Production Line Models: Push Vs Pull Control of Work Release

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A production line has four serial workstations. The number of servers at each workstation is [1, 2, 6, 2] with exponentially-distributed processing times of [2, 5, 10, 3] hours. The purpose of this exercise is to visualize differences between Push and CONWIP control paradigms for releasing work into a make-to-stock system, in which the external demand process is separated from the release of work.

1. Open the simulation model ProdSys_Push.slx. Configure the model with the parameters above, plus an initial WIP level of 10 (in the WIP_Queue) and a demand queue capacity of 100. Set an exponentially-distributed demand rate of 0.28 jobs/hour (in the Demand Generator), and an equivalent work release rate (in the Arrival Generator). Set the stop time to 50,000, run five simulation replications, and use the Simulation Data Inspector (accessible next to the stop time box) to create separate visualizations of both the demand backorder level (samples of the Demand Queue's length) and also the average cycle time. Copy & paste your figures below.
2. Open the simulation model ProdSys_CONWIP.slx. Configure the model in the same way as the push system; the only difference is that a CONWIP system has no independent Arrival Generator for work release. Run five simulation replications, use the Simulation Data Inspector to create separate visualizations of both the demand backorder level and also the average cycle time, and copy & paste your figures below.
3. Explain your results, and any differences between the relative performance of the Push and the CONWIP control paradigms for releasing work into a production line.

BIG PICTURE: This should be a straightforward exercise to visualize differences between the Push and the CONWIP control paradigms for releasing work into a production line. The particular numbers chosen here make the CONWIP paradigm look great - an expected result is that peak demand backorders, average cycle time, and cycle time variability are all lower. However, that is not a general result - while the CONWIP paradigm is generally better at controlling WIP and cycle times, it involves a fundamental tradeoff between demand backorders and finished goods inventory, and if the CONWIP level is chosen too small then it may perform worse than the Push paradigm at controlling demand backorders and hence the fill rate (the fraction of demands filled without backorder).

A production line has four serial workstations. Each workstation has a single server with exponentially-distributed processing rates averaging [1/2, 2/5, 6/10, 2/3] jobs/hour. The purpose of this exercise is to visualize differences between Push and CONWIP control paradigms for releasing work into a make-to-stock system, in which the external demand process is separated from the release of work. Demands arrive at a rate of 0.37/hour with no variability, corresponding to a bottleneck utilization of 92.5%.

1. Use Hopp & Spearman's Mean Value Analysis Calculator to estimate a CONWIP line's throughput and cycle time for WIP levels from 1 to 30. What is the smallest WIP level for which the throughput estimate is at least 0.37/hour?
2. Open the simulation model ProdSys_CONWIP.slx. Configure the model with the parameters above, plus the just-computed WIP level which allows a throughput of at least 0.37/hour. Set the stop time to 100,000, run five simulation replications, and use the Simulation Data Inspector (accessible next to the stop time box) to visualize both throughput and average cycle time. How do simulation results compare to mean value analysis' analytical approximations? (While you’re here, also create visualizations of the finished goods inventory level and demand backorders' average wait time, needed for a later question.)
3. Open the simulation model ProdSys_Push.slx. Configure the model with the parameters above, and set the work release rate equal to the demand arrival rate. Set the stop time to 100,000, run five simulation replications, and use the Simulation Data Inspector to visualize both throughput and average cycle time. Using Little's Law, how does the average WIP level compare to the CONWIP system's level?
4. Compare finished goods inventory levels and demand backorders' average wait times between the Push and CONWIP paradigms. Do you see any issues with these results? If so, what would be appropriate strategies for trying to resolve these issues?

BIG PICTURE: This exercise is designed to illustrate a tradeoff inherent in the CONWIP paradigm - demand backorders versus CONWIP and Finished Goods Inventory levels. By choosing the CONWIP level at the minimum possible number for a certain throughput, it is expected that demand backorders (and fill rate, the fraction of demands filled without backorder) will suffer. If minimizing backorders and their wait times is important, then a natural remedy with the CONWIP paradigm is to increase the CONWIP level (which should increase the Finished Goods Inventory level).