Optimal sublot determination in multiple batch stage, two stage production systems
One of the main objectives in the operation of production systems these days is to reduce production lead time. A reduction in production lead time directly translates into decrement in production cost thereby making the products competitive. One way to achieve this objective is to overlap operations among the machines by splitting the batches to process into sub lots. The technique used to split batches into sub lots is the Lot Streaming method. In this thesis, the Lot Streaming problem is mathematically analyzed for the multiple batch/two-machine case under the criteria of minimizing the production cost which consists of handling cost and makespan cost. The work is focused on the determination of the number of sub lots in each batch for both the continuous and integer versions of the problem. First, we solve the two batch/two-machine problem, which is a special case of the multiple batch/two-machine problem and is simpler in nature. A no-idling constraint is proven to be necessary for the minimization of the criteria considered. This constraint is used to reduce the size of the problem to a single dimension problem which allows the use of a line search method. A continuous optimal solution is generated and an algorithm is proposed to deduce an integer solution from it. The results of the two-batch problem are then generalized to the multiple batch/two-machine case, which is solved for both the continuous and integer versions of the problem.