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In this paper we propose three models for locating multiple facilities anywhere in the plane. The facilities serve demand points and require raw materials from a list of available sources. Problem characteristic originally proposed in 1909 by Weber for manufacturing systems. Weber argued that optimal locations involve minimizing total transport cost which was comprised of the costs of transporting the raw materials and the delivery cost of the final product when plant production and location costs were invariant across the plane. Both the parameters of raw material sources and demand points affect the best locations for the facilities. In this paper, a special algorithm is designed to heuristically solve these three models. The algorithm exploits the special structure of the models. Problems with up to 2000 demand points and 20 facilities were tested. The results are compared with applying available non-linear solvers in a multi-start approach. The special algorithm performed better in most instances especially for a large number of facilities and a large number of demand points. [ABSTRACT FROM AUTHOR]

Communities like Santa Barbara, California appear to have it all – beaches, mountains, sunshine, moderate temperatures, small urban population, and close proximity to the large metropolis of Los Angeles. What is not to love? Climate change, drought, flammable vegetation, and naturally prevailing weather conditions make a significant portion of the population vulnerable in many ways. Earthquakes and tsunamis might come to mind, but perhaps more of a threat is fire and/or flooding at, on or near the wildland-urban interface. The recent Thomas fire in December of 2017 and subsequent flooding, debris flow and mudslides in Montecito that followed in January of 2018 highlight what coastal vulnerability means under the new normal of extreme wildfire and flooding danger for this region. This paper discusses the unique hazards along with local weather conditions that contribute to vulnerability. We then detail spatial analytics to assess, model and predict risks. Insights are offered for the Santa Barbara region associated with extreme weather vulnerabilities. [ABSTRACT FROM AUTHOR]

The management of competing land uses is complicated by a range of issues and considerations. This is the case because of a concern for the long-term health of the earth and the obvious negative impacts of past and present human activities. Land use planning and management efforts have recognized this broader context and accordingly have devoted much care and attention to operational-level planning support. Spatial restrictions have long been recognized as central to limiting local impacts as well as ensuring landscape shape and structure irregularity. Unfortunately, planning to meet spatial restrictions may be disrupted, by fire, pests, or even on-the-ground conditions. For example, what if a fire destroys resources in a management unit that are adjacent to a unit(s) scheduled for harvest. In fact, this new opening/disruption may prevent the planned activity of any of its neighboring units. Disruptions do occur, but have rarely been addressed in any meaningful way in planning optimization problems. This paper details spatial optimization approaches to support better understanding of the range of potential outcomes when disruption and uncertainty are taken into account in land use planning involving forest resources. Application results highlight the significance of handling disruption risk and spatial data uncertainty, indicating that identifying and selecting planning alternatives that are consistent with goals and intended outcomes are a difficult task. However, improved modeling approaches are possible that better support land use decision making. [ABSTRACT FROM AUTHOR]

One of the classic operations problems in forest management is to select the harvesting system and to plan the layout, which has a significant impact on overall operational and environmental efficiency. This paper addresses the design of a harvesting system in areas characterized by steep slopes requiring cable-based harvesting under central European conditions. We present two computationally efficient methods (designated as set-covering model SCM and bounded set-covering model BSCM) for solving problems of cable road layouts and comparing them with a previously developed model (CaMLOC). Formulating the problem as a type of location set-covering model allowed us to delineate a much smaller problem that was easier to solve. By applying the new model formulations, it is possible to identify mathematical optimal CR layouts for real-world forests areas up to 50 ha within a reasonable period of time and to even estimate the maximum gap in optimality (only with the BSCM approach). [ABSTRACT FROM AUTHOR]

The p-median problem was first formulated as an integer-linear programming problem by ReVelle and Swain (1970) and further revised by Rosing, ReVelle and Rosing-Vogelaar (1979). These two forms have withstood the test of time, as they have been used by virtually everyone since then. We prove that a property associated with geographical proximity makes it possible to eliminate many of the model variables through a substitution process. This new substitution technique has resulted in the elimination of up to 60% of the variables needed in either of these classic model formulations. [ABSTRACT FROM AUTHOR]

Linear Programming and Mixed Integer Linear Programs have been used for forest planning since the 60's to support decision making on forest harvesting and management. In particular, during the last two decades of forest management there has been an increased interest in spatial issues. Further, new environmental concerns, such as resource sustainability and wildlife protection, impose that increased attention be paid to activities carried out on the ground. Road building needed for access also requires spatial definiton. As a result, more complex models must be used. We discuss the issues which have led to the combinatorial nature of some main forest management problems and the solution algorithms that have been proposed for these problems, including local search heuristics, random search approaches, strengthening of mixed integer model formulations and Lagrangian relaxation. In this survey, we discuss which of the proposed approaches have been used succesfully, the advantages and shortcomings of each and what are still open research problems. [ABSTRACT FROM AUTHOR]

Forest management and planning can involve large tracts of land involving numerous areal units. One approach to plan activities for a forested region over decades involves breaking down decision making into three components: strategic, tactical, and operational. Each level of the management hierarchy can involve the development and application of optimization models. These models typically aid in exploring management alternatives as well as multi-objective tradeoffs. Even though a strategic model can provide support for long term management at a broad scale, solutions may not be feasible at an operational level. Tactical level modeling helps to bridge solutions reached at a strategic level using operational planning information. This paper presents several tactical level planning models that have been developed as a part of a research effort supported by the US Forest Service. These models have been utilized in land use management and planning by the US Forest Service through a specially developed spatial decision support system. [ABSTRACT FROM AUTHOR]