A robust green location-allocation-inventory problem to design an urban waste management system under uncertainty Erfan Babaee Tirkolaee a,⇑ , Iraj Mahdavi a , Mir Mehdi Seyyed Esfahani b , Gerhard-Wilhelm Weber c,d a Department of Industrial Engineering, Mazandaran University of Science & Technology, Babol, Iran b Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran c Faculty of Engineering Management, Poznan University of Technology, Poznan, Poland d Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey article info Article history: Received 4 July 2019 Revised 17 September 2019 Accepted 20 October 2019 Available online xxxx Keywords: Municipal solid waste management Green location-allocation-inventory Robust optimization Robustness worthiness threshold abstract The excessive expansion of cities and the consequent increase in urban population, especially in recent years, have led to a significant increase in consumptions and generations of different types of municipal solid waste (MSW). In this research, a robust green location-allocation-inventory problem (LAIP) is inves- tigated to design an efficient MSW management system. Since the exact amount of MSW composition in different regions is not known and is uncertain, robust optimization technique is applied to formulate the problem as a mixed-integer linear programming (MILP) model. The objective is to minimize the total cost including fixed locational costs of collection and processing/disposal facilities, operational costs of facil- ities, transportation costs, penalty costs of non-collected waste and costs arising from pollution emis- sions. The validation of the proposed model is performed by different problems based on real-life data in deterministic and uncertain conditions using CPLEX solver of GAMS software. Then, the effects of greenness are evaluated by performing a sensitivity analysis on the parameter of pollution cost. Finally, the concept of robustness worthiness threshold (RWT) under budget constraint is introduced and discussed. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction The process of municipal solid waste (MSW) management is one of the most essential activities of each city. Ignoring its neces- sities can be problematic for the city residents and even its sur- rounding villages. Hence, organizations such as municipalities have established stations and waste collection facilities in various urban areas to provide fast and low-pollution services. However, studying this issue as a facility location problem (FLP) and consid- ering the uncertain nature of generated waste is of great impor- tance, whether in terms of cost or timely services. The purpose of this study is to increase the efficiency of waste collection through minimizing the total establishment costs of permanent and tempo- rary facilities, operational costs, traversing distances of waste col- lection vehicles and to reduce environmental pollution, especially air contamination. Despite all the benefits mentioned, there are some controversies in terms of location and the method of estab- lishment that can create great problems for the urban population if neglected. As a detailed discussion of the problem, there are sev- eral candidate locations for the establishment of permanent or temporary collection centers in different regions of the city. Each of these collection facilities has different amounts of capacity, establishment cost and pollution emission. An optimal decision involves determining the type, the number and the location of facilities in each region to cover the total amount of generated waste per time period. These facilities are also facing the limita- tions in the number of establishments of permanent or temporary type. Dimensions of the problem defined in this study can vary with respect to the size of the cities. In fact, in densely-populated cities, different regions of the city are categorized and the waste manage- ment of each one is specific to its municipality or related organiza- tions. In less populated cities and small towns, this responsibility is usually given to a single unit of the municipality, such that, it is responsible for waste management by locating and handling waste collection facilities. Moreover, these organizations often face the uncertainty problem in the amount of collected waste at any point of the city and should be finally allocated to potential processing/ disposal facilities that have already been established at the https://doi.org/10.1016/j.wasman.2019.10.038 0956-053X/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: e.babaee@ustmb.ac.ir (E.B. Tirkolaee), irajarash@rediffmail. com (I. Mahdavi), msesfahani@aut.ac.ir (M.M.S. Esfahani), gerhard.weber@put. poznan.pl (G.-W. Weber). Waste Management 102 (2020) 340–350 Contents lists available at ScienceDirect Waste Management journal homepage: www.elsevier.com/locate/wasman