Worker cross-training in paced assembly lines

Paced or Synchronous assembly lines are a popular class of assembly systems consisting of a series of assembly stations arranged in tandem. Every job (or order) visits all assembly stations in the same sequence and spends the same amount of time (known as the production cycle) at each station. Industries such as aircraft, fire-engine, and automobile assembly have production cycles of a few hours and are labour intensive. In spite of increased automation in such industries, human capital remains the most expensive and important contributor to a flexible production system. In this article we formulate the cross-training problem on a paced assembly line with m stations (mCT). We assume that each worker possesses a number of skills referred to as a skill vector. Our objective is to schedule a set of work orders through the assembly system so as to minimize the size of the required workforce and/or the workforce cross training costs. We analyze the complexity of mCT and identify polynomially solvable cases. A variety of lower bounds is developed based on optimization techniques. These lower bounds are used to develop a branch and bound algorithm as well as to evaluate our heuristics. A computational experiment reports the performance of all algorithms. Using these algorithms, we examine how the formation of skill vectors affects the workforce size and draw guidelines for cross-training programs in organizations with labour intensive assembly operations.