Exact and heuristic approaches for lot splitting and scheduling on identical parallel machines

In this paper, we address a lot splitting and scheduling problem existent in a textile factory. The factory we study produces a set of products that are made of, or assembled from, a list of components. During production, each component can be split into one or several lots of different sizes and each lot will be produced independently on one of a group of identical parallel machines. We formulate the problem into a mixed integer programming model and develop a heuristic method to solve the model. The heuristic method is based on a network flow model with the objective to minimise the weighted sum of the total tardiness of products and the deviations occurred during production of each product. The deviation of a product is measured by the deviation of product completion time (the last component lot completion time) and completion time of the rest of components lots for the same product. We present computational results and performance measures of the network flow heuristic for a set of randomly generated instances based on real world data.