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Queueing theory, variability, and capacity: Learn the nerdy principles behind fast shipping
Mochila is not your average 3PL. Unlike most 3PLs, our founder and leaders are mathematicians and computer scientists, and we rely on this unique background and knowledge toolkit to help us solve challenging logistics and supply chain problems through the most efficient use of process design and technology.
To that end, below is a little peek behind the curtain as to what this looks like in practice, and how we transfer these principles into strategic, efficient processes on the warehouse floor and beyond.
One important way in which we leverage this know-how? Facilitating faster shipping. In today's world of ecommerce fulfillment, faster shipping is a requirement for customer satisfaction and retention. As Amazon constantly raises the bar on customer delivery expectations, it is inevitable that all retailers need to increase the speed at which they can deliver orders to their customers.
To assist ecommerce retailers in meeting these customer expectations, it is critical that 3PLs design processes that are able to support these speeds – and support these speeds at scale.
All 3PLs understand the importance of faster shipping, but most 3PLs have not designed the processes to support it. They have overlooked – or in many cases, lack the sophistication to develop – this component that is absolutely critical to the services they deliver.
Queueing theory is a branch of mathematics devoted to modeling how long it takes for a specific operation to complete a task. For example, how long does it take a factory to produce a widget, how long does it take a call center to handle a call, or – in our case – how long does it take for a fulfillment center to fulfill an order?
Importantly, queueing theory is interested in the total time it takes to complete a task. The total time includes not only the time it takes to actually work on that task but also the “wait time” elapsed between the time a task could conceivably be started and the time that work on the task actually begins.
To place this in the context of a fulfillment center, when an order is sent to the fulfillment center to be processed, the order will most likely not be immediately picked, packed, and shipped upon receipt; it is much more realistic to assume that some amount of “waiting time” will elapse prior to the time at which someone begins picking that order, and then another "wait time" will elapse between the picking and packing processes as well.
Queueing theory models the total time it takes until that order is fulfilled – both the actual time spent processing the order plus the time that order spends waiting to be processed (in other words: total time to fulfill an order = waiting time + processing time).
To arrive at a model of the total time is takes to fulfill an order, queueing theory takes into account parameters such as the following:
(1) at what time intervals do orders arrive at the fulfillment center (e.g. an order arrives every 5 minutes)
(2) how long does it take to process an order (e.g. one operator can process an order roughly every 4 minutes)
(3) how many operators are available to process orders
Based on these parameters, queueing theory can then provide estimates of the total time it will take to process an order. (Note: there are many other parameters as well, but we have not included them here to try to keep things simpler.)
One of the key principles behind queueing theory is the fact that it is a probabilistic model. In other words, queueing theory specifically accounts for variation, both in the intervals at which orders arrive to be processed, as well how long it takes to actually process an order.
For example, on average, orders may arrive at the fulfillment center every 5 minutes, but sometimes orders may arrive earlier and sometimes they might arrive later. Similarly, it may take an operator 4 minutes to pick and pack an order, but sometimes orders may be picked and packed much faster and sometimes they will be picked and packed much slower.
Queueing theory helps us to model all of the complexity in that variation so we can develop the right processes, systems, and resources necessary for avoiding delays.
Skipping over a lot of the complicated math, below is a summary of the key insights queueing theory can give us into fast shipping:
1. The process of shipping orders inherently involves variability. In order to ensure orders ship quickly and on time, we need to account not only for the average time it takes to ship an order but also the variability in the time it takes to ship an order.
2. We should care about this variability because variability can increase processing times exponentially. This means that as you increase complexity (and hence, variability) in the system and as you also commit to faster shipping times, you need to have highly intelligent systems and processes to manage that variability and prevent catastrophic delays.
3. To achieve world-class service and shipping speeds, we need to work to both reduce variability and increase capacity. As I outlined in the article on the best ways to work with your 3PL, an important component to achieving world-class service for your customers is proactively collaborating with your logistics partner on ways to (1) simplify processes and make them more predictable, and (2) ensure your 3PL has ample capacity available to process orders. In order to be exceptional, you have to work on both simultaneously.
4. The right 3PL partner should understand these dynamics and should be building systems and processes to mitigate these causes of delay. There are plenty of 3PLs that can perform well in a world where there is not much variability and/or the shipping times are slower. But when you increase the complexity (and hence, the variability) and/or the shipping speed, delays can occur – especially when both are happening at the same time. And because there is an exponential relationship between variability and capacity on the one hand and the time it takes to process orders on the other, what may seem like small changes to the retail professional working with a 3PL can actually result in quite significant delays.
There are many different types of variation inherent in order fulfillment, but some of the primary sources of variation are:
1. The range of SKUs that are available for sale. The wider the range of SKUs offered, the higher the variation there will be in processing time. The reason: customers can choose any combination of different SKUs, so a picker in the warehouse may have to traverse the entire warehouse to pick all of the items in certain orders. For other orders, however, all of the items may be in the same part of the warehouse.
Relatedly, variation can result from the types of items being processed. For example, the handling of t-shirts is very different than the handling of bulkier winter coats; picking and packing ceramic mugs is very different from processing furniture orders. Both intelligent process design and technology can help to mitigate these sources of variation (more on this below).
2. There is a wide range in the number of units in an order. For example, wholesale orders will typically have a lot more units in a box while e-commerce orders will have fewer units per box. This usually means that it will take a lot longer to process a wholesale order than an e-commerce order (but it usually takes less time per unit for a wholesale order). It's important to plan for these differences when creating a fulfillment process – while maintaining the flexibility to shift resources between wholesale order processing and e-commerce order processing.
3. There are special packaging requirements for different categories of orders. Different packaging requirements will lead to variation in processing times. For example, certain wholesale orders – especially those for EDI trading partners – often have special prep requirements like labeling, tagging, and garment on hangers. Or e-commerce orders that require specialized handling like gift wrap or handwritten notes can also increase the variation in processing time. This can be especially challenging when the mix of orders shifts suddenly – like gift wrap around the holidays – and the fulfillment operation is not prepared to absorb that variation.
So what steps can be taken to reduce variability, and thereby, increase our shipping speeds? Thankfully, there are many options:
1. Shorten processing times with technology. Using the right combination of intentional process design, machines, and software, we can concentrate more of the order processing times around the average processing time. (In mathematical terms, we reduce the standard deviation of the process.) To continue with the example of the first type of variation noted above (the range of SKUs processed), smart software can optimize the distance a picker has to travel, and automation can bring inventory spread throughout a big area to a central location. Let's say an order containing SKUs spread out over the warehouse takes 5 minutes to process without any optimization. After we use software and automation, that time might shrink to 3 minutes – removing a large amount of variation from the process.
2. Group orders with similar processing requirements together. To reduce variability, we can group similar types of orders together and process them at the same time. For example, we might process all wholesale orders together, and then all e-commerce orders requiring gift wrap, etc. And while this does reduce variation, it also demands flexibility and cross-training so that the capacity does not become overly specialized: if wholesale order volume or gift wrap order volume surges, the operation needs to be able to shift resources seamlessly from one type of order processing to the other.
3. Reduce the processing time of the orders that require the most time to process. For example, if an order that requires gift wrap takes an average of 12 minutes to complete and that average can be reduced to an average of 9 minutes, this can also have a big impact - especially when the number of orders requiring gift wrap significantly increases.
4. We can intentionally process some orders on a delay. Having a buffer of orders helps to smooth out the variation in when orders arrive. For example, it may be able to process wholesale orders in advance. Even within e-commerce orders, it can be useful to have different service levels and same-day shipping cut-offs from different types of orders. Many brands will promise later cut-offs for express orders and implement earlier cut-offs for free shipping for this reason. While it is possible to have later same-day shipping promises for all orders, this means the variation and average processing times need to be low, and there needs to be a lot of additional capacity to handle unexpected increases in demand.
In addition to reducing variability, it is vitally important to also work on ways to increase capacity. Increasing capacity takes both time and resources, but there are steps smart 3PLs and their clients can take to efficiently increase capacity:
1. Reduce the average processing time for orders. If an order has an average processing time of 4 minutes, +/- 1 minute, shrinking the average processing time to 3 minutes, +/- 1 minute can dramatically reduce delays and shorten the total processing time. These improvements can often only be achieved with a close partnership between the 3PL and the brand. Examples of projects that reduce processing include collaborating on new packaging that reduces packing times and working with manufacturers to use barcodes that are easier and faster to scan.
2. Increase flexibility. Having a staff that is cross-trained as well as having flexible stations that can process a range of different types of orders are powerful ways to increase capacity, since resources can be shifted at a minimal cost to wherever the demand is greatest. In queueing theory, this is referred to as the benefits of pooling (resources are shared or pooled across potential tasks rather than being over specialized). From queueing theory, we know that the benefits of pooling are extremely powerful.
If a 3PL isn't taking advantage of the benefits of pooling resources or using its resources flexibly, then it will either have above-average costs or it will have difficulty scaling with increases in demand. It is important to note that in order to capture the benefits of pooling and maintain exceptionally high levels of quality, the operation must have very robust quality control measures. At Mochila, this means using our proprietary software to ensure operators cannot make mistakes, and deliberately building and managing a cross-training program to ensure all operators have the proper training, skills, and experience to process orders without defects.
3. Simplify tasks and operator training. To increase capacity, it is critical that we reduce the time it takes for a new operator to be trained and effective. At Mochila, this means breaking the process into the smallest possible parts and controlling every step of the process with software so new staff can be hired and trained in a short period of time. I have seen some 3PLs explain processing delays during times of peak demand by saying they deliberately do not hire new staff to meet the peak demand. However, every good operator knows how important it is to be able to add additional staff to handle changes in demand.
4. Reduce defects. Defects cause delays in processing. Think about what happens if an operator picks the wrong item: assuming every packer scans each item, the operator packing that order might prevent the wrong picked item from going to the customer. However, that incorrectly picked item still needs to be put back on the shelf, and the right item has to be picked in order to complete packing that order. Every defect introduces delay and waste, and reducing defects means that operators are only spending time on shipping orders (not re-work/fixing defects) – which ultimately means more shipped orders are produced.
1. Create a buffer of additional capacity. For instance, having a few additional packing stations above the projected required number of stations can be a very cost-effective insurance policy. This small buffer can have a disproportionate benefit when demand surges or processing needs increase.
A key insight from queueing theory is that a little more capacity gives a non-linear decrease in processing times and increase in shipping speeds - especially when the utilization of the system is high (i.e. over 85% utilized). It's not always cost effective to have extra capacity, but when there are efficient ways to do this, it is almost always worth it.
2. Stop defects and waste upstream. For example, ensuring new inventory arrives at the warehouse properly labeled with an accurate packing list and already organized in a manner that is ready to be stocked can go a long way to improving the speed and efficiency of the order fulfillment process.
3. Communicate changes in demand – both total volume and mix – with your 3PL. The more advance notice your 3PL has about changes in not just the aggregate volume, but also changes in the mix of orders, the better chance they have of increasing capacity ahead of demand.
As you've probably gathered, a good forecast should include not just the projected volume but also some estimate of the potential range of volumes so your 3PL can prepare for the full range of potential outcomes.
4. Work with a 3PL that can help recommend ways to improve your shipping speeds. A good, smart 3PL will understand these principles of queueing theory and their associated implications for process design, and will work with you to proactively reduce variation, increase capacity, and ultimately, increase your shipping speeds and keep your customers coming back.
Want to learn more about how we can apply these intelligent theories to improve your shipping speed? Schedule a call with us to learn more.
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