A competitive branch-and-bound algorithm for the simple assembly line balancing problem

In this paper we present a branch-and-bound algorithm for solving the simple assembly line balancing problem of type 1 (SALB-1). The algorithm relies on the precedence tree guided enumeration scheme introduced for dealing with a broad class of resource-constrained project scheduling problems. The general enumeration scheme ranks among the most powerful algorithms for solving the well-known single- and multi-mode resource-constrained project scheduling problem. By reformulating the SALB-1 as a resource-constrained project scheduling problem with a single renewable resource whose availability varies with time, the problem can be solved with the general algorithm. Only minor adaptations are necessary to implement an efficient assembly line balancing procedure. Taking into account SALE-1 specific information, the simplicity of the enumeration scheme allows one to generalize classical dominance concepts from Jackson and Johnson substantially. The computational complexity of some bounds is reduced, and the effect of others is strengthened. The procedure has been coded in C and implemented on a personal computer. The computational results indicate that the algorithm can compete with the best algorithms currently available for solving the SALE-1.