A branch, price and remember algorithm for the U shaped assembly line balancing problem

In this paper we propose a branch, price and remember algorithm to solve the U shaped assembly line balancing problem. Our proposed algorithm uses a column generation approach to obtain tight lower bounds. It also uses a modification of Hoffman algorithm to obtain high quality upper bounds. Memory is also used in our proposed algorithm to store generated columns to enhance the speed of column generation approach. Our computational results show that our proposed algorithm is able to optimally solve 254 of Scholl’s well-known 269 benchmark problems, which includes 13 problems that have been open for more than 10 years. Previous best known algorithm is able to solve 233 of the 269 benchmark problems. We also examined our algorithm on a new data set and the results show that our algorithm is able to solve 96.48 percent of all available benchmark problems.