Minimizing the make-span in a high-product mix shop-floor using integer programming.

摘要

In electronics manufacturing, Printed Circuit Boards (PCBs) are used as the most convenient devices for mounting electronic components. The assembly techniques used in the PCB manufacturing have been changing dramatically over the recent years. The initial method of assembly was populating the PCBs on one workstation either manually or machines. Later, this was converted into manual, semi-automated or automated assembly lines. In order to enhance the throughput of a PCB assembly line, it is important to streamline the production process and efficiently balance the assembly line. Most of the PCB jobs have multiple tasks that arise due to the different component types, number of components used, and lot sizes, resulting in high variation in process times of different jobs. Consequently making it difficult to allocate jobs between assembly lines, and assigning tasks on workstations.; The current problem focuses on the shop-floor of a small contract manufacturing organization that produces different models of PCB timers with lot size varying from 10 to 250. The shop-floor consisted of manual assembly workstations and each workstation assembles one order of same or different product families. This conventional assembly technique was converted into cellular assembly lines, with number of assembly lines corresponding to the number of primary product families of timers. The tasks were assigned to workstations based on the frequency of components usage and jobs were allotted to assembly lines based on the ship-date.; A methodical and systematic approach is required to determine the required number of assembly lines, jobs to be allotted to assembly lines, the tasks to be assigned to different stations and the sequence of jobs on lines. The primary objective of this research is to minimize the make-span by: (1) Allocating jobs to different lines, (2) Assigning (job) tasks to workstations, (3) Determining the sequence of jobs to reduce the changeover times.; Using a Principal Component Analysis (PCA) approach, the minimum number of assembly lines required to process the different product models are determined. A Binary Integer Programming (IP) model was formulated to allocate jobs to different lines based on their processing time, such that the cycle time for all lines were almost the same, and the tasks of each job are assigned to load-balance the line. The optimization software LINGO was used to solve this 0-1IP model. LINGO was also used to solve another IP model used to determine the minimum changeover time and the corresponding job sequence for all the lines. The proposed method was adopted for a set of 13 jobs and the output from optimization software were analyzed by calculating the make-span values.; LEKINRTM scheduling software was used to develop the Gantt charts and to calculate the make-span values for the outputs obtained from LINGO. The make-span values obtained through proposed method of job sequencing was compared with that of optimal sequencing of LEKIN. The stability of the IP model for job allocation and task assignment was analyzed using sensitivity analysis. This was done by varying the optimal job allocation and optimal task assignment of LINGO. It was observed, in all the cases, the make-span values obtained from the proposed method outperformed all the other scenarios. The IP model developed was found to be very effective in finding an optimal solution for the system under study.