## Time horizons in inventory optimization

You don’t need to explain the importance of time to a supply chain professional. Working out when you need something is as important as working out how much you need. But as a topic, time horizons in inventory optimization is an underappreciated factor.

There are various complexities related to time horizons in inventory management that are often imperfectly understood. In this article, we will set out some of the key time-related concepts for inventory management, starting with the simplest and getting progressively more complex. In our experience, most organisations have room to improve in at least one of the areas we explore below, meaning their inventories are sub-optimal.

(More advanced supply chain practitioners might like to skip Part 1.)

### Part 1 – Basic time concepts in inventory management

#### Lead Time

Lead time is the time between an order being placed and an item being received or manufactured. Lead time is very important in inventory management as the longer the lead time, the more safety stock is required, all other things being equal. Long lead times also make organisations less responsive and agile.

Lead time refers both to the time for materials to come from suppliers, and, in a manufacturing context, for the time it takes to produce something. Manufacturing lead time can be dependent on considerations such as capacity utilisation. With bill of material items, concepts such as cumulative lead time, exposed lead time and decoupling points are essential, but not the focus of this paper.

#### Cycle time

Cycle time is the time between orders and is not to be confused with the lead time. If you order a component every two months and it takes 2 weeks to arrive, then the cycle time is two months and the lead time is two weeks. Note that the cycle time will be greater or less than (or identical to) the lead time.

#### Review Periods

The review period is how frequently you check how much stock you have. You might, for example, check your inventory levels once per week and then decide whether to place an order or not. This is called periodic review.

The main alternative to periodic review in make or buy to stock scenarios is continuous review where inventory levels are constantly monitored and a new order is placed as soon as inventory drops to the reorder level or below.

Many equations and other applications assume continuous review. This means they assume that the instant inventories fall to the reorder level, an order will be placed. If this is not the case then the impact of review periods needs factoring into lead time.

There are good practical reasons why continuous review is not implemented in many situations. Wherever multiple items are being managed, it makes sense to aggregate orders at least daily, if not weekly or even monthly, rather than generating high numbers of individual orders. This aggregation allows procurement, logistics and production to optimize their own processes more easily.

However, infrequent reviews can be the cause of both excess inventories and shortages. Reducing a monthly review period to a weekly one will normally in itself reduce the need for inventory and improve responsiveness.

#### Planning horizon

The planning horizon is the period in the future for which plans are made. Organisations may well be working to multiple planning horizons at a time, combining, for instance, approximate plans for the coming 3 months, with very detailed plans/schedules for the coming week. Having the required materials to hand to execute the plan is a core function of inventory management. Plans are updated on a rolling basis and are subject to almost constant change. Obvious challenges arise where lead times are longer than planning horizons.

#### Fixed horizon

In order to reduce some of the inefficiency created by changes to production schedules, it is common to have a fixed horizon, during which production proceeds according to plan regardless of changes in end demand. During the fixed horizon, orders cannot be cancelled and production schedules should not be changed.

While beneficial for production efficiency, fixed horizons propagate end demand variability further upstream and can cause or exacerbate bullwhips: with a two-week fixed horizon, for instance, you are constantly producing to the expectation of demand from two weeks ago. The difference between actual demand and that expectation needs mitigating in the next period.

On the other hand, fixed horizons do provide certainty in the short term: orders can be placed and labour scheduled with a high degree of certainty for everything within the fixed horizon. In principle you shouldn’t need safety stock for a fixed horizon in as much as you have removed the demand uncertainty from it.

#### Safety time

Safety time is a sister concept to safety stock. Instead of buffering uncertainty with quantity (i.e. safety stock), you buffer it with time (i.e. by producing or buying it ahead of when you think it is needed). The simplest way to think about it is that safety time is usually good at dealing with uncertainty in timing (on the demand and supply sides) whereas safety stock is usually best at dealing with uncertainty in quantities.

#### Variability

Variability describes how much values vary from the mean (demand and lead time being the main two values whose variability influences inventory management). Variability can be measured using the coefficient of variation (the standard deviation divided by the mean), or a related measure, so that it is comparable between items. Important is that as the dispersion from the mean goes up then the measure of variation goes up.

To give a simple illustration:

- Item 1 has average weekly demand of 1,000 units and a standard deviation of 200 units.
- Item 2 has average weekly demand of 100 units and a standard deviation of 30 units.
- Item 1 has a larger standard deviation than item 2 (200 vs 30) but item 2 has greater variability than item 1 (30/100 vs 200/1000).

#### Intermittence

Intermittence describes how likely it is that you have demand in a given time period. Demand series with many zero values, such as for rarely-needed spare parts, are intermittent.

### Part 2 – Time concepts for inventory analytics

#### Buckets and slices

When analysing inventory, two basic concepts relating to time are essential: the slice and the bucket.

A slice is the granularity in which transactional data is (made) available. With modern ERP systems, every stock movement might be time stamped to the second, but for most practical purposes it is not necessary to use slices any more granular than a day, i.e. demand can be aggregated at a daily level to create the basic “slices” of data.

A bucket defines the frequency with which it is meaningful to analyse the data. If, for instance, inbound deliveries are only possible once per week, then it makes sense to work with weekly buckets of data rather than daily buckets.

Buckets can be expressed as a number of slices. So you might have 365 slices in a year and each bucket is just one slice (a daily bucket). Or you might have 12 slices in a year and each bucket is 3 slices (a quarterly bucket). And so on.

These terms may seem fussy or overly technical, but in inventory analytics they are the essential building blocks of everything else. Generally speaking, organisations can benefit from increasing the granularity with which they analyse their inventories.

Your choice of bucket size also in itself influences your perception of variability. Variability decreases as your bucket size gets larger. So monthly variability is usually lower than weekly variability which is lower than daily variability. (This is why forecasts tend to be more accurate the more you aggregate them.)

One further important consideration here relates to working days. You might operate 7 days per week, in which case you might work with 365 slices in a year. But if you only operate 5 days per week then you should choose 260 slices in a year (or fewer, if you also factor in other non-working days like public holidays). Otherwise, any subsequent analysis will be significantly thrown because of the impact of the zero values.

To give a simple illustration:

Demand per day:

- Monday 8
- Tuesday 12
- Wednesday 10
- Thursday 11
- Friday 9
- Saturday 0
- Sunday 0

Considering all 7 days, average daily demand = 7.14 and standard deviation = 5.04. Coefficient of variation (CV) = 0.706

With just 5 days (Monday to Friday), average daily demand = 10 and standard deviation = 1.58. Coefficient of variation (CV) = 0.158

(Note also that if you work with weekly buckets, the working day problem disappears, since regardless of the number of slices that are greater than zero, weekly demand is identical.)

*Appropriateness and “one size fits all”*

In the previous section we talked about the frequency “with which it makes sense” to analyse data. But how do you determine what makes sense when it comes to setting bucket size?

Consider a fresh produce business. For one half of the year, it sources fruit and vegetables from local or regional suppliers, with lead times ranging from 1 to 3 days, in order to supply retailers based on daily requirements. For the other half of the year, however, it sources the same products from the other side of the world, with lead times ranging from 4 to 6 weeks.

During the first half, it makes sense to look at daily data, since inventories can be run much leaner with such short lead times. But during the second half there is both a logistics constraint (there are a finite number of vessels sailing each week) and a greater need for safety stock due to the increased lead time. At this stage it makes more sense to consider weekly data.

The simple example above is intuitive. However, in more complex manufacturing contexts, there are usually significant differences on both the demand and supply sides. Demand may vary greatly by day but not by week, or it might vary significantly by week too. Lead times may be as low as a day or as high as six months or more and are themselves subject to variability. Logistics constraints will vary. High runners may be closely monitored and managed “day to day”. Some C articles may be provisioned for the whole year and then ignored.

This range poses a challenge for the inventory analyst. Some items might most meaningfully be considered in daily buckets, others in weekly buckets, others in monthly or even larger buckets.

There is also a distinction to be made between how an item is currently being managed and how it might optimally be managed. For instance, planners may place monthly orders with suppliers simply because they don’t have time to do it more often or just because “that’s how it’s always been done”. But this monthly review cycle might be sub-optimal for the demand being managed.

To avoid the complexity of working with multiple bucket sizes simultaneously, a “one size fits all” approach might be taken to inventory analytics. This is often a good, pragmatic move that shouldn’t even matter too much in a first instance.

However, a differentiated approach can, in a second phase, add significant value over a one size fits all approach. If you’re working with a standard bucket size across all items regardless of their own characteristics, then how optimal each item’s inventories are will be influenced by how close their most appropriate bucket size is to the standard in use.

### Part 3 – The impact of using mismatched or sub-optimal time horizons

Time is an essential factor in inventory management. Failure to take account of the time horizons in play leads to several sub-optimal outcomes. It affects both your understanding of your inventories and, accordingly, how you manage your inventories.

Here we are going to look at the impact on inventory management of using sub-optimal time horizons in three areas: variability, intermittence and forecasts.

#### Working with Variability

Variability is one of the most important concepts for inventory optimization, but it tends to be poorly understood, perhaps because dealing with it well requires a certain understanding of statistics.

In practical terms, to optimize inventories, variability should inform two main decisions: the setting of safety stocks and the setting of stock policies. But there are very important time-related considerations here that we often see under-appreciated, both of which come down to one key concept:

**The variability that really matters is variability over the lead time.**

Once an order is placed, you have to wait at least the lead time before it is received. The whole purpose of safety stock is to protect you against this variability. (This is still the case even if your cycle time is shorter than your lead time.)

What matters when setting safety stock levels is the deviation (how far expected values are from the mean) over the lead time.

The more important consideration when choosing appropriate inventory policies (such as whether to use replenishment or not) is variability. It is not that replenishment cannot handle variability – quite the opposite – but it is important to understand that replenishment ceases to be a good model at very high levels of variability. (Variability is of course not the only factor when deciding whether to use replenishment or not – forecastability is the most important consideration.)

But to do both of these things well, you should ideally look at them over the lead time.

To continue with the simple example we gave above, with 5 days of demand in a week:

Monday 8

Tuesday 12

Wednesday 10

Thursday 11

Friday 9

Looking at daily variability:

Average demand = 10

Variance (s2) = 2.5

Standard deviation = 1.581

CV = 0.158

However, the lead time is 3 days. So over that (3-day) lead time:

Average demand = 30

Variance (s2) = 9

Standard deviation = 3

CV = 0.1

Comparing the two, the deviation is larger over the lead time (3 vs 1.58) – logically, since there are more days’ demand – but the variability (the CV) is smaller (0.1 vs 0.158) because the values are closer to the average as a percentage of the average.

The deviation is the number which should be factored into safety stock decisions, and the variability is the number which should be used to help inform inventory policies and XYZ classification.

*XYZ analysis** is a method to classify your inventory based on variability, typically using the Coefficient of Variation (CV). Items are classified as flat (X), variable (Y) or erratic (Z).XYZ analysis should in principle deliver different splits depending on how variable demand is relative to a pre-defined standard. Eg you could have predominantly X’s if demand shows little variability for most items, or you could have only Z’s if demand is erratic for all items. Sometimes we see organisations manipulate the thresholds between X, Y and Z to deliver a certain proportion in each. This is fair enough if the purpose is purely to divide up responsibility (although that could be done with significantly less mathematical effort!) but that is not the best approach if you want to use XYZ analysis to actually understand and manage variability.*

#### Working with intermittence

We gave a simple illustration above of the impact of including or excluding zero demand days (i.e. weekends in the example given) on some of the key statistics such as mean and standard deviation. Including zeros will tend to reduce the mean and increase the standard deviation.

The same principle applies to intermittent demand. Intermittence relates to the time between demand points.

Demand can be variable and intermittent or just variable or just intermittent.

Here is a data sequence that has significant variability but low intermittence:

5,15,20,7,10,2,15,4,9,11,6,6,19,0,14

Here is a data sequence that has high intermittence but low variability:

0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1

And here is a data sequence that has high variability and high intermittence:

25,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,142,1,0,0,0,0,0

Like XYZ, you can divide demand into 3 classes (frequent, intermittent or sporadic) based on the probability of having zero demand in any given time period.

Here a distinction again needs to be made on the basis of buckets. If you receive monthly orders, then demand is not intermittent just because you have ~29 days of zero demand followed by one day with demand. Instead, you need to work with monthly buckets and then you find have frequent demand. But for genuinely intermittent demand, when you don’t know when orders might come and they are not evenly spread out by week or month, there is value in separating variability from intermittence.

Because in day-to-day work planners are confronted with both variability and intermittence (how big will demand be and when will it come?) the two challenges can seem to be just one (uncertainty). But to optimize inventories it is useful to separate the two.

There are many things to be said on how best to manage inventories that are variable, intermittent or both, but the main point here is that to do it well you need to understand which of those combinations you are dealing with.

It is also worth being aware that some analyses, including software commercially on the market, do not separate variability from intermittence. This is not wrong if you only want to consider variability in one dimension instead of two, but we believe there is value in separating the two since the three sample data sets above can clearly, from a practical standpoint, usefully be managed in different ways.

To summarize these sections on variability and intermittence, your selection of time horizons has an important impact on the analysis you carry out. Especially since many of the most common inventory management models like replenishment break down beyond a certain degree of variability and/or intermittence, there is significant value in being able to segment inventories and manage them accordingly. Often, we find, the problem is not that replenishment is over-used, but that it is under-utilised because it has been found not to work equally well for all items.

#### Forecasts

Another common blind spot in inventory management relates to forecast value added.

Forecasts themselves are usually bucketed by time – i.e. forecasts are made per time unit, such as a week or a month.

It is sometimes said that forecasts are always wrong, but the essential thing to understand is that the point of a forecast is to add value, not to be right or wrong per se. Forecasts are made to facilitate better decision making. While, as we have written elsewhere, the importance of forecasting in inventory management tends to be overestimated, one of the principal functions of a forecast is to allow decisions concerning inventory to be made.

This is why the concept of Forecast Value Added (FVA) was developed. FVA measures whether your forecast is adding or destroying value relative to a naïve forecast (i.e. that whatever happened in the last time period will happen again in the next time period). It does this by comparing actual demand with forecast demand, such that you can see if your forecast gets closer to actual demand than a naïve forecast would. (FVA can also be used to compare the value of two different forecasts.)

The issue arises when it comes to timing. Since it is normal to update forecasts periodically, for instance weekly, it seems natural to also measure forecast performance using that same time period. For example, what was the forecast for week 10 and what were the actuals in week 10?

Measuring your forecast performance from one forecasting period to the next is a valid measure of how “good” your forecast is, but it is not necessarily a valid measure of how much value it is adding if your forecast review period is not aligned with your lead times.

To give a simple example of this: Imagine your forecast accuracy for the chance of rain tomorrow is higher than assuming the weather will be the same as today. Great, your forecast is adding value! But only if you have to choose today whether to wear a raincoat tomorrow. If you can decide tomorrow, then your forecast is worse than waiting to see whether it really is raining tomorrow. Or if you had to make a decision last week whether or not to have a BBQ party tomorrow, when the rain forecast for tomorrow might have been 50/50 at best, then your forecast is in reality no better than a naïve one.

In other words, to judge whether your forecasts are really adding value or not, you need to measure the forecast at the point in time when the related decisions are being made, which is often when orders are placed, which depends on the lead time.

Unfortunately, to measure the true value of a forecast in this way means measuring it separately for every item you stock given all items don’t have the same lead time. And even then, it is subject to lead time variability. You can understand why, for simplicity, many prefer a “one size fits all” approach, where lead times are ignored and FVA is just measured weekly or monthly, but you can also see how this can easily give a misleading impression of how “good” or useful your forecasts really are.

### Conclusions

In summary, the impact of sub-optimal time horizons on the management of inventory comes down to sub-optimal safety stock levels, to the underutilisation or rejection of replenishment models, since it is poorly understood for which items it can best be used and how, and to a lack of transparency as to how variable demand really is or how good forecasts really are.

It is not uncommon to find organisations who think their forecasts are strong and their variability well understood, but with inventories far from optimal. What makes it worse is that precisely because they think their forecasts are strong and their variability well understood, they don’t even realize how far from optimal their inventories are!

So what are some practical steps that organisations can take to better master time in their inventory management?

- Straightforward, pragmatic steps include reducing lead times, reducing cycle times and reducing review periods. While there is an optimum minimum for each – and at nVentic we base all our analysis on such optimization calculations – as long as you can reduce these three things without adding cost then there are clear benefits to be had from the shortened time horizons.
- Another thing to pay attention to is the quality of data in your systems, especially lead times. Since so many inventory optimization calculations rely on lead time, having poor lead time data in your systems is a common Achilles heel for automation and other digitisation initiatives. Sometimes organisations are not so much held back by a lack of understanding of the importance of lead times as frustrated by their inability to reliably ascertain them.
- Once you have made good progress on the first two steps, it is worth delving deeper into some of the more advanced concepts discussed in this paper. With an improved understanding of time, inventories can be better classified and optimal approaches applied to different classifications. Rather than going straight to bespoke time horizons per item, a good intermediate step is to segment your inventories based on lead times, eg items under 1 week, 1-4 weeks, 1-3 months and over 3 months.

Is it time you had another look at time in your inventory management?

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