A robust green location-allocation-inventory problem to design an urban waste management system under uncertainty

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 investigated 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 facilities, transportation costs, penalty costs of non-collected waste and costs arising from pollution emissions. 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.