Hybrid flow shop environment generally refers to the flow shop with multiple parallel machines per stage. Hybrid flow shop scheduling problem (HFSP) is a complex combinatorial optimization problem that came across in many real-life problems. In this study, a real-life HFSP of a lubricant company is considered, where the aim is to minimize total weighted completion time of the jobs. Apart from classical HFSPs, the studied problem has additional constraints such as machine eligibility, sequence-dependent setup times and machine capacities. Due to the additional constraints in the system, a novel mixed integer linear programming model is proposed for the studied HFSP with three stages. As the problem is NP-hard, two constructive heuristic algorithms and an improvement heuristic algorithm are also developed. The performance of the proposed heuristic algorithms is evaluated by comparisons with the optimal results obtained from the mathematical model. The extensive computational results show that proposed heuristic algorithms find near optimal results in reasonable computational times. Sensitivity analysis is also performed for the weight parameter of the problem, which indicates that the proposed heuristic algorithms also perform very well for different weight parameter values. Finally, the proposed heuristic algorithms are integrated into a user-friendly decision support system using Microsoft Excel VBA interface to provide an efficient scheduling tool for the company.