bi-objective optimisation model is proposed to make the resource transfer decisions, which aims to minimise the transfer cost and maximise solution robustness in the presence of activity duration variability. The proposed model employs a novel resource-oriented flow formulation that is different from those of the previous literature. A NSGA-II and a Pareto simulated annealing (PSA) algorithm have been applied as the solution methodologies. Besides, the effectiveness of the metaheuristics are evaluated in comparison with a $\epsilon$-constraint method. In detail, the algorithms are carried out on a set of benchmarks and are compared to test their efficiencies based on four performance metrics: number of non-dominated solutions, general distance, hypervolume and spacing. Finally, a case study of a real project further indicates that the suggested model and algorithms are applicable and beneficial to the problem in practice.

This article addresses the project scheduling and the materials ordering problem (PSMOP) with uncertain activity durations. A two-stage optimisation approach is proposed to generate a robust schedule in order to protect the project execution from the duration uncertainty. First of all, a mixed-integer programming model under a deterministic environment is formulated to address this issue, which aims to minimise the corresponding costs and is solved by the genetic algorithm (GA). Second, a robust project scheduling integrated with materials ordering method (RPSMOM) is developed to build a proactive schedule on the basis of the baseline schedule generated by the given deterministic model. In this method, a novel index that measures the risk of activity delay (RAD) is suggested by taking the uncertain activity durations into account. Finally, computational experiments are conducted under different levels of activity duration uncertainty. The results demonstrate that the integrated proactive scheduling method is highly effective in decreasing the total cost and improving the robustness of the project schedule in most circumstances.