# To stock or not to stock that inventory?

Retail Managers are responsible to ensure stock availability to customers by replenishing stocks regularly. At the same time, they are also responsible for profitability of their category or division, leading to questions on – whether we should carry that product and how much inventory should we carry on hand? This is where it gets interesting. Because if you want to cater to all customer demand, then theoretically you must carry infinite inventory so that you cater to all customers who may or may not come. And, carrying infinite inventory is a loss-making proposition, leading to unhealthy inventory and write-offs. Let us understand this through an example below.

Let’s say the product you are going to sell costs \$8 and you will sell it at \$20, making a profit of \$12. However, if you cannot sell that product then you will incur a loss of \$8 (product cost).

Therefore, the tradeoff here is between:

a). the profit that you’d earn if the customer walks in and you have it in your inventory

b). the loss that you’d incur if you stock and the customer doesn’t turn up

To make the right decision of whether to hold that extra unit of inventory or not, you need to understand the probability of selling that inventory (say one unit) denoted as Px.

• If the probability of selling that extra unit is 100% (P100), then you should surely stock it and make a profit of \$12.
• If the probability of selling that extra unit is 25% (P25), then the payoff is

25%*\$12 + 75%*(-\$8) = -\$3 (negative payoff). Since this is going to make a negative payoff, you shouldn’t stock that unit of inventory.

• If the probability of selling that extra unit is 50%(P50), then the payoff is

50%*\$12 + 50%*(-\$8) = \$2 (positive payoff)

• If the probability of selling that extra unit is 40%(P40), then the payoff is

40%*\$12 + 60%*(-\$8) = \$0 (critical point). So, as long as the probability of selling that extra unit is 40% or above, you should keep stocking inventory.

The mistake that we did in the above calculation is we wrongly assumed that profit that we will make out of the sale is only from that particular unit. We should also include the profit that we could’ve made by that particular customer in all future purchases at our store – customer lifetime value (CLV). So, the tradeoff has to be between the customer lifetime value of the customer vs. the loss you’d incur if the customer doesn’t turn up at all. Also, the above calculation should take ‘time’ into account in the form of cost of capital (inventory holding costs) because many times the loss is not the entire cost of the product.

In conclusion, the value of having that inventory in stock changes basis a lot of parameters such as CLV, importance of that category or brand to the image of the retail store, brand equity of the store, type of store and many other business parameters.

The one question that we are yet to answer is: how do we determine the probability of sale?

Intuitively you know that the probability of selling that first unit of a TV is 100%, the 100th unit is say 80%, 500th unit is 40% and 1000th unit is 10%. Probability changes by quantity.

To get the probability you should simulate a demand distribution basis past historical sales data. Demand in retail scenarios are usually normal distributions. So, we will need the average and standard deviation. It is what we learnt in our MBAs – you will calculate the probability for the random variable (sellout of a TV model) to take the value 500 units and that is P (X=500). One of the ways is for you to calculate the Z value =  (500 – average)/SD and then lookup for that Z value in the Z table to get the probability. There are many ways to get this accurate estimate basis various distribution fits, which I will write in the next article.

Thank you.

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# A primer on the picture and sound technology behind your television

No matter what your preference is in terms of brand or size, picture quality and sound quality are the two most important parameters for a good TV viewing experience. In this post, we will get an understanding on how to evaluate picture quality and sound quality of your TV.

#### Understanding Picture Quality

The quality of a picture is primarily determined by resolution, contrast ratio, refresh rate, picture engine, panel type and color depth (and viewing angle for some).

Resolution – how much data (number of pixels) is carried or shown in one frame, the greater the resolution the larger the data and hence a clearer picture. At an ideal viewing distance for a particular screen size, one shouldn’t be able to see individual pixels in a TV with a good resolution. It is important to check for pixel resolution especially around corners and edged objects on the screen.

###### IDEAL VIEWING DISTANCES

Contrast ratio – the ratio of the brightest whites to darkest blacks. As shown below, the right side picture has a poor contrast.

A good contrast ratio will produce a bright image without lightening up the darks as shown below

Refresh rate Long back, somebody has discovered that if you run 24 pictures or frames per second (fps) then humans will perceive the act as a motion or a video. Therefore, refresh rate is how fast is the frame refreshed physically – it is the number of frames per second the TV can display – the higher it is, the more smoother and natural looking the motion of the video. Typically, you see 60 Hz (that’s 60 frames per second) and 120 Hz. Anything more is not required and not accurately described. These days all brands claim higher refresh rates by super-imposing frames or introducing blacks between two frames. These are artificial ways to improve refresh rates, but the native refresh rate is what one has to depend on while purchasing a TV. Check for blurs and noise around curves and edges before buying. While 120 Hz is a definite advantage over 60 Hz, most data sources are not beyond 60 Hz and hence 60 Hz is good enough. The advantage of 120 Hz comes in being able to play a 24 fps video smoothly.

Picture Engine – A picture engine is an image processing system that takes individual signals from various video output sources and throws an output onto the screen. Video processors typically include buffers, sequencers, colorizers, mixers and other linear and non-linear acts. They use various parallel computing technologies to enhance image and video production on digital devices such as TVs and Cameras. Since each manufacturer has its own ways of enhancing picture, there is no clear quantifiable way to rank a picture engine. Sony’s X-Reality picture engine is considered to be a state of the art picture engine. Similarly, there are top quality picture engines in other major brands such as Apple and Samsung. A recommendation to TV buyers is to watch out for the image processor and the picture engine in your TV before the purchase and check its performance online.

Panel Type – There are three major technologies used behind panel technology: ADS/TN (twisted nematic), VA (vertical alignment) and IPS (in-plane switching).

TN panels don’t provide great viewing experience, but however they provide high refresh rates (120 Hz) and high pixel response times required for gaming.

VA panels are the most common panels in LEDs and are often considered as a middle child between TN and IPS. VA panels have better viewing angles and dark blacks, however they sacrifice the response time (8 millisec) when compared with TN.

IPS panels have the best color reproduction, viewing angles and response time (4 millisec). While the earlier IPS technologies were slow in responsiveness and refresh rates, there has been significant improvement in recent IPS technologies with refresh rates of 120 Hz and 144 Hz.

Color depth – Color depth is the number of colors that a pixel can take. If a pixel is represented by 16 bits, then it will give you 65536 (2^16) colors.

24 Bit Colour: This format stores the Red, Green and Blue value for each pixel. Each of these can be one of 256 values, giving a total of 16,777,216 colours (256x256x256). Using 16 million colours allows for very photorealistic images, but increases the storage space requirements to three Bytes for each pixel.

32 Bit Colour: This format uses the same format as above for the Red, Green and Blue colours but also stores transparency information for each pixel. This allows each pixel to be one of 256 values from fully opaque to fully transparent. Because of the extra transparency information, the storage space for each pixel now requires four Bytes.

Viewing Angle – While may not be a very important attribute for Indian houses, a wide viewing angle complements to the experience. Some brands specially call out the 178 degree viewing angle.

#### Understanding Sound Quality

The quality of a good sound output is determined by output power, signal to noise ratio and frequency response (sound quality). If your TV box doesn’t describe these in detail, you can check the original manufacturer’s website to check these technical parameters in detail.

Output Power – Output power is the raw energy in your speakers and it is measured in watts. It is described as peak output or RMS. Peak output is the maximum energy output of the speaker for a short duration. Root Means Square (RMS) is the average output power over a long period of time. Usually, televisions in India come with 10W and 20W outputs. Typically, smaller TVs don’t come with decent speakers and therefore some people might want to augment the experience with a TV sound system.

Frequency Response – Humans can hear sounds ranging in frequency from 20Hz to 20K Hz. Below 310 Hz sounds are considered as bass frequencies, 310 Hz to 12 K Hz are mid-range frequencies that include human voice, piano, guitar and other instruments, 12K Hz to 20 K Hz are high frequencies that include high treble notes, high notes of human voice and some string instruments.

As you might’ve guessed, most speakers will give you the entire range. However the important parameter is: how does the speaker behave and how accurately is the sound reproduced at each of these frequencies? This is determined by frequency response. A sample frequency response chart is as below.

It tells you what sound pressure level (decibel level) variations will your speaker have at each of the frequencies. Ideally, you would want a flat line across the range, but this is not possible for any speaker. Therefore, a good parameter to check is smooth transitions across the frequency range without any rugged highs and lows.

If a speaker specification only mentions the frequency range, then it is not helpful. You should always look for a specification such as 20 Hz to 18K Hz with +/- 3 dB. This will let you know that the sound pressure won’t drop beyond 3 dB across the frequency range.

While these specifications are not readily available with retailers, with little research on the internet or brand website you can find the detailed technical specifications for your TV or speaker that you are about to buy.

Hope this is useful, thank you.

# Credit Card penetration in India

By the end of Mar 2016, India had 24.5 million credit cards and 661 million debit cards in operation (not issued).

The total number of transactions on credit cards grew by 27% while it rose by 48% for debit cards for the year ending March 2016. In March, total number of transactions through credit cards were 72.22 million while the figure for debit cards was 112.87 million.

The average amount transacted on credit card is 2.5x higher than that of debit card.

Which banks have the largest credit card base?

HDFC Bank and ICICI Bank lead in the total credit card base.

Which cities have the highest penetration?

While I don’t have the exact city-wise penetration data, CIBIL research shows that maximum number of credit card applicants came from Mumbai, Delhi and Bangalore. An indicative numbers on city-wise credit card penetration is as below.

• Coimbatore – 12.5%
• Jaipur – 12%
• Chennai – 11.7%
• Delhi – 11.6%
• Nagpur – 11%
• Mumbai – 9%
• Bangalore – 9%
• Surat – 8%
• Ahmedabad – 7.7%
• Pune – 7.6%
• Faridabad, Kolkata, Chandigrah – 7.5%
• Kanpur – 7%
• Amritsar – 5.4%
• Ludhiana – 5%

On usage, CIBIL data shows that Delhi, Ahmedabad, Pune and Mumbai have a higher usage of credit cards than Kolkata, Bangalore, Chennai and Hyderabad.

Credit card penetration has largely been low in India for ages. Certain retail categories such as large appliances and other high value purchases are bought a lot on credit and hence it is imperative for ecommerce and offline retailers to look for other opportunities of offering credit to customers for growth in these categories.

Thank you.

# To serve or not to serve, to stock or not to stock – by Supply Chain Detective

If you asked any CEO, Sales Executive or Marketing head what is the customer service level they desire in the organization they’d invariably say 100%. And hearing that answer the Supply Chain VP will invariably shake their heads and flee the room before you could ask them the same question.

But why, you might ask, such an expectation is unreasonable for any organization in any industry? Intuitively, it seems alright to want to sell to anyone who is willing to pay you in crispy greens. In fact, primary purpose of existence of organization is shareholder value creation? Which in simple words mean that organizations solely exist to earn profit by selling their stuff.

Before we delve deep – keep this thought at the back of your mind –

Organizations aim to maximize their profit

Let us try to understand this problem and define our problem statements more clearly.

1.Why it is unreasonable to have customer service level at 100%? And if it is, indeed, unreasonable then,

2.What is the optimum service level?

Qualitative Approach

Let us suppose you are the store manager in the said organization that sells consumer goods. You are responsible for managing stock on the shelves and ordering them before they go out of stock. Customer Service Level is your primary KPI and it is defined as percentage of times customer gets on the shelf whatever he is looking for.

Let us also imagine that one fine morning you get a memo from the CEO, the Sales VP and the marketing head (who must truly hate the supply chain guy) have decided to set this Customer Service Level as 100% as the new target.

Just yesterday you had to turn a guy back who wanted to buy five dozen television sets. With this new policy you’d have to stock everything that the next customer might need.

Oh heck, you realize that you need to stock your party supplies section for the next customer who accidentally invited 21,000 guests on her birthday. Even though the probability of this happening is very small, it is not zero. And the customer service target of 100% nudges you to be stocked for this small probability. Even if this means tons of overstocking and surely lot of wastage later, you have to be ready for all the extreme cases of demand.

You let out a muffled scream and consider quitting your job before sending a polite reply to your boss asking for permission to stock infinite inventory.

Quantitative Approach

We now intuitively understand why the customer service level can not be 100%. It would mean keeping infinite inventory for any possible customer demand that may or may not come. Keeping high inventory is almost sure to lead to excess inventory and write-offs ultimately making it a loss making proposition. But how much then should we “serve” before it starts becoming a loss making proposition.

Let us first take an example to understand the underlying logic before we go on to make complex models.

Imagine that you are that poor store manager responsible for customer service as well as inventory cost. The product that you sell costs \$8 and you sell it at \$20 for a net profit of \$12. However, if you are unable to sell it, you’d incur a loss of \$8 that was product cost.

The trade-off here is the profit that you’d earn if the customer walks in and you have it in your inventory

Vs

The loss that you’d incur if you stock and he doesn’t turn up.

So, should you buy the next unit  of inventory (it is very important to note that we are only talking about a single incremental unit) if there is only 25% chance that you’ll be able to sell it? What if this probability is 50%? 75%?

If the probability is 100%, that is you are sure to sell that next unit (I repeat, only one incremental unit) of product, then it’s a no-brainer that you’d want to stock it for a sure-shot profit of \$12.

Now let’s take the next case where there is only 25% chance that you’ll sell it and make a profit of \$12 but there is 75% chance that you won’t be able to sell it thereby incurring a loss of \$8.

Your expected payoff from this extra inventory is = (25% x \$12) + (75% x – \$8)

= – \$3

Since your expected payoff is negative when the probability is 25% , you’d not want to store this next unit of stock.

Similarly, the payoffs at 50% selling probability (Let’s call it P50 ) is  +\$2 and at P75 is +\$7

Let us summarize these results:

P25 = – \$3

P50 = +\$2

P75 = +\$7

So, somewhere between 25% and 50% selling probability, keeping that extra unit in inventory became a profit making proposition. With little bit of maths we can find that probability is 40%

So, as long as probability of selling the next unit exceeds 40%, you’ll keep stocking the inventory.

40% looks like a pretty high number. In real life, you’ll find that organizations are willing to stock that extra unit, for far lower selling probabilities. There is a logical quantifiable reason behind this behavior even though a vast majority don’t know about it. The reason is that profit on immediate sale (\$12 in our case) is not the only gain you make from that customer. When a customer walks-in into your store and finds what he/she is looking for, he will continue coming to your store and give you all that future business. This value of all future goods that the customer would buy is called Customer Lifetime Value.

Continuing with the previous example, suppose Customer Lifetime Value at the above store is \$100. i.e. if the customer keeps on coming to your store then you stand to profit \$100 from that customer. However, if he doesn’t find the product he is looking for, he’ll take this business to your competitors. What is that selling probability at which you’ll keep that unit of inventory? Let’s call it S:

PS = (S x \$100) + ((1-S) x -\$8)

At the cut-off probability, payoff would be zero.

0 = 108S -100

S = 7%!

Surprising. 93% of the times you are not expecting to sell that one unit and yet you’ll keep it in store because in long run that one customer is going to pay-off by becoming your loyal customer.

So, in a nutshell, keeping extra inventory is determined by probability of us selling it for acquiring a customer lifetime value vs having to write-off the extra inventory.

Some of you might be wondering why we did this analysis for only one unit (and kept on harping upon the point repeatedly). This is because the probability of selling keeps on changing as you add more stock. The probability of selling the 1st unit is very different from probability of selling nth unit.

I’ll be bet my arm that a liquor store in the middle of alcoholic town will sell its first bottle during the first hour of the day. 50th bottle – maybe. 1000th bottle – all bets are off (because I love my arm way too much).

So, coming back to the original point, how do we do this analysis for all of stock and not just one unit? It is the next level of analysis of service level that deserves its own article. Keep tuned in – it’ll be releasing soon.

# Whose Inventory Is It Anyway? – by Supply Chain Detective

This is one of the most contentious questions that is often raised in review meetings especially during months of high inventory. We’ve all been there – where all the inventory indicators are in red, warehouses are overflowing with stuff, several leaning Towers of Pisa in the warehouses are a common sight and trucks are waiting for hours to unload their stuff. The supply chain VP’s phone is ringing non-stop and when it seems that nothing can go worse, you suddenly realize that you have an S&OP meeting to attend to.To muddy the waters even further, that one person from finance mumbles how “Inventory” is on the asset side of the balance sheet but still recommending to reduce it as the cost of borrowing is getting higher.So, who is responsible for the inventory after all?As the norm has become with this blog, the answer is – “Well, it’s more complicated than that.”You see, inventory is not a single homogenous bloc that can be assigned or attributed to a single department or function, but a culmination of several direct and indirect causes across the organization.

In fact, Harold S. Geneen, has famously said, apart from his many other famous quotes,

All the problems of business end up in inventory

That’s true. Isn’t it?

Bad forecasting accuracy? – you’ll end up with unsold stock in inventory

Quality problems? – you’ll end up with returns in inventory

Bad roads? – you’ll end with damaged stock in inventory

Failed new product launch? – you’ll end with dead stock in inventory

Bad customer service? – you’ll end with canceled orders and… you guessed it, inventory

Very high customer service? – you’ll need to maintain high safety stock which is…inventory

So, are we doomed to live with this inventory mess forever without figuring out the real culprits? Is there no one who can save us from this impending inventory apocalypse?

Cool down, cut down on dramatics and dial a supply chain detective.

The solution to this mess is actually quite simple. A quick word of advice for SCZs out there – whenever you come across what seems like an insurmountable problem and you are unable to make a headway, start breaking the problem into its individual pieces, trace them back to their source and treat them individually. Once you solve the pieces, put them back together and voila – you have a solution.

For inventory ownership, the problem may look unassailable but let’s start breaking it. The good news is that we already know some of the inventory components. See! The moment we said inventory components, you’d know what is about to come already.

Cycle Stock

The first and often the biggest component of inventory is Cycle stock. It is the inventory that is needed to fulfill the average customer demand between the orders. Simply put, it is all the stock that is meant for selling before you receive the next inbound.

Cycle stock is dependent on two factors = Annual Demand and Inventory turns2.

While annual demand is an independent variable, inventory turns (the ability to churn your inventory) is something that is inherent in organizational strategy which in turn impact supply chain design and policies3 around it.

Let’s take an example –imagine there are two organizations named SavingPrivatePenny Inc (SPP) and FastAndFurious (FAF) Inc. SPP focuses a lot on cost efficiencies while FAF tries to be more responsive to their customers. With these different high-level strategies, SPP has a supply chain policy that prohibits less than 80% FTL load to be shipped. FAF Inc. Doesn’t have such policies and their trucks often go half unutilized.

In this example, SPP will have lower inventory turns vs FAF Inc. By extension – SPP will have higher cycle stock than FAF due to a. Organizational Strategy b. Supply Chain design.

[Some professionals blindly assume that SPP is a better organization than FAF. We’ll discuss this in another article why it’s a wrong pre-assumption without proper assessment.]

In a nutshell, cycle stock seems to be the responsibility of SCM function. However, supply chain design which has set a lower bound on cycle stock, also depends on financial constraints and overall organizational strategy.

Safety Stock

Demand-supply fluctuations are the name of the game and safety stock is the secret weapon in the arsenal of the organization that can help maintain the desired service level despite these fluctuations. However, this weapon comes at a cost. And that cost is inventory in form of safety stock. Higher the target service level, higher is the safety stock you need that may or may not be used that leads to higher inventory. In fact, the service level is the only deciding factor in determining the safety stock.4

So who owns the safety stock?

Simple. Whoever decides on the service levels. In most cases, this is something that is defined by Strategy (since they define the market positioning of the organization) and Sales (as they back-feed the strategy on customer requirements). But it varies widely from organization to organization.

Hence, safety stock inventory component is something that should be owned by strategy or sales. (Or whosoever is taking call on the service level).

Other Miscellaneous Inventory

You’ll notice that even after accounting for cycle stock and safety stock, you’re left with unaccounted inventory. This is something that is often reported as “Excess Inventory”. It is a curious mix of different types of stock that ends up in excess inventory bucket.

Unsaleable Stock: This one is my personal favorite. It consists of all kinds of expired, damaged or otherwise unsaleable stock. The reason this is my favorite is that more often than not this represents a good percentage of overall inventory. And it’s relatively easy to get rid of – you have to simply write it off.

The expired products are due to over-forecasting, and that ownership needs to be shared between the businesses and the demand planning. Damages fall right on SCM and should hit their KPIs.

Interestingly, most of the organizations are aware of this bucket but they don’t want to do the write-offs. Why? Remember when we said at the beginning that inventory is treated like an asset on the balance sheet. Well, write-offs of this inventory, that could be valued millions of dollars on the balance sheet, forces the company to take a huge one-time loss that could be detrimental to its share prices.

This hesitation is natural since no CEO wants to take this dent on the share prices and on his/her bonuses. But keeping this bad stock not only reduces its salvage value but also eats up valuable warehousing space. So, a good SCD must always push for continuously identifying and reducing this unsaleable stock from their supply chains.

This problem was quite visible in the banking industry (Surprise! You can apply SCM concepts to the banking industry too!) in 2008-09 where banking behemoths refused to identify their own toxic assets leading to the biggest global meltdown the world had ever seen since the great depression.

Bonus question: What is “inventory” in banking context? Does EOQ formula hold any significance in such context? What does ‘quantity’ in Economic Order Quantity refers to?

QC Stock: The stock under quality check can be quite significant especially for high-value items or high-tech industry where the quality process can take several days. The ownership of this stock is with Quality, Manufacturing or procurement depending upon your organization. Being in QC doesn’t mean that this inventory can not be reduced. We’ll have an entire post detailing inventory reduction

Promotional Stock: Remember that promotion scheme when you gave out Boyfriend Pillow to your customers for free – when your customers looked long and hard at you wondering if they should be seen in the vicinity of your products; and where, even after six-months of trying to push it down the throat of unsuspecting customers, dealers, wholesalers and mortal enemies, there are still mountains of this abomination lying somewhere in the corner of your warehouse.Yeah, that one.

Dispose it off and put it on marketing’s account. Done.

Blocked Stock: All ERP systems offer stock blocking to prevent multiple sales commitments on the same stock. Once the stock is “blocked” it is unavailable for committing to another customer. However, this functionality is sometimes used to game the system to hoard the stock even for tentative sales. We’ll see various means by which this can be reduced but one thing is clear that the ownership of this inventory lies with the sales.

In conclusion, I want to reiterate that high inventory can be a real big pain for the organizations as it locks up capital, occupies valuable warehousing space and chokes us the free movement of stock though the supply chain. Identification of its ownership goes a long way towards taking the corrective action because if you don’t know who owns it, you will never know how to fix it.

This ownership should be built directly into the KPIs to ensure that right action is taken at the right time.

Do you have something to ask or say about inventory ownership? Please let us know through your comments.

Footnotes:

1 It is important to note that balance sheet inventory also includes raw material and WIP inventory. However, in the current article, we are focusing on FG inventory.

2 Hardcore SCDs might argue that the equation is other way round, where inventory turns is calculated from average inventory and COGS. Secondly, average inventory and cycle stock are two different things as former also includes safety stock and other misc inventory like returns, damaged good etc.

While these arguments are correct, in this article’s context we are looking at inventory turns more from a network capability viewpoint and not as a performance metric.

3 If your policies aren’t centered around overall supply chain design and organizational strategy, your supply chain goals will always be in conflict with the organizational goals. For e.g. If you claim to be a super-responsive pizza delivery chain, then your supply chain’s goal can’t be vehicle utilization. You’d have to be prepared for small orders that need to be delivered in 30 mins even if it means carrying one pizza in one van.

4 All other variables in safety stock calculation are not directly controllable e.g. demand variability, Lead Time etc.

As you expected, the meeting is a bloodbath – S&OP chair, with deep burrows on his face, points finger at supply chain, others join in. Supply chain, on the other hand, blames faulty forecasting numbers. Demand planning, in turn, blames the inputs especially the sales projections; and when confronted, sales talks about their top-down targets and narrate in vivid detail how they didn’t receive right marketing support and how Supply Chain didn’t ensure that inventory was at the right place at the right time, thus completing the full circle of shrugging the responsibility of inventory ownership.

# The Myth called EOQ -by Supply Chain Detective

All you supply chain zombies (SCZs), who are now vying for the blood of the crackpot who wrote such a blasphemy as the title of this post, take a deep breath, cool down a bit and think back at the time when you last implemented the EOQ formula in its basic form. That is – NEVER.

Hmmm…and now that you are thinking about it, doesn’t it seem strange that one of the most popular supply chain concepts and most widely recognized formula that is literally taught on the first day of supply chain classes in college, is rarely used in the real world?

Well, there is a solid reason behind it. Rather, reasons behind how the real world considerations make our basic EOQ formula difficult to use in practical situations.

And you can too traverse this journey from Supply Chain Zombie to the supply chain detectives by understanding these factors and then tweaking the formulas to make it more suitable for your organization’s context.

But before you scram to your boss to make him salivate with your \$545 million formula and start planning o spend that six figure bonus that he’ll shower on you, lets first clear up our basics about EOQ.

For the seasoned Supply Chain Detectives, who understand the basics of EOQ inside out – feel free to skip to the second part of this article. For the rest of us lesser mortals– read on.

The Basic EOQ Formula

While your soporific professor mumbled something about carrying costs and ordering costs in Supply Chain 101 you dozed off while doodling aliens and space rockets in your notebook. Well, don’t worry, we’ve got you covered.

EOQ stands for Economic Order Quantity. Well, what does it mean?

Everyday billions of individuals and millions of organizations across the globe buy stuff. For individuals, it varies from buying eggs, bread & butter to 8 iPhones for a Dog.  And for organizations, it varies from manufacturing raw materials to office supplies, and from toilet papers to million dollar office decorations.

But, unless you are a billionaire owner of that Apple Watch brandishing dog, those billions of individuals and millions of organization must decide on one crucial factor while buying stuff – How much?

It may be intuitive for us to make the decision of ‘how much’ in some simple situations. E.g. eggs – On one hand you don’t want to buy too few eggs to save you trips to the grocery store everyday, one the other hand you also don’t want to buy too many to risk rotting them. And by using this rationale you settle on something in between say 1 week’s worth of supply.

What you are essentially doing here is trying to find a balance between two opposite cost elements – cost of visiting the grocery store too frequently vs cost of overstocking it.

This is what EOQ tells you. It finds the right balance between the Ordering Cost (cost of placing one order. In our example cost of visiting the grocery store once) and Carrying Cost (cost of carrying the inventory – storage costs, cost of capital etc.) mathematically and tells you exactly how much to buy.

Essentially what you are trying to minimize is the total cost of owning something.

Total Cost = Ordering Cost + Carrying Cost — (1)

Let us look at both the components theoretically. Later in this article, we elaborate what actually constitutes ordering and carrying costs from the organization perspective. For now, we’ll stick to formulas.

Ordering Cost

Ordering Cost = Number of orders per year x Cost per order (K)

Number of orders per year = Annual demand (D) / Ordering Quantity (Q)

Carrying Cost

Carrying Cost = Average Inventory (in \$) over the year x Inventory Carrying Costs (h)

Average Inventory (in units) = (Q/2)

Average Inventory (in dollar) = (Q/2) x c

[Because we are ordering Q units at a time and it uniformly depletes to zero as the inventory is consumed. Hence, the average inventory is (Q+0)/2]

Carrying Cost = ( Q/2) x c x h

Let’s put back these numbers in total cost equation (1)

Total Cost (TC) = [( D/Q) x K] + [(Q/2) x c x h]

Now do you see why we need to find a sweet-spot of ordering quantity to minimize total costs? No?

Alright, pay close attention to the Q in the above equation. In the first term Q is in the denominator. So when the ordering quantity Q decreases, the first term, Ordering Cost increases. Obviously.

However, in the second term, ordering quantity Q is in the numerator. So when Q decreases, the second term, carrying cost decreases. Obviously.

It is more obvious visually. Below, we have plotted the total cost for various ordering quantities (on the X- axis) and Total cost on Y-axis.

Download the workbook here.

As you can see Total Cost (TC), the purple line, first decreases and then increases with changing Q. Though it is hard to see but the minimum Total Cost occurs at around ordering quantity of 20 units.

Using equation 3 we can derive (see footnotes for a detailed derivation) the order quantity for which the total cost is minimum. Voila! This order quantity is called Economic Order Quantity or EOQ.

We can also put the relevant data that was used to create the graphs above:

D= 100 units per annum, K = \$ 2 per order, c = \$ 5 per unit and h= 20%

And Q= 20 units that confirms our graph. Hence, we should order 20 units at a time.

This also means that we’ll place 5 orders per year and our average inventory will be 10 units.

Theory is fine but…

Now that you have a solid understanding of the basic EOQ formula, the trick to using it – even the basic version – depends on understanding those variables in the corporate context.

Product Cost (c) : This is the most straightforward variable to find out. Do keep in mind though that we need product’s landed cost and not the price.

Annual Demand (D): Another easy one. Just head down to your forecasting department and ask them politely to give you the projections for the next year. In all probability, they’ll throw a dart at the dart board and give a number to you. If they don’t – come back to your desk and prepare a forecast yourself by using some simple algorithms. That’s another post for another day.

Inventory Carrying Cost (h): Ah! Now we enter into exciting and tricky stuff. The basic premise of inventory carrying cost is any cost that is associated with holding extra inventory on our books. This typically includes cost of capital, cost of holding in warehouse (storage, insurance etc.)

However, this is not an exhaustive list – we should incorporate any other cost or risk that is associated with holding that extra inventory. E.g. risk of obsolescence, risk of damages etc.

Typically inventory carrying costs are taken to be around 17%. But remember, higher cost of capital, increasing risk and dynamic business environment (e.g. risk of design changes frequently) push this number up.

We’ll talk more about these in the next part of this article.

Ordering Cost: How much your organization spends on placing one order. It sounds simple but it is somewhat tricky to calculate. We should only add those ordering cost components that are variable in nature. That is, those costs components that are incurred every time there is an order.

Cost of stationery – ordering cost

Cost of courier – ordering cost

Inspection costs at inbound – ordering cost

Salary of the ordering manager – not an ordering cost

The last one is not an ordering cost because it doesn’t change with the number of orders placed and hence doesn’t impact our EOQ. In a strict sense however, this cost is a step function. Let’s say that up to a certain number of orders 1 ordering manager can handle the work. But for a large increase in orders, you may have to hire more people.

Well, now that we have a proper handle on the basic EOQ formula, we are now ready to take on the real world. But wait! Didn’t we say in the beginning that real world can put a spanner in using this formula in the basic form?

Well, that’s what the next part of this article deals with. Now that you are thorough with the basics , get your Cuban cigars out and get ready to become a true Supply Chain Detective.

Where,

Q is Economic Order Quantity

D is Annual demand (in units)

K is Ordering Cost (in \$) per order

c is Cost of the product (in \$ per unit) and,

h is the inventory carrying cost (as %age of product cost, incurred annually)

In this post we’ll see why EOQ formula should be rarely used in its basic form. And even if you were to use it, you must at least be aware of the caveats and assumptions that have gone into it.

We’ll do that in two parts. First let us challenge some assumptions that we made earlier and then we’ll put in some real world complications that require us to tweak the formula or add in some layers of analysis before we start using the order quantity recommendations.

Assumption #1: Inventory Depletion is uniform

One of the major assumption while deriving the formula was uniform inventory consumption. And that is how we arrived at Q/2 as average inventory. However, this is seldom true. Rate of consumption changes from season to season, week to week and even day to day.

Solution: An ideal solution is to come up with a consumption curve (Inventory vs Time graph) and use it to calculate average inventory over time. However, this may involve doing an integral of a complex curve. If you want to be super-precise then that’d the way to go but there are more practical and easier approximations to this problem that will give you “good” solutions with a lot less effort.

Approximation: Rather than one continuous curve, we can break our time period into two or more sub-periods each having a simpler consumption pattern. For example,  a vast majority of FMCG organizations make most of their sales during the last week of the month. This could be a typical case of student syndrome where sales team is pushing to meet their monthly targets. [This takes a significant toll on supply chain infrastructure and many organizations struggle to manage these last week peaks. We will dedicate a separate post to this topic.]

So, let us say that 50% of the monthly demand is consumed in first three weeks while remaining 50% is consumed in last week itself. In other words, consumption rate during last week is thrice that of first three weeks. Over long-term1, the average inventory can be calculated to be 5Q/8. We leave it to the readers to derive this number. You may notice that this average inventory is higher than (Q/2) that we calculated earlier where the inventory depletion was uniform throughout. This makes sense as earlier we had consumed 75% of the monthly demand in 3 weeks whereas we have only consumed 50% in the current scenario, leaving us with slightly higher inventory.

If we put 5Q/8 as average inventory in Total cost equation:

We can derive modified EOQ as:

Similarly, now you can derive your own EOQ formula given any consumption rate or consumption pattern.

Assumption #2: Cost of the material is constant regardless of quantity

Remember when we wrote the total cost equation as

We deliberately didn’t consider one element of cost in the above equation which was buying cost. We ignored it because it wasn’t relevant as we were spending the same amount annually despite of ordering quantity.

However, this assumption doesn’t hold true especially when buying quantities are large. Suppliers often provide bulk discount options as they save on producing at a scale. In fact a typical supplier quote looks like this:

#### \$ 4

As the quantity increases our buying cost decreases significantly. In fact supplier is willing to offer 20% discount if we buy more than 150 units of the product. But is it worth it?

Now, let us rewrite the total cost equation, this time around we’ll have to include the buying cost as it has become relevant.

The product price c* is now a function of Q –

c* = \$ 5 per unit (for Q between 1-20)

c* = \$ 4.5 per unit (for Q between 21 -50)

…and so on.

Graphical Solution

Let us recreate the chart that we made earlier. This time around, we have an additional line for buying cost.

Download the workbook HERE.

As you can see in the graph above, buying cost is a step-curve. Those “steps” represent the bulk-discounts that supplier has offered. We also see these “steps” in total cost curve (the thick blue line) since it includes the buying cost. You’ll notice that now it is not so easy visually to find the minimum cost point on the total cost curve.

I checked the table that was used to create the graph in the workbook, and it turns out that minimum total cost is \$ 461.7 while buying 151 units. Note that this is different from our non-discounted EOQ number where we got the answer as 20 units.

How will you sell this to the CEO? You can’t show derived EOQs and complex graphs, right? Well, you can simply state the following – “Usually, we should only buy 20 units at a time which is roughly one month of supply, however this time around the supplier is giving 20% discount on bulk orders. Sure, this increases our inventory costs a bit but it’ll be more than compensated by the discount.”

Interestingly, the next lowest cost \$ 470 occurs at 101 units. So, if your CEO still frowns at you for asking to buy huge inventories, you can always fall back on the second best solution, where incurring 9 dollars extra reduces your inventory from 150 to 100.

[The second best or even third best solution may be more acceptable in some cases. True – that absolute minimum occurs at 151 units but just paying additional 9 dollars we can mitigate some of the unaccounted risks that come along with the additional inventory. This is a typical problem with all kinds of optimization algorithms. They try to reduce the objective function to the absolute minimum, a phenomenon that we describe as chasing the pennies. This is sometimes not desired. And this is where multi-objective optimization comes handy. However, that is another discussion for some other day.]

Analytical Solution

Above, we arrived at the solution by looking at the graph and corresponding data but that’s not feasible especially when large quantities are involved or we don’t have access to spreadsheet software.

While there is no straightforward formula for EOQ with bulk discount because buying cost is a step-function and hence non-differentiable, we still have a step-by-step procedure that can help us arrive at the best quantity.

Step 1: Find normal EOQ for ALL buying costs

In our example, there are five different costs. While we are not showing the detailed calculation their corresponding EOQ values are shown below. Subscript represents the cost(in \$ per unit):

EOQ5       = 20 units

EOQ4.75  = 20.5 units

EOQ4.5    = 21.1 units

EOQ4.25  = 21.7 units

EOQ4      = 22.3 units

[Bonus Question: Keeping all the other factors constant, why does EOQ increases as the cost per unit decreases?]

Step 2: Eliminate “Invalid” solutions

Some of the EOQ quantities doesn’t belong to the buying cost. Eliminate them.

EOQ5       = 20 units

EOQ4.75  = 20.5 units X

EOQ4.5    = 21.1 units X

EOQ4.25  = 21.7 units X

EOQ4      = 22.3 units X

Note: You may be left with none or more than one solutions.

Step 3: Calculate and compare total costs for all the valid EOQ solutions and buying qty break-points

#### 461.7

Total minimum cost is at Qty 151 which is our answer.

Assumption#3: Inventory Carrying Costs are constant

As briefly touched upon in previous part of this article, inventory carrying cost consists of several components – cost of capital (typically the borrowing rate of your organization), cost of storage (Warehousing costs and salaries) and cost of servicing the inventory (insurance, damages, obsolescence). Though it is highly organization dependent, finding the exact value might be a tricky task. It is usually taken between 17% and 25% depending the nature of the inventory and opportunity cost of capital to the organization.

However, some of these variables are not constant and vary with the quantity of inventory kept in the organization. Couple of examples are below:

Insurance cost: Per unit insurance cost decreases as average inventory increases.

Risk of damages/obsolescence: Risk of damages and obsolescence increases as average inventory increases.

Solution:

The solution requires some understanding of basic differentiation. If you don’t get it in the first attempt, don’t worry about it too much as we are now

Let us say that by some measure of analytics, one has arrived on a inventory carrying cost equation

Inventory Carrying Cost (h)= r + f(Q)

h = 20% + 2%* ((Q/D)*12)

Don’t get scared by the above equation. It simply states that inventory carrying cost is 20% plus 2% for addition of every month to order quantity. This 2% is attributed to the increasing risk because of incremental inventory. Hence for one month’s inventory, carrying cost = 22%, for two months its 24% and so on.

Putting this in the basic equation

Differentiating both sides by dQ

For min TC,

Simplifying the equation we get,

Replacing the variable values, D = 100 units, c = \$ 5, K = \$2

This is a cubic equation with three solutions for order quantity Q.

Q= 19.96, -6000, -20

We can reject the negative solutions. Hence, the EOQ for dynamic carrying cost is 19.96.

Note that this is slightly lower than our original solution of 20 units that considered fixed carrying cost of 20%. This seems logical as slight increase in carrying cost is reflected in decreased EOQ.

Conclusion

If you have reached this far, then CONGRATULATIONS! You’ve mastered the science behind ordering quantities and their trade-offs, you are now ready to take on any challenge that anyone in your organization can throw at you. Well, let me scratch that. You are almost ready.

There are some teeny-weeny complications that are often put to question your EOQ numbers. While some of those do not impact our EOQ too much, it is important to be aware of them to pave way for smooth implementation of your ideas. Part 3 of this article is dedicated to those complications and work-arounds.

[At this juncture, some of you might be feeling that we are splitting hairs on EOQ formula. Do yourself a favor and do a back of the envelope calculation on how much total cost changes just by changing the ordering quantity 2% on either side. Total cost swings a lot, even for tiny changes in the ordering quantity.]

Complication #1: Your EOQ is not your supplier’s EOQ
Alright, so you’ve created fancy versions of EOQ models, gathered data on ordering cost and carrying cost through hook or crook, done tons of calculations, and checked and rechecked your numbers. And to your delight, it looks perfect. Not only that, it seems that implementing new EOQ numbers will save a few million dollars for your company every year. But just when it seems that there is nothing between you and that Employee of the Year award, your order is rejected by…the supplier.

But why? Simple. Your order quantity might be the best thing that has ever happened to your organization, it is not feasible for the supplier to manufacture. Supplier has his own manufacturing processes, its own suppliers and his own optimal batch sizes, and the order quantity you are demanding isn’t financially viable for him. For example, remember when we calculated the EOQ of 20 in previous illustration earlier. But what if supplier’s batch run produces only 15 units at a time. This means that he’ll have to run two batches of production to produce 30 units and after fulfilling your “optimal” order of 20, sit on remaining 10 units waiting for your next order. The problem is even worse if his batch size is, say, 50 units.

Well, there are two ways out of the situation – the easy way, where you arm-twist the supplier to your will and push him to absorb the loss which is the most common practice in such situations but in long term results in supplier mistrust, higher inventory at the supplier, and maybe renegotiation of the whole contract.

The slightly difficult way –that will ensure more transparency, collaboration and even bigger savings than the EOQ formula – is called Joint EOQ formula.
[Also known as Joint Economic Lot Size (JELS) formula]

The underlying principle behind Joint EOQ is pretty simple as you might have guessed from its name – it tries to find an optimal EOQ for the supplier-buyer system considered as one. Imagine if supplier was part of your organization – in that case how would you calculate the optimal order quantitiy that needs to be produced.

Let us re-write our total cost equation

Total Cost = Ordering Cost (for both supplier and buyer)+ Carrying cost (for both supplier and buyer)
Where, D is annual demand
Q is the order quantity
Kb is the Ordering cost for the buyer
S is the set-up cost for the supplier
hb, hs Inventory carrying cost for buyer and supplier respectively
cb, cs purchasing cost for buyer and supplier respectively.
We repeat the same procedure of differentiating both the sides by dQ and solve for Q.

The beauty of this JELS quantity is that is leads to even lower cost than what buyer and supplier could have individually achieved. THAT is the power of collaboration right there.

Bonus question: What are the total savings for supplier and buyer combined by moving to JELS than their individual optimal quantities? What should be a fair split of benefits between them?
[For a detailed read on JELS you may want to read this famous paper. Please note that the notations used in the paper are slightly different.]

Complication #2: FTL ≠ EOQ
If you pay your logistics provide by the unit then don’t read further. You can merrily start implementing EOQs and punching those 1 unit orders.

However, if you pay your logistics provider by the trip or the route, you’d notice that EOQ quantities may lead to lower utilization of your vehicles. And since you pay for the whole vehicle whether it has one unit inside it or one hundred, you lose some money on every trip when you order EOQ.

Solution:
First check whether there are “right-sized” vehicles available with your logistics service provider. Your ideal situation is where EOQ matches exactly with the vehicle capacity.

If EOQ doesn’t align with the vehicle capacity, compare the total cost between partially filled vehicle (LTL) and FTL vehicle. When vehicle is FTL you end up increasing your inventory. It might still be worthwhile to under-utilize the vehicle.

[There are modified EOQ models available where transportation costs are taken as a step function.]
Multi-product ordering : If the supplier deals in multiple products, explore an option to combine multiple products in the same order.

Supplier clustering and multi-pick ups: If there are other suppliers in the vicinity, you may want to club your other orders in the same vehicle. This can also be implemented at buyer’s end where multiple buyers of the same suppliers combine their orders for better efficiencies.

This strategy to maximize vehicle utilization, albeit without EOQ reasons, is quite a common practice for non-competing organizations. Best example, perhaps, is where Nirma sent its heavy detergent packets inside Sintex’s empty water tanks to maximize the vehicle utilization leading to the savings for both the organizations.

Vehicle utilization and idle time reduction is an area of prime focus for the organizations with lot of resources and effort going into improving it. Hence, there will be whole another post to discuss it in detail.

Complication #3: Warehouse Capacities
At times, especially when pushed by deep discounts from the suppliers, EOQ formula may recommend huge buys. However, warehouse capacities are not infinite and handling additional inventory may require additional manpower, equipment or space.

Solution:
In such rare cases, it is useful to consider warehousing costs as increasing with inventory. This is something we tackled in part 2 where we considered inventory carrying costs to be a function of quantity.

Closing Remarks
Phew! That was a long read. But I hope that has you transformed from a Supply Chain Zombie (SCZ) who used to take orders from bosses and the clients to a Supply Chain Detective (SCD) who doesn’t rely on “thumb rules” and “common practices”.

In fact, the aim of this article wasn’t to cover each and every possible scenario in the book and churn out dozens of formulas but arm you with the thought process and the techniques to handle all sorts of complicated situations that might come your way. If I’ve succeeded in this attempt, do let us know through your comments.

Go ahead, now, change the world.