Lotsizing and Scheduling in A Multistage Production System with Sequence Dependent Setup

Do Ngoc Anh Dung

Lot sizing and scheduling is one of the major problems in the production planning. In this study, we consider the Lotsizing and Scheduling in a Multistage Production System with Dependent Setup problem. The production time is described in term of small bucket. At a machine, the setup cost and time depend on the previous produced product. A mixed integer programming (MIP) model is formulated with the objective function to minimize the total cost of holding and setup. The balance inventory and limitation capacity are two main constraints. We propose the Bender¡¯s decomposition combined with genetic algorithm as a new approach to solve this problem. The problem is separated in IP part and LP part, then reformulated as a master problem. The chromosome are encoded and presents for the setup patterns. The fitness value is calculated by solving the master problem. The crossover and mutation are performed at machine level. A study of GAs parameters is performed on the maximum generation and population size, crossover method and mutation rate, and the number of non-improvement generations. We also study the number of cuts and remaining cuts. Several test cases of up to 12 machines and 20 jobs are generated randomly. The results are presented throughout the computation study. Then convergence index and gap index is carried out to evaluate the performance. The result shows that the algorithm carries out some benefit. In most of the test case, the gap index is small and this indicates good performance. Throughout the studying, it proves that the all GAs parameters affect to the results and runtimes.