Lower bounds for the scheduling problem with uncertain demands

This paper proposes various lower bounds to the makespan of the flexible job shop scheduling problem (FJSP). The FJSP is known in the literature as one of the most difficult combinatorial optimisation problems (NP-hard). We will use genetic algorithms for the optimisation of this type of problems. The list of the demands is divided in two sets: the actual demand, which is considered as certain (a list of jobs with known characteristics), and the predicted demand, which is a list of uncertain jobs. The actual demand is scheduled in priority by the genetic algorithm. Then, the predicted demand is inserted using various methods in order to generate different scheduling solutions. Two lower bounds are given for the makespan before and after the insertion of the predicted demand. The performance of solutions is evaluated by comparing the real values obtained on many static and dynamic scheduling examples with the corresponding lower bounds

A multi-period shelter location-allocation model with evacuation orders for flood disasters

Floods are a significant threat for several countries, endangering the safety and the well-being of populations. Civil protection authorities are in charge of flood emergency evacuation, providing means to help the evacuation and ensuring that people have comfortable and safe places to stay. This work presents a multi-period location-allocation approach that identifies where and when to open a predefined number of shelters, when to send evacuation orders, and how to assign evacuees to shelters over time. The objective is to minimize the overall network distances that evacuees have to travel to reach the shelters. The multi-period optimization model takes into account that the travel times vary over time depending on the road conditions. People’s reaction to the flood evolution is also considered to be dynamic. We also assume that shelters become available in different time periods and have a limited capacity. We present a mathematical formulation for this model which can be solved using an off-the-shelf commercial optimization solver, but only for small instances. For real size problems, given the dynamic characteristics of the problem, obtaining an optimal solution can take several hours of computing time. Thus, a simulated annealing heuristic is proposed. The efficiency of the heuristic is demonstrated with a comparison between the heuristic and the solver solutions for a set of random problems. The applicability of the multi-period model and of the heuristic is illustrated using a case study which highlights the importance and the benefits of adopting a dynamic approach for optimizing emergency response operations

Post-disaster multi-period road network repair: work scheduling and relief logistics optimization

We develop a multi-period bi-level programming model for the post-disaster road network repair work scheduling and relief logistics problem. A maximum relative satisfaction degree-based steady-state parallel genetic algorithm is designed to solve this model. In order to validate and test the effectiveness of the presented mathematical model and method, we use a network generator to create numerical examples with different scales and characteristics of road network. Our numerical analysis of the solutions shows that the proposed mathematical model and method can effectively assist the decision-makers to deal with the road network repair work scheduling and relief logistics optimization problem during the emergency response phase. This mathematical model and the approach being developed are applied to deal with the case of Wenchuan earthquake in China. The results show that the required CPU time is short enough such that it meets the time limitation in the emergency response phase, and the strategy of road network repair scheduling will allow repair of the damaged roads to be completed before the end of the planning time horizon by 14.93%. Furthermore, the strategy of relief logistics can provide an efficient relief allocation and transportation path