# MBA in 2 minutes | Lesson 24: Operations Using Little's Law

We will be solving practical challenges through MBA concepts. No theory only applications!

In this lesson, we will be delving deeper within 2 minutes on our first operations lesson. It is by far the most applicable tool I have used I have ever used during and post my MBA (examples- consulting case interviews, as a management consultant and very often as a founder).

The simple equation that I will be sharing is extremely transformational to resolve time and bring efficiencies in the processes. The law is called The Little Law and with that let's directly jump into the lesson.

** Step 1**
Have you ever considered how to reduce the long queues in front of Mcdonald's counters (pre-pandemic era) ? If not, you need to evaluate such problems as long queues typically lead to customer dissatisfaction, implying future revenue losses.

Similarly, as an operations enthusiast or as a strategist, you very often evaluate how to reduce the time taken during logistics ( a booming sector in India) and other deliveries'. In today's day and age, there is time value to money. So from saving seconds on trading on stock exchange to saving time duration at airport security counter, all have a time value to money associated.
** Step 2**
In such use cases, we apply Little's Law (John D.C. Little at MIT devised the first mathematical proof of the ‘law’ in 1961). In hindsight, it would have been extremely beneficial for me had I known about this as a strategy consulting during my pre- MBA days. So the law simply states -

**I = R x T**where, I= Average Inventory (The number of units between the start and end of the process (customers at restaurants, vehicles, patients, dollars, etc.).

R= Average Throughput Rate (The number of units that flow through the process per unit of time (in parts/month, patients/hour, Rs./year, etc)

T=Average Flow Time (Time from the entry of a unit into the system to its exit (in years, months, days, hours, etc.).
Given the simple linear relation between the variables, it is not hard to understand that for you to in order to reduce T(time), one needs to either reduce a) Inventory/Units b) Enhance the rate at which the units flow per unit time.
** Step 3**
Let's apply the above principle in practice via a short

__cafeteria problem__with below information: 1. Customers arrive at the Cafeteria either individually or in pairs. Per hour, 60 single customers and 30 pairs of customers enter the café. (Hint: 120 customers per hour) 2. 75% of the customers order coffee; it takes 2 minutes to serve each of these customers.Of the coffee‐ordering customers, 40% order food also; this adds 5 minutes to their serving time.

Coffee‐ordering customers who do not order food leave the cafeteria as soon as their coffee is served. Coffee‐ordering customers who also order food spend only as much time in the café after their food arrives as those customers who just come in to chat.

3. 25% of the customers do not order anything; they just come to study and chat.
4. On average, there are 10 customers either waiting for their order or standing in line at the cash register; and there are 30 customers having coffee, food, or chatting or studying.
**Question: What is the average time that a customer spends at the cash register in the café?**

Frankly it is a little complex problem but of course I didnt want to choose an extremely basic problem too.

By now, we understand, we need R and I values to compute T from the equation. Now, as a next step why don't you take active action.

1. Calculate R (rate of customers entering) seperately for a) coffee only b) coffee+food c) chat only

2. Calculate I (customers waiting) for a) coffee only b) coffee+ food c) find cash counter number also from a), b) and data given for total customers waiting for their order

3. Calculate T (time at cash counter) basis equation= I/R

(Hint: Final Answer: 2.67 minutes)

Don't get intimidated by the problem. For a newbie, it is complex but in reality there are even more complex problems. My professor at ISB was pretty cool as he eventually sang a really nice song on guitar at the end of his course. Times have changed. Experiences are also changing. Given the time in the century I am writing this in, there is a lot of chaos and panic, I wish and hope everyone is taking care of themselves and their family members :)

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