Lot-Sizing and Scheduling on Parallel Machine due to Earliness and Tardiness Cost

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.