Scheduling with fixed maintenance, shared resources and nonlinear feedrate constraints: A mine planning case study Given a short term mining plan, the task for an operational mine planner is to determine how the equipment in the mine should be used each day. That is, how crushers, loaders and trucks should be used to realise the short term plan. It is important to achieve both grade targets (by blending) and maximise the utilisation (i.e., throughput) of the mine. The resulting problem is a nonlinear scheduling problem with maintenance constraints, blending and shared resources. In this paper, we decompose this problem into two parts: the blending, and the utilisation problems. We then focus our attention on the utilisation problem. We examine how to model and solve it using alternative approaches: specifically, constraint programming, MIQP and MINLP. We provide a repair heuristic based on an outerapproximation, and empirically demonstrate its effectiveness for solving the realworld instances of operational mine planning obtained from our industry partner.

A LazyConstraints Approach to ResourceConstrained Project Scheduling We study the complex combinatorial optimization problem to schedule the activities of a single project with the objective to complete the project within the shortestpossible amount of time such that the limited resource capacities as well as the prescribed precedence relations between pairs of the activities are taken into account. In addition to various specific solution algorithms, the related literature proposes several MixedInteger Linear Programming (MILP) models, but these models remain complex to solve even for smallsized instances. We present a novel approach based on an MILP model in which the resourcecapacity constraints are formulated for all inclusionminimal sets of activities which, due to the limited capacities of the resources, cannot be processed simultaneously. We propose to remove these constraints from the model and iteratively add those constraints back which are violated in the solutions obtained. For a set of test instances from the literature, our computational results indicate that with respect to both, the deviation of the project duration obtained from the lower bound devised from the criticalpath length and the number of instances solved to optimality, the novel lazyconstraints approach outperforms ten stateoftheart MILP models.