University of Tehran Press Advances in Industrial Engineering 2783-1744 51 3 2017 09 23 Lot-Sizing and Scheduling on Parallel Machine due to Earliness and Tardiness Cost تعیین اندازۀ دسته و زمان‌بندی روی ماشین‌های موازی با توجه به جریمۀ زودکرد و دیرکرد 363 374 63980 10.22059/jieng.2017.132300.1006 EN Hossein Falahati Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran Mehdi Bijari Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran Journal Article 2015 11 14 In this research, lot-sizing and scheduling problem on parallel machines has been studied. Holding inventory and backlog cost has been considered as an earliness-tardiness penalties. A mixed integer programming formulation has been proposed based on TSP. Number of product batch is calculated as a parameter before solving the model. The computational result demonstrated that the MIP uses large CPU time to get result due to the problem complexity. So in the next step, problem has been modeled by constraint programming method that reduces solving time significantly. So that for an instance with 2 hours CPU solving time in MIP, the CP method reduces solving time to 2 minutes. To complete the solving process, a heuristic algorithm is proposed to assign orders to products. A case-study in steel-mill industry shows the efficiency of designed system rather than the existing system. Experimental results show that the proposed system have planned the orders less than 10 minutes solving time for different instances; while this is 1 to 2 hours for the existing system. https://aie.ut.ac.ir/article_63980_554daa3c08785ca6a69cd362db2b7efb.pdf