Behnaz Zanjani - Department of Industrial Management, Faculty of Accounting and management, Allameh Tabatabai University, Tehran, Iran.
Maghsoud Amiri - Department of Industrial Management, Faculty of Accounting and management, Allameh Tabatabai University, Tehran, Iran.
Payam Hanafizadeh - Department of Industrial Management, Faculty of Accounting and management, Allameh Tabatabai University, Tehran, Iran.
Maziar Salahi - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

Scheduling is an important decision-making process that aims to allocate limited resources to the jobs in a production process. Among scheduling problems, Hybrid Flow Shop (HFS) scheduling has good adaptability with most real world applications including innumerable cases of uncertainty of parameters that would influence jobs processing when the schedule is executed. Thus a suitable scheduling model should take parameters uncertainty into account. The present study develops a multi-objective Robust Mixed-Integer Linear Programming (RMILP) model to accommodate the problem with the real-world conditions in which due date and processing time are assumed uncertain. The developed model is able to assign a set of jobs to available machines in order to obtain the best trade-off between two objectives including total tardiness and makespan under uncertain parameters. Fuzzy Goal Programming (FGP) is applied to solve this multi objective problem. Finally, to study and validate the efficiency of the developed RMILP model, some instances of different size are generated and solved using CPLEX solver of GAMS software under different uncertainty levels. Experimental results show that the developed model can find a solution to show the least modifications against uncertainty in processing time and due date in an HFS problem. 

scheduling, Hybrid Flow Shop problem, robust optimization, fuzzy goal programming