The impact of risk on the integrated cellular design and control

Design and control aspects of cellular manufacturing systems (CMSs) have been studied extensively and several robust procedures have been proposed to deal with cell formation and cell scheduling problems, separately. However, less attention has been paid to the interaction between the design and control aspects in the presence of uncertainty. In this paper, stochastic cell formation and cell scheduling problems are jointly studied where product demand and processing times are assumed as probabilistic. First, stochastic CMS design phase is handled and then stochastic cellular control phase is studied. Two stochastic non-linear mathematical models are developed to solve cell formation and cell scheduling problems consecutively. Later, Monte Carlo simulation is utilised to analyse the impact of uncertainty in design phase on the control phase. Various design risk and control risk scenarios are experimented with the proposed hierarchical approach to evaluate the chain impact of the risk taken during the cell formation (design risk) and the risk taken during the cell scheduling (control risk) on the scheduling performance: the number of tardy jobs (nT). A total of 3 cell formation and 300 cell scheduling scenarios are solved and results are summarised by design, control and integration subjects. Results indicate that higher design risk results in more pressure on control, which pushes scheduler to take lower risks during the cellular control. However, when lower design risk is taken, greater control risks can be taken, which provides more flexibility to scheduler. All in all, this paper presents a handy framework to practitioners to deal with modelling the uncertainty prior to design and during the control of CMS and deal with such short- and long-term decisions.