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 $6 and you will sell it at $10, making a profit of $4. However, if you cannot sell that product then you will incur a loss of $6 (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% (P
_{100}), then you should surely stock it and make a profit of $4. - If the probability of selling that extra unit is 25% (P
_{25}), then the payoff is

25%*$4 + 75%*(-$6) = -$3.5 (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 80%(P
_{80}), then the payoff is

80%*$4 + 20%*(-$6) = $2 (positive payoff)

- If the probability of selling that extra unit is 60%(P
_{60}), then the payoff is

60%*$4 + 40%*(-$6) = $0 (critical point). So, as long as the probability of selling that extra unit is 40% or above, you should keep stocking inventory. Most auto-buying systems are designed in this way to stock inventory until the probability of selling that unit of inventory goes below 60%.

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 100^{th} unit is say 80%, 500^{th} unit is 40% and 1000^{th }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.