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Minimal covering unrestricted location of obnoxious facilities: bi-objective formulation and a case study

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Abstract

This paper addresses the problem of locating obnoxious facilities aiming to mitigate the adverse effects of such facilities by minimizing the total covered demand and reducing the harmful effects of multiple-coverage by placing the facilities far from each other. Unlike the classical approaches, it is assumed that the facilities can be located not only on the nodes but also on the network’s edges. Additionally, demands are not restricted to reside on the nodes but are distributed along the edges. In such a condition, the problem of locating obnoxious facilities is much closer to the real-world. A bi-objective mixed-integer linear programming formulation is developed for this novel problem. This bi-objective problem is solved using the ε-constraint method and NSGA-II. The ε-constraint method can be used to solve the small and medium-sized problems optimally in a reasonable time. As a realistic example, this approach is implemented in a case study in Isfahan for a particular urban planning problem. The case is locating obnoxious solid waste disposal facilities that should be located as far away as possible and simultaneously cover the least demands. Large scale problems cannot be solved efficiently using the ε-constraint method. However, the numerical analysis showed the efficiency and effectiveness of the NSGA-II approach for these problems. Finally, sensitivity analysis is applied to evaluate the effect of changes in coverage distance and the number of facilities on the conflicting objective functions.

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Availability of data and material

All relevant raw data of the case study are provided in two excel files: “Length_and_Distance.xlsx” and “Weight.xlsx”. The first file includes Isfahan’s length matrix in the first sheet (Sheet 1) and Isfahan’s distance matrix in the second sheet (Sheet 2). “Weight.xlsx” includes the weight of demand along each edge on the Isfahan network city.

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Authors and Affiliations

  1. Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

    Kayhan Alamatsaz & S. M. T. Fatemi Ghomi

  2. Department of Industrial and Systems Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    Mehdi Iranpoor

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  1. Kayhan Alamatsaz
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  2. S. M. T. Fatemi Ghomi
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  3. Mehdi Iranpoor
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Correspondence to Mehdi Iranpoor.

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Alamatsaz, K., Fatemi Ghomi, S.M.T. & Iranpoor, M. Minimal covering unrestricted location of obnoxious facilities: bi-objective formulation and a case study. OPSEARCH 58, 351–373 (2021). https://doi.org/10.1007/s12597-020-00487-0

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