A cost-effective approach to stochastic line balancing with off-line repairs

This paper describes a methodology for designing approximately minimum cost paced assembly lines under conditions of random task times and off-line repair of uncompleted tasks. Task times are assumed to be normally distributed random variables with known means and variances. The methodology consists of heuristically identifying a large number of feasible balances for each of which total costs are computed. The line design with the lowest total is retained as the ‘best’. An experiment was conducted in order to compare the proposed methodology with a purely deterministic approach and a commonly used industrial approximation method for dealing with task time variability. The experiments applied the three methods to four problems from the literature under a variety of repair cost and time variance conditions. In 21 out of the 24 cases studied, the stochastic method produced a lower cost balance than the two alternatives. In the remaining 3 cases, the deterministic method also found the lowest cost balance. The stochastic method saved an average of 22.5 percent in total operating cost over the deterministic method and 8.4 percent over the industrial method. The experiment clearly showed the need to explicitly consider task time variability in arriving at a line balance. The stochastic approach of this paper offers large potential savings with no risk of obtaining a less desirable balance and so should be considered for implementation whenever there is a variation in task times. Even for large-scale problems, the computational cost is infinitesimal in the context of assembly line balancing, where very small improvements in productivity can mean substantial increments to profitability.