A new fuzzy tri-objective model for a home health care problem with green ambulance routing and congestion under uncertainty

•Designing a new tri-objective model for a home health care problem under a fuzzy uncertainty.•Investigating the ambulance routing and congestion in a green pharmaceutical supply chain.•Considering the expected objective function value and fuzzy chance-constrained programming.•Proposing the goal attainment and LP-metric methods to tackle a hybrid fuzzy model.•Performing the wide sensitivity analysis and specifying the rank of the two proposed methods. With the increasing number of older people and high hospital treatment costs, older people tend to receive cures at home and more demand for home health care centers (HHCCs). Therefore, HHCCs should use appropriate planning to carry out their activities to reduce costs while maintaining health care quality and patient satisfaction. According to previous studies, the present study shows that most studies have examined the problem in terms of logistical costs and have used lower multi-criteria decision-making (MCDM) methods. This has driven our efforts to simultaneously consider the financial, human resource, time and environmental pollutants, and problem-solving through MCDM methods. In this research, a mixed-integer linear programming (MILP) model with three objectives in both definite and indefinite states is presented to optimize the basic HHC processes. In the first objective function, an attempt is made to minimize costs. On the other hand, due to the high importance of environmental pollutants, the second objective function minimizes the greenhouse gas (GHG) emitted by ambulances. Furthermore, for the first time, a new objective function is presented to minimize the congestion of laboratory samples in HHCCs with the M/M/C queueing system. Then, a hybrid model based on the expected value (EV) and fuzzy chance-constrained programming (FCCP) is presented to bring the problem closer to reality. Finally, this mathematical model is solved using goal attainment (GA) and LP-metric methods ranked by a simple additive weighting (SAW) method.