By Joannes Vermorel, October 2020

A lead time is the delay between the initiation and completion of a process. In supply chains, whenever goods are purchased, transformed or serviced, lead times usually measured in days are involved. From a planning point of view, lead times matter because they imply that most routine decisions must be made ahead of time in order to deliver the intended effect, such as maintaining the quality of service. The need for demand forecasting also typically emerges from the existence of lead times, as the adequacy of a decision - such as an inventory replenishment - depends on unknown future events that will impact the supply chain for the duration of the lead time.

Causes and consequences of lead times

Lead times largely shape how the supply chain operates, and most of its financial elements, such as required working capital and return on capital employed (ROCE). Indeed, longer lead times imply that it takes longer to complete an inventory cycle where materials or products are purchased, possibly transformed, and sold again.

Longer lead times mechanically entail higher stock commitments, even when stocks on hand may seemingly remain low. For example, if a company in Europe orders goods from Asia to be delivered through containers, from the date where the purchase order is passed the company is committed to sell or consume the goods. Yet, in this situation, it will typically take over 6 weeks for the stock levels in Europe to reflect this commitment.

Also, longer lead times increase the dependency on forecasting. When revisiting the example above, the company cannot afford to merely pass a purchase order based on its present needs; by the time the order is delivered, the situation will have evolved. Present stock levels will have been lowered further due to ongoing consumption, and demand will most likely have changed, if only due to seasonality.

Lead times represent a lower bound of the maximal agility that a company can achieve. As a rule of thumb, if the market conditions brutally change then the company remains committed to its past decisions for roughly the duration of the lead times. There are various ways to mitigate these effects, starting with contractual terms with suppliers. However, the underlying risks can rarely be eliminated and are merely displaced within the supply chain.

Considering all the negative impact of longer lead times, one may wonder why companies are frequently opting for what appears to be (subjectively) long lead times. It turns out that there are multiple economic factors that tilt the scales in favor of longer lead times.

Specialization is driving longer lead times: some countries have fairly unique industries (1) that are difficult or costly to replicate locally. Such concentrated industries historically emerged primarily due to high-value materials, which were easy to transport. However, even if aircrafts can reach any point of the globe in less than 24 hours, customs and processes tend to substantially increase the actual lead times when considering overseas suppliers.

Economies of scale are also leaning towards longer lead times. By increasing the batch sizes (frequently materialized as MOQs), manufacturers or transporters can lower their costs. However, as the batched quantities become larger, the number of batches also becomes lower and thus less frequent - with all other things being equal, notably the demand. Nevertheless, industries are not all equally susceptible to economies of scale, which tend to plateau depending on the applicable technology.

Lowering the high quantiles

While a lead time can be improved by reducing its average duration, it’s just usually the improvements concerning the worst cases - i.e. the longest situations - that matter the most. In supply chains, the biggest problems - when measured in dollars of impact - tend to be concentrated at the tail: it’s the unexpectedly high lead times that cause stock-outs or interruptions in production, not the small bumps.

One of the simplest ways to assess those worst case scenarios consists of using quantile measurements. For example, if a supplier is said to have a 7-day lead time for the 95% quantile, it means that 95% of the orders passed to this supplier are delivered in less than 7 days. Those “high” quantiles, i.e. close to 100%, can substantially diverge from the average lead time. The same supplier might be delivering in 2 days on average, which is less than a third of its high quantile estimate of the same lead time.

In order to avoid these quality of service problems, all the inventory buffers within the supply chain - no matter the methodology used - tend to grow linearly, not with the average of the lead time, but with some high quantile of the lead time. Indeed, inventory buffers exist precisely to accommodate variations of the supply chain conditions. The two dominant factors behind the unexpected variations impacting the supply chain tend to be: varying demand and varying lead time.

The total lead time from the original purchase orders from the suppliers to the client deliveries can usually be decomposed in many, possibly dozens, of intermediate steps. In order to either reduce the lead time value or its variability, it is usually effective to decompose this total lead time into its notable sub components, which are simpler to analyze and to improve.

For example, a wholesaler distributing goods from overseas suppliers may face:

• An ordering lead time, caused by the weekly purchase process of the wholesaler itself.
• An opportunity lead time, caused by the MOQs imposed by the suppliers.
• A manufacturing lead time, required by the suppliers to fulfill the purchase order.
• A transport lead time, required by the freight company.
• A reception lead time, for inventorying and quality control by the wholesaler.
• An expedition lead time, required by the distribution center to fulfil client orders.
• A last-mile delivery lead time, required by a transporter to make the client delivery.

For each operation, it is usually of interest to lower both the average delay and the variance of the delay.

Keeping track of all these operations involves a lot of clerical work, which can be massively alleviated via modern IT systems either through barcodes and/or RFIDs. Electronic records are typically stored in the IT systems of the company(ies) involved. Benefits extend well beyond optimizing the lead times, as those systems ensure the traceability of the goods, and to some extent, prevent inventory shrinkage.

Up until the late 1990s, storing and processing all those records used to require costly computing resources, hence, it was not always economically feasible to acquire, and even less to preserve all the minute records generated by the flow of physical goods within a supply chain. However, since the early 2010s, the costs of data storage and computing has fallen well below the point where raw computing resources hardly matter whenever physical flows are involved. Nevertheless, IT costs, notably system integrations, may prevent the acquisition of those electronic records.

In order to improve lead times, and thus typically reduce their high quantiles as discussed above, measurements are needed. Fine-grained lead time measurements are very useful when it comes to root cause analysis. In fact, as the operations vary greatly from one step to the next, the nature of the improvements brought tends to vary greatly as well.

The order lead time typically refers to the time that elapses between the customer order and the delivery of the goods. This duration is notable because it’s the “flavor” of lead time that the general public - as opposed to supply chain specialists - is most accustomed to. In many industries beyond B2C ecommerce, the order lead time is closely related to the quality of service. In particular, stockouts tend to be the dominant factor driving abnormally long order lead times.

Part of the challenge in improving the order lead times consists not of shortening the lead times themselves but of setting the right expectations from the customers with regards to the date of delivery. In particular, several large ecommerce companies seem to have adopted for over a decade the approach of sharing a quantile forecast estimate of the order lead time, which acts as a probable upper bound on the delay. The bias in the delay estimate is introduced on purpose in order to minimize the frequency of the situations where the goods aren’t delivered on time.

The proper anticipation of future lead times is an essential ingredient for the optimization of a supply chain. Much like demand, lead times can and should be forecasted, typically leveraging the existing historical data whenever relevant.

While lead time forecasting is not (yet) a prevalent practice among “demand” planning teams, it must be noted that most of the cyclicities that apply to the demand also apply to lead times. For example, lead times tend to exhibit seasonality, day-of-the-month and day-of-the-week effects. Lead times change over time. For example, a supplier may revisit its own processes to lower the lead times, or increase them to lower its costs. Quasi-seasonality also matters, with events like the Chinese new year, which periodically inflates the lead times as many factories are closed in Asia during this period.

Probabilistic forecasts should be favored for lead times, because as pointed out above, it’s the high quantiles that drive the economic implications of the lead times. The costs and problems are concentrated at the tail of the distribution. However, let’s immediately point out that normal distributions (Gaussian) should not be used for lead times. As a rule of thumb, lead times are never normally distributed, and leveraging such a model leads to vast underestimation of the high quantiles, which in turn, is the recipe to generate an ongoing stream of service problems.

Lead times can be more appropriately modeled as multi-modal distributions that reflect the underlying physical system. For example, when triggering a production line, the production lead times tend to be highly predictable, except if one of the raw materials happens to be missing, in which case the manufacturing lead time may take considerably longer. Thus, the practical modelization of the probability distribution typically involves a mixture of discrete and parametric distributions.

The probabilistic forecast of the lead time is expected to produce a discrete random variable for each inner phase. It is frequently reasonable to assume that those inner phases are statistically independent (eg. the delay imposed by the customs is strictly independent from the manufacturing delay). In those cases, the random variables can be canonically summed, which technically entails a convolution operation performed over the underlying distributions.

Controlled modalities

While the appropriate probabilistic lead time forecasting model is typically multi-modal, there are certain modalities that require a specific treatment if there is a degree of control involved, as opposed to passive observations. For example, if it’s possible to request an air shipment or a sea shipment from a supplier, the two transport modes should not be lumped together from a forecasting perspective. There is a degree of control involved. Each mode of transport has its own variability, and thus, two distinct forecasts are required.

Demand coupling

As production capacities are limited when the demand surges, the manufacturing lead time tends to increase as well. This coupling between demand and lead time negatively impacts the quality of service, as it diminishes the company’s capacity to mitigate a surge of demand through extra purchase or manufacturing orders, precisely due to the extra lead time involved. Thus, it can be relevant to have a joint predictive model of both the demand and the lead time, as the required inventory buffers depend on two factors.

However, when considering manufacturing units that have enough flexibility to (re)organize their job queues, the observed lead times heavily depend on the prioritization given to each specific job. Thus, the appropriate predictive lead time modelization should take into account the queuing aspect of the problem, as lead times can vary dramatically depending on arbitrary prioritization choices. This extra degree of control can be leveraged to mitigate the impact of a surge of demand.

The lead demand presents the quantity of items to be serviced over the duration of the lead time. This value is of particular interest because in order to avoid stockouts, the total stock (sum of the stock on hand plus the stock on order) must remain above the lead demand at all times. When the total stock drops below the lead time, a stockout is guaranteed to happen.

Assuming that probabilistic forecasts can be produced for both the future demand and the future lead time, it becomes possible to compute (high) quantile estimates of the lead demand, as defined by:

$$\text{QLeadDemand}(\tau, y, L) = Q_\tau \left[ \sum_{t=1}^{L_\omega}{ y_\omega(t) } \right]_{{\omega \in \Omega}}$$ Where:

• $0 \leq \tau \leq 1$ is the target of quantile estimate
• $y$ is the demand, varying over time
• $L$ is the lead time
• $Q_\tau[..]$ is the quantile of the inner real-valued function
• $\Omega$ is the set of possible outcomes
• $t$ is the time, 1 being the first future period
• $y_\omega$ is the demand associated to the outcome $\omega$
• $L_\omega$ is the lead time associated to the outcome $\omega$

This quantile estimate of the lead demand is of interest when trying to maintain a target service level. Assuming a simple single-SKU single-supplier no-MOQ inventory model, then the quantity to be replenished at any point of time can be defined by the formula:

$$\text{ReorderQty}(\tau) = \max\left(0, \text{QLeadDemand}(\tau) -\text{OnHand} -\text{OnOrder}\right)$$ Where:

• $\text{OnHand}$ is the stock on hand
• $\text{OnOrder}$ is the stock on order

This formula implicitly assumes that no demand gets lost when facing stockouts. This assumption is not reasonable in many situations, e.g. consumer retail, where typically clients either renounce, go for a substitute or go for a competitor instead of merely postponing their consumption. In order to lift this assumption, the impact of the lost demand must be explicitly modeled. This is particularly important when demand is highly seasonal, as the goods that become available after the seasonal peak may remain unsold or unused for a long period of time.

The lead time can be seen as an input factor to compute the replenishment, as detailed in the previous section. However, the lead time itself depends on the ordering (or production) schedule. Moreover, the schedule itself is typically intended to be suitable to achieve expected economies of scale by reaching the desired EOQ (economic order quantity), MOQ (minimal order quantity), or the nominal production batch size.

Thus, supply chain practitioners are frequently faced with a feedback loop between the decision that needs to be made today (replenishment and ordering) and the point of time when this decision is expected to be repeated in the future. Put in simpler words, the quantity to be ordered today depends on the date of the next reorder: a later reorder means that a larger quantity is required. However, the date of the next reorder is also influenced by the present day reorder: a larger immediate reorder means a later date for the next reorder.

As the explicit modelization and numerical optimization of this feedback loop are nontrivial, supply chain practitioners frequently establish a rough schedule (i.e. one order per week, per month), somewhat in line with the target quantities to achieve the desired order size (i.e. the EOQ, MOQ or batch size). This schedule is then assumed to be rigid, letting the reorder quantities vary as needed. However, the fixed-schedule approach introduces inefficiencies by design, as the supply chain does not leverage all its degrees of freedom.

Better numerical solutions can be devised to natively address this feedback loop angle. The algorithms involved in those solutions typically fall under the umbrella of reinforcement learning. Detailing those algorithms is beyond the scope of the present document however.

Vertical specific problems

Lead times are varied and the adequate perspective typically varies along with the vertical being considered. In the following section, we review a few verticals that present notable specific challenges relevant to the lead times.

Shelf life for fresh food

Fresh food is highly perishable, and as a result, products come with short shelf lives. Shortening the lead times is typically critical in order to preserve the market value of the products to be put on display as much as possible. Thus, when balancing options (packaging, transport) that impact the lead times, those options influence not only the quality of service, but frequently also the expected revenue and expected waste to be generated by the supply chain as a whole.

Also, brands or distributors typically face multiple sourcing options with distinct lead times vs. shelf life tradeoffs. For example, a brand can directly buy from the producer, which involves a long lead time but, upon reception of the products, a high self-life; or the brand can buy from a wholesaler, which involves a short lead time, but the reception of products with a short shelf life. In these situations, a proper supply chain optimization balances the two options, which in turn requires a predictive analysis of the respective lead times and shelf lives.

Turnaround time (TAT) for MROs

MROs (Maintenance Repair & Overhaul) manage repairable components. For every component change to take place, a serviceable component must be readily available while the dismounted component is unserviceable until repaired. The total delay from the request for the component change to the renewed availability of the serviceable unit is referred to as the turnaround time.

The stock of components kept by the MRO is directly dependent on the TAT. Indeed, if the MRO had the (theoretical) capacity to instantaneously repair an unserviceable component, there would not be any need for stock. As a result, lead time forecasting and optimization tend to be even more critical than demand forecasting, as far as MROs are concerned.

The emphasis on TAT analysis (vs. demand analysis) is typically compounded by the nature of the unscheduled repairs, which are precisely due to breakdowns that involve some degree of irreducible uncertainty to perform the underlying physical processes - i.e. if there was a way to proactively address the problem, then, diagnostics would turn those operations into scheduled repairs.

Reverse logistics for ecommerce

Most consumer ecommerces in most countries offer nowadays the possibility to return the goods if the consumer doesn’t like what they’ve received. However, the rate of consumer returns varies greatly from one country to the next, mostly for cultural reasons. For example, in fast fashion ecommerce, German consumers typically exhibit greater than 50% return rates. Those high rates are driven in part by the habit of ordering multiple sizes and returning all sizes but one.

When return rates are high, the online retailer needs to anticipate that a sizable portion of the stock will actually flow back; otherwise, the retailer is at risk of systematically ending-up with overstocks as the items flow back, after replenishment orders are passed. However, there are three uncertainties with regards to the future returns: first, whether the items will be returned or not, second, whether the items will pass quality control after being received, and third, how much time will have elapsed until the items can be resold.

Those forecasting problems are quite amenable to highly specific structured analysis. Indeed, the maximal number of items that can be returned at any point of time is capped by the volume of recent shipments. Putting a cap on tail events is of prime interest from a supply chain perspective. Also, when facing the “3 sizes picked, 2 sizes returned” situation, it is possible to anticipate with great certainty the fraction of the consumer orders that will be returned.

Leasing businesses, such as car leasing companies, or office furniture leasing companies, face situations that are partially akin to MRO situations, but not quite. Indeed, the proper level of inventory depends on the future demand, but also on the future retention rates, as inventory flows back to the leasing business at the end of the lease. As the leasing company does not have full control over the lease duration, those durations need to be forecast in order to optimize the inventory. The duration of these retention periods and their effect on inventory can be analyzed and forecast through the lense of the regular lead times.

However, most leasing businesses have some degree of control over the retention period via their pricing and the special offers they can grant to their clients. Similarly to a retailer that can boost the demand for a product by putting it on promotion, a leasing business can boost its retention period by offering more favorable terms. Thus, in leasing situations, the pricing analysis is entangled to a large extent with the lead time analysis.

The term “antipatterns” refers to practices, processes or tools that are intended as solutions but fail to deliver the expected results. In supply chains, lead times are prone to a series of antipatterns that we review in this section.

Unappreciation

Lead times are one of the core reasons why planning and forecasting matter at all from a supply chain management perspective. Yet, lead times - as a phenomenon to be modeled and shaped - usually only receive a tiny fraction of the attention that other competing phenomena, such as demand, get. There are multiple institutes dedicated to the demand forecasting, but none dedicated to lead time forecasting. This vast imbalance in terms of allocation of efforts frequently leads to situations where quantitative analyses are made down to the gram - on the demand side - in order to later round them to the nearest ton - on the lead time side. Most verticals require lead times to be first class citizens of the supply chain optimization - on par with the demand -, both in terms of process and in terms of tooling.

Over-utilization

In most supply chains, the bulk of the inventory - including raw materials and semi-finished goods - spends most of its time immobile and waiting for the next operation. Processing queues tend to form at every single step of the supply chain, and each queue comes with a wait time of its own. However, as utilization of any asset gets closer to 100%, the wait time in the queue gets closer to infinity. Thus, the asset utilization rate is a tradeoff between the amortization of the asset itself and the lead times involved. This tradeoff consists of balancing the diminishing returns of the higher utilization rates against the exponentially growing waiting times.

Flying blind

Improving the lead time usually starts by properly assigning blame to the specific part of the process that is causing the biggest avoidable delay. However, the lead time measurements themselves can be misleading. For example, when measuring a supplier lead time, if the delivered pallets frequently happen to sit unprocessed pending their electronic reception on a dock, the measurement can largely inflate the supplier lead time, while the process at fault is the reception itself. These problems typically cannot be addressed through data analysis, but require onsite observations to understand whether the data acquisition process can be trusted or not. Also, the very acquisition of electronic “tops”, as it represents an extra workload for the staff, can itself increase the overall lead time - which defeats the original intent.

Emergent LIFO

Processing jobs or orders with a FIFO (first in, first out) ordering, is nearly always a requirement in order to ensure a reasonable quality of service. Indeed, violations of the FIFO principle erratically generate excessively long lead times. However, at a physical level, the LIFO (last in, first out) ordering tends to emerge naturally in many situations, and it takes specific efforts to prevent these emergent LIFO situations. For example:

• Every incoming job order (picking, production, repair, etc.) gets automatically printed as a “job sheet”. All the incoming job sheets lay printed in a box. However, due to the nature of the printing process, the latest incoming jobs lay on top of the pile, steering operators toward LIFO.
• If a conveyor happens to be too short, goods tend to overflow the conveyor and may get put on the ground at the start of the conveyor. Quickly, a heap of goods is formed, and the goods that have been around the longest happen to be at the bottom of the pile. Unpiling the goods follows the LIFO ordering.
• When boxes or pallets are unloaded on a dock through a flow of transporters, unless the dock is emptied after each unload operation, the freshly arrived goods tend to be put in front or on top of the previous ones, which results in LIFO later, when the goods are processed.

Notes

(1) As of 2020, there are only three countries that produce RAM (Random Access Memory), a fundamental hardware component of modern computers. There are also three countries that account for nearly 90% of the worldwide reserve and production of lithium, an essential element of modern batteries.