Facilities layout is concerned with the spatial arrangement of a set of departments or equipment items. This is an important stage at the design level, which often results in a complex problem due to the high number of decisions involved. A Mixed Integer Linear Programming (MILP) formulation, for the optimal layout of facilities within a two-dimensional (2D) continuous space has been developed (Barbosa-Póvoa et al . 2001). In this paper, the proposed model is extended to account for the location of equipment units within a 3D multi-floor continuous space. Different topological characteristics are considered such as equipment items orientation, distance restrictions, equipment connectivity inputs and outputs, rectangular and irregular equipment shapes, space availability and multifloor locations. In operational terms, production or operational sections are modelled as well as safety and operability restrictions. The final model is again described as a MILP where binary variables characterize topological choices and continuous variables describe the distances and locations involved. Finally, the applicability of the proposed formulation is shown through the resolution of a set of representative examples exploring the different model characteristics.

Layout is an important aspect of the design of industrial plants. In this paper a mathematical model is presented for the design of efficient and generic industrial layouts where a simultaneous solution of the block and detailed layout problem is considered. The optimal plant layout is obtained based on the minimization of the connectivity cost. Connectivity can describe simple pipe connections, guided vehicles or conveyors amongst others. Different topological characteristics are considered such as different equipment orientations, distance restrictions, non-overlapping constraints, different equipment connectivity inputs and outputs, irregular equipment shapes and space availability over a two-dimensional continuous area. In operational terms, production together with operational sections are modelled as well as safety and operability restrictions. A Mixed-Integer Linear Problem (MILP) is developed where binary variables are introduced to characterize topological choices and continuous variables describe the distances and locations involved. To conclude, the applicability of the proposed formulation is illustrated via a set of representative examples.

Aim of study: In this paper, we present a decision support system (DSS) to support decision making where different stakeholders have to generate landscape and forest level strategic plans. We further present an interactive approach that may take advantage of a posteriori preference modelling (i.e. Pareto frontier technique) to facilitate the specification of the levels of achievement of various objectives.Area of study: The approach was applied to one planning cycle of a real world study case, the Leiria National Forest in Portugal. The Leiria National Forest, a managed area of approximately eleven thousand hectares in which 8,679 hectares are even aged stands of maritime pine (Pinus pinaster Ait) aimed at the production of wood.Material and methods: The interactive approach, at first, tries to generate Pareto efficient frontiers for different objectives. Then, multiple decision makers are involved in the process to seek an agreement towards the definition of a consensual strategic plan.Main results: The system developed in this article integrates an information management subsystem, a module to generate alternative management regimes, growth model routines and a decision module that generates and solves mathematical formulations. It also provides a module to display reports and view the resulting solutions (management plans). We also build the Pareto frontier for different criteria. The results show that the proposed DSS can help solve strategic planning problems subject to sustainable management constraints where people organize themselves and participate jointly to manage their natural resources.Research highlights: The interactive approach facilitates the involvement of multiple stakeholders in the decision making process.Keywords: decision support system; participatory planning; linear programming; mixed integer goal programming; sustainable forest management.