Balancing Workload and Workforce Capacity in Lean Management: Application to Multi-Model Assembly Lines

While multi-model assembly lines are used by advanced lean companies because of their flexibility (different models of a product are produced in small lots and reach the customers in a short lead time), most of the extant literature on how to staff assembly lines focuses either on single-model lines or on mixed-model lines. The literature on multi-model lines is scarce and results given by current methods may be of limited applicability. In consequence, we develop a procedure to staff multi-model assembly lines while taking into account the principles of lean manufacturing. As a first approach, we replace the concepts of operation time and desired cycle time by their reciprocal magnitudes workload and capacity, and we define the dimensionless term of unit workload (load/capacity ratio) in order to avoid magnitudes related to time such as cycle time because, in practice, they might not be known. Next, we develop the necessary equations to apply this framework to a multi-model line. Finally, a piece of software in Python is developed, taking advantage of Google’s OR-Tools solver, to achieve an optimal multi-model line with a constant workforce and with each workstation performing the same tasks across all models. Several instances are tested to ensure the performance of this method.

Cavitation onset caused by acceleration

Striking the top of a liquid-filled bottle can shatter the bottom. An intuitive interpretation of this event might label an impulsive force as the culprit in this fracturing phenomenon. However, high-speed photography reveals the formation and collapse of tiny bubbles near the bottom before fracture. This observation indicates that the damaging phenomenon of cavitation is at fault. Cavitation is well known for causing damage in various applications including pipes and ship propellers, making accurate prediction of cavitation onset vital in several industries. However, the conventional cavitation number as a function of velocity incorrectly predicts the cavitation onset caused by acceleration. This unexplained discrepancy leads to the derivation of an alternative dimensionless term from the equation of motion, predicting cavitation as a function of acceleration and fluid depth rather than velocity. Two independent research groups in different countries have tested this theory; separate series of experiments confirm that an alternative cavitation number, presented in this paper, defines the universal criteria for the onset of acceleration-induced cavitation.