Designing an Assembly Line for Reliability
Read this article. It deals with production efficiency and human behavior. Despite advanced technology and automation, systems are still dependent on human interaction. How can the human component enhance performance, and conversely, how does this human interaction contribute to system failure?
Mathematical Formulation
Let us consider the binary variable, such that
The following condition must hold for each , under the restriction that the
task can be assigned to only one workstation:
Further, according to precedence constraints if task is to be assigned before assigning task
, that is
, then
Since the task times are random variables, the condition for completion of tasks in a workstation within the assigned cycle time can be described in terms of reliability measure,
under normality of the each elemental times.
Thus,
The reliability of the assembly line, , can be expressed as
following the properties of the series system and the fact that workstations are arranged in series.
Thus, the optimization framework of the line balancing problem can be expressed in terms ofthe following objectives:
subject to the following constraints,:
We prefer to address the above optimization problem in two stages. First, we undertake the task of minimization of and thereby generate, in the first instant, feasible solutions with minimum value of
. Then we obtain the final solution of the problem by imposing the second objective of maximization of
. Even for generating the set of feasible solutions, we consider a sequential approach of assigning trial cycle time that results in slack time. This slack time is to be assigned to each workstation meeting the optimality condition arising out of the first objective of the above formulation. In this approach the trial cycle time starts from some lowest value and gets increased step by step some lowest value and gets increased step by step so as to reach the maximum limit C. Determination of the lowest value for trial cycl time depends on the following consideration.
Given a choice of , it may be noted that the theoretical minimum number of workstations,
, must satisfy the following constraints:
from where we arrive at , the minimum value of
, as
Thus, given a cycle time, C, one may conceptually consider a trial cycle time, , satisfying the condition
, to arrive at the set of feasible workstation configurations and maintain the same cycle time
by uniformly adding to each workstation a slackness
to
, where
. This will help to increase the system stability.