Optimally allocating processing time variability on a synchronous assembly line.

Abstract

Processing time variability exists in assembly lines for many reasons including several models of a product being assembled on the same line, optional product features, changing product mix over time, disruptions due to machine or tool failures, variation in worker skill and experience across different tasks, and natural human variation in a repetitive manual work environment. This dissertation examines how to allocate processing time variability on a synchronous assembly line where jobs with incomplete tasks are reworked at the end of the line. The allocation of processing time variability refers to determining the processing time variance at each station on the line given a fixed amount of total variability. Being able to determine the optimal allocation of variability is critical for the design, planning, and improvement of assembly lines. Two objectives for the cost of rework are examined. The first objective assumes that rework cost is proportional to the amount of work not completed on a job, also known as the work overload. The second objective assumes that rework cost only depends upon whether or not a job requires rework. Each objective depends on several factors including the mean processing time at each station, the number of stations on the line, the cycle time of the line, the total variability in the system, and the allocation of variance. Three models are examined for each objective. The first model assumes that the mean processing time at each station is the same. The second model assumes that the mean processing time at each station is not the same. The last model assumes that both processing time mean and variance can be allocated. For each of these models it is shown that beyond certain levels of reasonable variability, most of the variability should be isolated at as few stations as possible. Stations that do have significant variability should be compensated for this high variability via lower average processing requirements when possible. For both objectives, such an approach for allocating variability leads to significant improvements in performance over a line where each station is allocated the same processing time mean and variance.