A cost‐effective approach to stochastic line balancing with off‐line repairs
Authors: Carter John C. , Silverman Fred N. 
Published: October 2002

The layout of production facilities is an important determinant of the productivity potential of a manufacturing enterprise. It is particularly important in the design of assembly lines where the objective is to assign tasks to work stations in such a way as to minimize total variable production costs.

Early approaches to the line balancing problem assumed known constant task times and sought a line layout which would produce the desired output with the fewest number of work stations, which is equivalent to minimizing idle time. Studies have shown that task times are random variables, therefore the cost of task incompletion must be considered a part of total production cost. Incompletion cost will be the cost of repairing or completing tasks which cannot be completed within the cycle time after the item has reached the end of the assembly line.

This paper describes a methodology for designing approximately minimum cost paced assembly lines under conditions of random task times and off‐line repair of incompleted 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.”

In order to evaluate candidate line layouts, a total cost model is developed. Total cost is the sum of normal operating cost—which is simply a function of the number of work stations—and the cost of repairing products containing incompleted tasks. Because this latter cost is a random variable for a given balance, the expected value is used to evaluate a candidate layout. The cost associated with one or more workers exceeding the cycle time is the product of the probability of this happening and the expected cost of off‐line repair.

The heuristic method for generating feasible balances builds work stations from continually updated lists of precedence satisfying tasks. Qualifying tasks are added to the station as long as the probability of the station exceeding the cycle time remains below a pre‐specified threshold. The methodology requires systematically varying this threshold to permit a lowest total cost solution to emerge. The process of generating a large number of balances for a particular threshold is efficient. Evaluating the total costs of the resulting balances takes the majority of the computational time.

An experiment was conducted in order to compare the above cost‐effective methodology with a purely deterministic approach and a commonly used industrial approximation method for dealing with task time variability. The experiment applied the three methods to four problems from the literature under a variety of repair cost and time variance conditions. In 21 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.