Designing of an Assembly Line based on Reliability Approach

The problem of Assembly Line Balancing is to assign a set of tasks to an ordered sequence of workstations without violating the precedence constraints. The efficiency of the line will increase when tasks are more evenly distributed. In general, the efficiency measure(s) should be optimized subject to cycle time restriction and precedence constraints. Under the deterministic setup, efficiency of the system can be measured in various ways. Research works, reported so far, mainly deal with balancing loss as an inverse measure of efficiency. As a result, in earlier works balancing loss has been minimized subject to precedence constraints. In case the work elements are best described in terms of stochastic time, the entire problem has to be addressed with a different measure of efficiency. Expected variance of the idle times of workstations can be viewed as an inverse measure of stability of the system. A more appropriate and direct measure could be the reliability of the system such that each workstation adheres to assigned cycle time with high chance. The present work defines the reliability of the assembly line in terms of cycle time and distribution of the tasks times and offers an optimization formulation for the problem under precedence constraints. For demonstration purpose, one well known example in the literature has been addressed under stochastic setup.