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Robotics Tech Papers

How lot sizes change your efficiency

Robotic Materials Inc.

The saying goes that single-item flow is a lot more efficient than batch processing. This is easy to see when considering that seeing large inventories piling up anywhere in your factory and other stations waiting to process a batch are one of the Seven Deadly Wastes. But how bad is it? Would reducing batch sizes make your process 20% more efficient? Or double? Will it compensate the additional motion and transportation – other deadly wastes or is the cure worse than the disease?

Let’s consider a simple scenario comparing lot sizes of four that have to be processed by three stations. For simplicity, we assume that each item has to be processed individually, which takes one time step, and moving one or all items to the next station also takes one time step. The animation below shows processing the items in lots of four.

Processing items in lots of four at three different stations. Moving the material through the system takes 15 time steps.

We can now compare this with a process in which each processed item is immediately moved to the next station. The advantage is here that all three stations will be able to work in parallel. The difference is dramatic:

Moving items to the next station immediately allows processing the same amount of material in 9 time steps.

Processing the same amount of materials is almost double as fast. This is no surprise, as work is done in parallel, requiring up to three workers, whereas processing the entire lot can be done by a single worker. (The cost of labor remains the same, as the same amount of work overall is being done.)

The key difference, however, is that materials have to be moved 12 times vs. 3 times. This works on a so-called flow line, where stations are next to each other and workers can pass parts from one to the other, but will increase cost substantially in a job shop setup, where each transfer of material requires significant transportation. This is why flow-lines are so much more efficient than job shops.

Would it be worth to put in a dedicated material handler to simulate a flow shop in such a scenario? Let’s do the math real quick. Assume we have lot size L with L=4 in this example. Assume we have stations with S=3 in this example. Processing the entire lot therefore takes O(LS) time steps with O(S) moves. (Indeed, LS=12 plus S=3 is 15.) The “Big-O” notation is used to analyze algorithms in computer science and reads “on the order off”. It allows us to ignore details like differences in processing time across different stations, but focus on the fact that lot size and number of stations are multiplied.

The time it takes to process lots of size L through stations is proportional to the product of and S.

Let’s look a single item flow line now. Once the first item has been processed, it is moving to the next station. The first station is done after time steps. By this time, the other stations have begun working, however, and the first item is leaving the line after being processed at stations. The total time is therefore O(L+S). Another way to think about is that the first item will be done after S time steps and the last L time steps later. The total number of transportation events is now O(LS).

The time it takes process L items through stations using a single-item flow is proportional to the sum of L and S.

Assuming you need to process L=1500 parts through S=6 stations, the difference in processing time is one order of magnitude, or it is almost 10 times slower to process items in a lot. If material handling would be free in terms of cost and the extra head-aches it creates, moving your process time from O(LS) to O(L+S), would be a no-brainer. It would allow you to substantially decrease lead time, rent, and facility cost.

Transportation is never free, however. Workers need not only to move materials from station to station, they would also need to know where to move each item, something this would change with every product being made. A trade-off is to chose intermediate lot sizes. For example, instead of processing 1500 items at the time, workers could work in batches of 100 and then pass on these smaller batches to the next station. Note, that the same math applies: is now 15 (15*100=1500) and O(L+S) is still better than O(LS), only the difference is less accentuated.

In practice, the batch size B should be chosen so that processing B items at a specific station takes as much time as moving these parts from that station to the next. For example, when using a dedicated material handling worker who picks up processed items every 10 minutes, should be the number of items a worker can process in 10 minutes.

An elegant solution to this problem (and one that we can help with) is using material handling robots that connect the different stations at a constant rate of flow, picking up whatever number of items already have been processed and moving it to the next. Operating such robots is substantially cheaper than the cost of a worker (up to 8 times in industries such as aerospace engineering) and will automate a lot of the book-keeping, such as when to move materials where.

Reducing lot sizes becomes problematic, when processing times at different stations widely vary. There are two extremes: in one, all materials will need to be processed at once, for example when washing or coating the parts. In the other, processing takes much longer, leading to inventory build-up at this station. The solutions are simple, however. In the first case, the simulated robotic flow line needs to end just before the batch processing station, with another one starting right afterwards (if necessary) to maintain all the benefits. In the second case, additional resources (workers) should be added to balance the line. Here, the robots can help with arbitrating the load, for example, by automatically switching between delivery to two different stations.

Robotic Materials Inc. mobile manipulation solution is available for rent or purchase, contact us today!

Nikolaus Correll is the CEO of Robotic Materials Inc. and a Professor of Computer Science at the University of Colorado at Boulder. He has been designing and building large-scale distributed robotic systems from swarms of robot as small as a ping-pong ball to teams of mobile manipulating robots with fine manipulation skills. He is manufacturing robots for manufacturers in Colorado since 2016.

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