Production Scheduling
A simple model is sometimes used in order to illustrate the production-scheduling maxim, ‘‘balance how, not capacity.’’ Consider a factory that consists of three workstations where each work piece must proceed through the workstations in sequence. Next, suppose that the workloads are balanced, which means that, on average, each order requires equal amounts of work at each of the three stations. Assume that the most likely operation time at each station is 60 seconds.
If there were no variability in the processing times at each workstation (as, for example, if they were fully automated), each work piece would take three minutes to complete the process. The throughput would be exactly 60 pieces per hour and there would always be three units being worked on (work in process).
Now suppose that there is variability at each work station and that it is log-normally distributed. For purposes of simulating this randomness, the mean of the underlying normal distribution (µ in the example formula given in the PowerPoint) is Ln(60) = 4.094. Assume that the standard deviation (σ in the PowerPoint) is 10% of the mean or 0.409.
Simulate the processing of 1,000 pieces through this process. Assume that each work station works in “Push” mode, meaning that if it is finished with one part and the next one is available, it starts work immediately.
1. What is the average throughput in pieces per hour?
2. What is the average level of WIP? (Hint: calculate the transit time for each piece and apply Little’s law.)
3. Increase the standard deviation of the processing times to 20% and 30% of the mean value given above. What do you conclude about the effects of variability on throughput and WIP?
4. Now convert the model to have the workstations work in “Pull” mode, meaning that even if a work station is idle and it has material available to work on, it doesn’t start work until the job just completer begins processing at the next station. Answer questions 1-3 for this model. How would you characterize the differences between push and pull systems?