This article proposes a risk assessment method based on interval intuitionistic integrated cloud Petri net (IIICPN). The cloud model is widely used in data mining and knowledge discovery, especially in risk assessment problems with linguistic variables. However, the cloud models proposed in the literature do not express interval-valued intuitionistic linguistic satisfactorily, and the reasoning methods based on the cloud models cannot perform risk assessment well. The work in this article includes the definition of IIIC and IIICPN, the method of converting the interval-valued intuitionistic uncertain linguistic numbers into IIIC, and the reasoning method of IIICPN. As proofs, a subway fire accident model is adopted to confirm the feasibility of the proposed method, and comparison experiments between the IIICPN with general fuzzy Petri net and the trapezium cloud model are conducted to verify the superiority of the proposed model.

We investigate the discrete parallel machine scheduling and location problem, which consists of locating multiple machines to a set of candidate locations, assigning jobs from different locations to the located machines, and sequencing the assigned jobs. The objective is to minimize the maximum completion time of all jobs, that is, the makespan. Though the problem is of theoretical significance with a wide range of practical applications, it has not been well studied as reported in the literature. For this problem, we first propose three new mixed-integer linear programs that outperform state-of-the-art formulations. Then, we develop a new logic-based Benders decomposition algorithm for practical-sized instances, which splits the problem into a master problem that determines machine locations and job assignments to machines and a subproblem that sequences jobs on each machine. The master problem is solved by a branch-and-cut procedure that operates on a single search tree. Once an incumbent solution to the master problem is found, the subproblem is solved to generate cuts that are dynamically added to the master problem. A generic no-good cut is first proposed, which is later improved by some strengthening techniques. Two optimality cuts are also developed based on optimality conditions of the subproblem and improved by strengthening techniques. Numerical results on small-sized instances show that the proposed formulations outperform state-of-the-art ones. Computational results on 1,400 benchmark instances with up to 300 jobs, 50 machines, and 300 locations demonstrate the effectiveness and efficiency of the algorithm compared with current approaches. Summary of Contribution: This paper employs operations research methods and computing techniques to address an NP-hard combinatorial optimization problem: the parallel discrete machine scheduling and location problem. The problem is of practical significance but has not been well studied in the literature. For the problem, we formulate three novel mixed-integer linear programs that outperform state-of-the-art formulations and develop a new logic-based Benders decomposition algorithm. Extensive computational experiments on 1,400 benchmark instances with up to 300 jobs, 50 machines, and 300 locations are conducted to evaluate the performance of the proposed models and algorithms.

It is challenging to perform emergency scheduling for fighting forest fires subject to limited rescue resources (i.e., vehicles with fire engines), since extinguishing each fire point should take into account multiple factors, such as the actual fire spreading speed, distance from fire engine depot to fire points, fire-fighting speed of fire engines, and the number of dispatched vehicles. This paper investigates a bi-objective rescue vehicle scheduling problem for multi-point forest fires, which aims to optimally dispatch a limited number of fire engines to extinguish fires. The objectives are to minimize the total fire-extinguishing time and the number of dispatched fire engines. For this problem, we first develop an integer program that is an improved and simplified version of an existing one. After exploring some properties of the problem, we develop an exact dynamic programming algorithm and a fast greedy heuristic method. Computational results for a real-life instance, and benchmark and large-size randomly generated instances confirm the effectiveness and efficiency of the proposed model and algorithms. Besides, a bi-objective integer program is developed to address the multi-depot fire engine scheduling issue.

Limited resources are a prevalent and challenging problem in the field of emergency management. Emergency scheduling is an effective way to make full use of resources. However, designing an effective emergency plan to minimize rescue time is a major challenge. This study focuses on large-scale emergency scheduling for fighting forest fires with multiple rescue centers (depots) and limited fire-fighting resources, which aims to determine the optimal rescue route of fire-fighting teams at multiple rescue centers to minimize the total completion time of all fire-fighting tasks. For this problem, we first assign rescue priorities to different fire points according to the speed of the fire spread. Then, we formulate it into a mixed-integer linear programming (MILP) model and analyze its NP-hard complexity. To deal with large-scale problems, a new fast and effective artificial bee colony algorithm and variable neighborhood search combined algorithm is proposed. Extensive experimental results for large-scale randomly generated instances confirm the favorable performance of the proposed algorithm by comparing it with MILP solver CPLEX, genetic algorithms, and particle swarm optimization algorithms. We also derive some management insights to support emergency management decision-making.