Mathematical algorithm to transform digital biomass distribution maps into linear programming networks in order to optimize bio-energy delivery chains

Many linear programming models have been developed to model the logistics of bio-energy chains. These models help to determine the best set-up of bio-energy chains. Most of them use network structures built up from nodes with one or more depots, and arcs connecting these depots. Each depot is source of a certain biomass type. Nodes can also be a storage point for a certain biomass type or a production facility (e.g. power plant) where the biomass is used. Arcs represent transport between depots. To be able to combine GIS spatial studies with linear programming models it is necessary to build a network from a digital map. In this work a mathematical calculation method is developed to select the actual points on the map where to collect biomass that will then be considered as biomass sources in a network model

GIS Application to Define Biomass Collection Points as Sources for Linear Programming of Delivery Networks

Much bio-energy can be obtained from wood pruning operations in forests and fruit orchards. Several spatial studies have been carried out for biomass surveys, and many linear programming models have been developed to model the logistics of bio-energy chains. These models can assist in determining the best alternatives for bio-energy chains. Most of these models use network structures built up from nodes with one or more depots, with arcs connecting the depots. Each depot is a source of a certain biomass type. Nodes can also be biomass storage points or production facilities (e.g., power plants) where biomass is used. The arcs in the networks represent transport between depots. In order to combine GIS spatial studies with linear programming models, it is necessary to build a network from a digital map of biomass production centers, such as orchards. Biomass collection points should therefore be defined as sources in the delivery network model. In this work, a mathematical calculation method is developed to select the actual biomass collection points on a map. The database for this model is composed of area surveys of forest and agricultural biomass storage points given in GIS maps (shape files). The limits of the area studied and different types of biomass are defined and located in different layers of the GIS maps. These energy-biomass production maps are overlaid with a 1 km - 1 km grid of the area studied. The result is a grid in which the different types of total available biomass in each quadrant are known. Harvesting and collection costs are also defined. The connections between all n - m quadrants of the area studied are defined by the available road network. Every quadrant is associated with a point on the road network. The selection criteria for sources of biomass (sub-areas) are the following: firstly, a minimum production of available biomass type is required; and secondly, harvesting and collection costs should be minimal. The algorithm provides the location of points where biomass from the associated area can be concentrated. These biomass collection points are then taken as source nodes in the network during the implementation of the logistics models. In the next step, the network is analyzed by linear programming techniques to supply the optimal position of energy plants or factories, given the available biomass source

Mathematical algorithm to relate digital maps of distribution of biomass with algorithms of linear programming to optimize bio-energy delivery chains

Many linear programming models have been developed to model the logistics of bio-energy chains. These models help to determine the best set-up of bio-energy chains. Most of them use network structures built up from nodes with one or more depots, and arcs connecting these depots. Each depot is source of a certain biomass type. Nodes can also be a storage point for a certain biomass type or a production facility (e.g. power plant) where the biomass is used. Arcs represent transport between depots. To be able to combine GIS spatial studies with linear programming models it is necessary to build a network from a digital map. In this work a mathematical calculation method is developed to select the actual points on the map where to collect biomass that will then be considered as biomass sources in a network model