An linear programming based lower bound for the simple assembly line balancing problem

The simple assembly line balancing problem is a classical integer programming problem in operations research. A set of tasks, each one being an indivisible amount of work requiring a number of time units, must be assigned to workstations without exceeding the cycle time. We present a new lower bound, namely the LP relaxation of an integer programming formulation based on Dantzig-Wolfe decomposition. We propose a column generation algorithm to solve the formulation. Therefore, we develop a branch-and-bound algorithm to exactly solve the pricing problem. We assess the quality of the lower bound by comparing it with other lower bounds and the best-known solution of the various instances from the literature. Computational results show that the lower bound is equal to the best-known objective function value for the majority of the instances. Moreover, the new LP based lower bound is able to prove optimality for an open problem. (c) 2004 Elsevier B.V. All rights reserved.