Scheduling the charging periods for a large set of electric vehicles with the objective of satisfying the user demands may be a very hard problem due to the physical constraints of the charging stations. In this paper, we consider a problem of this family which is motivated by a real life situation where a set of users demand electric charge while their vehicles are parked. Each stall has a charging point which is connected to one of the lines of a three-phase electric feeder. There are power constraints that limit the number of vehicles that can be charging at the same time on the same line and balance constraints that limit the difference in the number of vehicles charging in every two lines. We model this problem in the framework of Dynamic Constraint Satisfaction Problem (DCSP) with Optimization, and propose a solution procedure that requires solving a sequence of CSPs over time. Each one of these CSPs requires in its turn solving three instances of a one machine sequencing problem with variable capacity. This procedure was implemented on a simulator of the charging station and evaluated on a number of instances defined from different scenarios of vehicle arrivals and energy requirements. The results of the experimental study show clearly that the proposed algorithm is effective and that it produces schedules much better than those computed by a classic dispatching rule.

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Abstract. We consider the fuzzy job shop problem, where uncertain durations are modelled as fuzzy numbers and the objective is to minimise the expected makespan. A recent local search method from the literature has proved to be very competitive when used in combination with a genetic algorithm, but at the expense of a high computational cost. Our aim is to improve its efficiency with an alternative rescheduling algorithm and a makespan lower bound to prune non-improving neighbours. The experimental results illustrate the success of our proposals in reducing both CPU time and number of evaluated neighbours.

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This paper is concerned with local search methods to solve job shop scheduling problems with uncertain durations modelled as fuzzy numbers. Based on a neighbourhood structure from the literature, a reduced set of moves and the consequent structure are defined. Theoretical results show that the proposed neighbourhood contains all the improving solutions from the original neighbourhood and provide a sufficient condition for optimality. Additionally, a makespan lower bound is proposed which can be used to discard neighbours. Experimental results illustrate the good performance of both proposals, which considerably reduce the computational load of the local search, as well as a synergy effect when they are simultaneously used.