Surviving in a competitive spatial market: The threshold capture model

Most facility location decision models ignore the fact that for a facility to survive it needs a minimum demand level to cover costs. In this paper we present a decision model for a firm that wishes to enter a spatial market where there are several competitors already located. This market is such that for each outlet there is a demand threshold level that has to be achieved in order to survive. The firm wishes to know where to locate its outlets so as to maximize its market share taking into account the threshold level. It may happen that due to this new entrance, some competitors will not be able to meet the threshold and therefore will disappear. A formulation is presented together with a heuristic solution method and computational experience.Discrete facility location, threshold, competitive location

Biological reserves Rare Species and the Opportunity Cost of Diversity

The preservation of species diversity generally suggests protection of either the greatest number of species possible or all species. Requiring representation of each species in at least one parcel in the system and seeking the minimum number of parcels in the reserve system to achieve this requirement is termed the Species Set Covering Problem (SSCP). Nonetheless, it is important, as well, to consider the rarest of species, as their populations are the most in need of protection to assure their survival. This paper uses zero-one programming models and an existing data set to study species protection, rarity and the opportunity costs of diversity. We employ for this purpose an integer programming model that uses the SSCP format to require at least one representation of each and every species, but that seeks in addition protection of the rarest species. This is achieved by maximizing redundant coverage of those species designated as rare. Results are then compared to those of the SSCP. Recognizing that resources available for conservation purchases could well be insufficient to represent all species at least once, we structure a model aimed at trading-off first coverage of the greatest number of species against redundant coverage of rare species. We develop a tradeoff curve for this multi-objective problem in order to evaluate the opportunity cost of covering more species as redundant coverage of rare species decreases ­and vice versa. Finally, various possible rarity sets and various budget proxies are considered along with their impacts on conservation policies, Pareto optimality and on the opportunity cost of diversity

Sourcebook on the environment: the scientific perspective

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