Providing a multi-objective programming model for U-shaped assembly line balancing with equipment assignment and task performing quality level

This paper focuses on a novel model of the U-shaped assembly line balancing problem, in which the objective functions include cost, capacity, and quality are simultaneously examined. It is assumed that each task requires a set of equipment. In addition, the quality of tasks performed by each worker varies. Hence, the purpose of the model is that the total cost of the equipment is minimized and the quality of the work is maximized. Additionally, the number of workstations is minimized. To this end first, a multi-objective non-linear mixed-integer programming model is provided. Then, the model is linearized, and simulated annealing (SA) algorithm and two of its modified modes have been proposed to solve the problem. The proposed algorithm includes a new encoding/decoding scheme, as well as a local search for assigning the worker to each station. To determine the parameters in three algorithms, the experimental design has been used and various modes have been created by combining the parameters. Moreover, numerical examples were established based on the graphs found in the literature and the solution is compared with three algorithms, revealing the efficiency of each algorithm. Additionally, a case study on the nozzle assembly line in oil refineries was conducted to evaluate the efficiency of the proposed model and algorithm. Results from the case study show that the modified SA algorithms performed better.