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 P_{50 }) is +$2 and at P_{75} is +$7

Let us summarize these results:

P_{25} = – $3

P_{50} = +$2

P_{75} = +$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:

P_{S} = (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 1^{st} unit is very different from probability of selling n^{th} 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. 50^{th} bottle – maybe. 1000^{th} 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.