Minimisation of equipment cost for transfer lines with blocks of parallel tasks

This paper deals with the design of single product lines without buffers (transfer lines), which dispose of several types of multifunctional tools (equipments) allowing the parallel execution of many different tasks by the same equipment (blocks of tasks). The production line design is stated as a multi-criteria optimisation problem: balancing the line and minimising the equipment cost. It is decomposed into two sub-problems: first, the blocks are obtained by assigning the tasks to equipments, subject to the precedence constraints; secondly, these blocks are assigned to workstations, subject to the cycle time constraint, which is just the ALB problem. To solve the first sub-problem, a branch-and-bound algorithm, enhanced by using two lower bounds and a dominance rule, is proposed.