Abstract
This paper describes a study of planning vehicle routes for the collection of urban recyclable waste. The aim is to create collection routes for every day of the month, to be repeated every month, minimizing the operation cost. Two important features of the problem are the planning of a relatively long period of time and the separate collection of three types of waste. The collection operation was modelled in accordance to the practice of the company that manages the collection system. Heuristic techniques were developed to solve the model in three phases: definition of the geographic zones served by the vehicles, definition of the waste type to collect on each day of the month, definition of the collection routes. Preliminary results suggest that significant economies in collection costs are possible.

Abstract
Nesting problems are particularly hard combinatorial problems. They involve the positioning of a set of small arbitrarily-shaped pieces on a large stretch of material, without overlapping them. The problem constraints are bidimensional in nature and have to be imposed on each pair of pieces. This all-to-all pattern results in a quadratic number of constraints. Constraint programming has been proven applicable to this category of problems, particularly in what concerns exploring them to optimality. But it is not easy to get effective propagation of the bidimensional constraints represented via finite-domain variables. It is also not easy to achieve incrementality in the search for an improved solution: an available bound on the solution is not effective until very late in the positioning process. In the sequel of work on positioning non-convex polygonal pieces using a CLP model, this work is aimed at improving the expressiveness of constraints for this kind of problems and the effectiveness of their resolution using global constraints. A global constraint "outside" for the non-overlapping constraints at the core of nesting problems has been developed using the constraint programming interface provided by Sicstus Prolog. The global constraint has been applied together with a specialized backtracking mechanism to the resolution of instances of the problem where optimization by Integer Programming techniques is not considered viable. The use of a global constraint for nesting problems is also regarded as a first step in the direction of integrating Integer Programming techniques within a Constraint Programming model.

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