Stochastic cell loading to minimize nT subject to maximum acceptable probability of tardiness

• In this paper, stochastic cell-loading problem with normally distributed operation times is addressed.
• The problem is observed in labor-intensive cells.
• Risk level concept is integrated into the classical Maxwell algorithm.
• Unlike the deterministic model, the results of proposed approach with lower risk level are sensitive to the change in operation time variance.
• The proposed approach permits scheduler to specify a risk level and optimize the schedule based on the risk level taken.

In this paper, stochastic cell loading problem is addressed. The problem is observed in labor-intensive manufacturing cells where operation times and hence in-cell times are probabilistic due to continuous operator involvement throughout the manufacturing processes. The objective is to minimize the number of tardy jobs subject to maximum acceptable probability of tardiness (risk level). A job is called “tardy” if the probability of tardiness is greater than the risk level otherwise it is called early. The risk level is used as a preferred scheduling risk that will be taken by operations planner. A stochastic non-linear mathematical model is developed. Normally distributed processing times and deterministic due dates are used in the experimentation. Various experiments are carried out to study the impacts of risk level, problem size and operation time variance on the optimal schedule. Proposed stochastic approach lets scheduler to sequence the jobs subject to an acceptable risk level. As the risk level increased, the number of jobs included in the schedule increased as well. Similarly, as the risk level increased, the probability of tardiness also increased especially for the jobs that are scheduled in the later positions. Unlike the deterministic model, the results of proposed approach are sensitive to the change in operation time variance. It is recommended to work with the safest schedule (0% risk), when the operation time variance is significantly high.