Bahadorgholi Aryanezhad - Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
Mehdi Karimi-Nasab - Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
Seyed Mohammad Taghi Fatemi Ghomi - Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

Model building is a fragile and complex process especially in the context of real cases. Each real case problem has its own characteristics with new concepts and conditions. A correct model should have some essential characteristics such as: being compatible with real conditions, being of sufficient accuracy, being logically traceable and etc. This paper discusses how to build an efficient model for a real case production planning problem. This process is reinforced by providing the proofs confirming the special characteristics of the final model such as proving its NP-Completeness. Also, the extremes of both objective functions – production smoothing versus cost minimizing – are calculated analytically. Finally, the case study and its solution methods are discussed briefly

Multi-objective; Single machine; Production planning; Multi-Product; Multi-Period; Controllable processing time; Pareto-optimal solutions