Abstract: Given a discretized representation of an ore body known as a block model, the open pit mining production scheduling problem that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. Although it has been established that this problem can be modeled with mixed-integer programming, the number of blocks used to represent real-world mines (millions) has made solving large instances nearly impossible in practice. In this article, we introduce a new methodology for tackling this problem and conduct computational tests using real problem sets ranging in size from 20,000 to 5,000,000 blocks and spanning 20 to 50 time periods. We consider both direct block scheduling and bench-phase scheduling problems, with capacity, blending, and minimum production constraints. Using new preprocessing and cutting planes techniques, we are able to reduce the linear programming relaxation value by up to 33%, depending on the instance. Then, using new heuristics, we are able to compute feasible solutions with an average gap of 1.52% relative to the previously computed bound. Moreover, after four hours of running a customized branch-and-bound algorithm on the problems with larger gaps, we are able to further reduce the average from 1.52% to 0.71%.

Abstract: We develop a heuristic for the consistent vehicle routing problem with time windows (ConVRPTW), which is motivated by a real-world application at a food company's distribution center. Besides standard VRPTW restrictions, ConVRPTW assigns each customer just one driver to fulfill his or her orders during the whole multiperiod planning horizon. For each driver and period, a route is sought to serve all their customers with positive demand. For each customer, the number of periods between consecutive orders and the ordered quantities is highly irregular. This causes difficulties in the daily routing, negatively impacting the service level of the company. Similar problems have been studied as ConVRP, where the number of drivers is fixeda priori, and only the total travel time is minimized. Moreover, the clients present no time window constraints, but the visits should be scheduled with a small arrival time variation. In our model, the objective is to minimize the number of drivers. We impose hard time windows but do not consider time consistency in more detail. We compare solutions given by the heuristic with solutions of a mixed-integer linear programming model on a set of small artificial instances and solutions used by the food company on real-world instances. The results show the effectiveness of the heuristic. For the company, we obtain significant improvements in the routing plans, with a lower number of vehicles and a higher rate of orders delivered within the prescribed time window.

Abstract: A line balancing problem considers the assignment of operations to workstations in an assembly line. While assembly lines are usually associated to mass production of standardised goods, their advantages have led to their widespread use whenever a product-oriented production system is applicable and the benefits of the labour division and specialisation are significant, even when some of its characteristics may deviate from classical assembly lines. In this work, we study a line balancing problem found in the textile industry in which the line must be balanced for multiple types of goods taking into account resource requirements. In order to solve the problem, a hybrid method that combines classical methods for line balancing with an Estimation of Distribution Algorithm is proposed. Computational experiments show that the new procedure improves upon the state of the art when compared using a benchmark set derived from the literature, as well as when compared using data from the manufacturer that originated this research work.

Abstract: Availability, defined as the fraction of time a network service is operative, is a key network service parameter. Dedicated protection increases availability but also the cost. Shared protection instead decreases the cost, but also the availability. In this article, we formulate and solve an integer linear programming (ILP) model for the problem of minimizing the backup resources required by a shared-protected static optical network whilst guaranteeing an availability target per connection. The main research challenge is dealing with the nonlinear expression for the availability constraint. Taking the working/backup routes and the availability requirements as input data, the ILP model identifies the set of connections sharing backup resources in any given network link. We also propose a greedy heuristic to solve large instances in much shorter time than the ILP model with low levels of relative error (2.49% average error in the instances studied) and modify the ILP model to evaluate the impact of wavelength conversion. Results show that considering availability requirements can lead up to 56.4% higher backup resource requirements than not considering them at all, highlighting the importance of availability requirements in budget estimation. (C) 2016 Wiley Periodicals, Inc.