A Branch and Bound for single machine stochastic batch scheduling with delivery costs. A Chance Constraint approach (Case study in Iran)

This paper study a single machine stochastic scheduling problem based on an Iranian real case study in Saipa company in which the objective is to minimize total completion times and delivery costs. According to existence data sets of this company the processing times follows a Normal distribution and based on the managerial decisions two objectives have to be achieved simultaneously including total completion times and controlling tardiness values so that their values are lower than an specified penalty. So, a Chance Constraint Programming (CCP) approach is employed and a mathematical model is presented. In order to solve the problem a Branch and Bound (B B) method is used to solve the problem optimally and a Particle Swarm Optimization (PSO) metaheuristic is used to find near optimal solutions for large scales. The results show that using the proposed mathematical model and solution approach, could increase the effectiveness and efficiency of production line as 16 to 40 percent. Computational experiments validate the accuracy of proposed method.