Pradeepan Sekar

Queuing Theory:
1.   Queuing Theory is mathematical study of waiting time or queues in a model.
2.   Queuing theory is used to predict the queue length and waiting time in the simulation for the better business decisions such as planning of resources, space allocation, charges for the premium etc.
3.   Queuing is not only applicable to the customers, but also to the product, raw materials, Services, or projects which are lined up.
How queuing works?
An entity will be arriving to the queuing node, where the entity will be treated by service. But it needs to wait before getting treated and then it will take some duration while it been serviced and then leaves the node.
 
Some applications of Queuing theory:
1.   Raw materials are stored and then consumed as per requirement.
(Queue length – Inventory | Waiting Time  - Capital of WIP/ shelf life)
2.   Ships waiting for the clearance. (Waiting time and Service time -Demur-rage)
3.   Car parking in the mall (Queue/ service length – Number of Parking slots)
 
Scheduling policies:
There are different ways to assign or schedule the next entity to the server which are called as scheduling policies.
1.   First in, First out:
a.   This policy states that the first come will be served at first, which means the entity with longest waiting time will be treated first.
b.   It is considered as an ethical way to schedule the service for the customers. Token system in Bank or Hospital
c.    In Manufacturing, First in First out have been considered to keep track on the shelf life of the product. Raw material consumption.
 
2.   Last in, First out:
a.   This policy states that the last come will be served at first, which means the entity with Shortest waiting time will be treated first.
b.   It is also stated as stack, It is applicable in most of the cases where you have constraint in such a way that you need to treat the last item first
c.    In Drive in Racking, We need to pick the last item placed as first.
 
 
3.   Processor sharing:
a.   In Processor sharing, more entities will be served at the same time. In this case it can be multiple or as many as possible
b.   In a mall/ theater, it can accommodate more customers.
 
4.   Shortest Job First:
a.   Shortest job will be scheduled first , which helps to reduce the queue length.
b.   In super markets, there will be separate queue for less than 5 billing items,  they will treat other customers only after treating the shortest job.
 
5.   Longest Job first:
a.   Longest Job will be scheduled first.
b.   In case of Project funding (Project funding as server), Longest job can be allocated with funding to start first.
   
6.   Priority:
a.   Customers with high priority are treated first.
b.   It can be primitive (Where customer in service will be interrupted) or non- Primitive.
c.    Priority can be given in the form of premium queue or even emergency
d.   Patients at life risk will be treated immediately in hospitals.
e.   High paid premium queue in the amusement parks.
 
7.   Shortest remaining processing time:
a.   Customers who have been treated already and having shortest remaining processing time.
b.   In Banks, after filling the forms, priority will be given to the submission of forms.
 
Key Points:
1.   Types of Service facility: Single server, Multiple server with single queue, Multiple server with Multiple queue
2.   Queue length, waiting time and service time are the key parameters.
3.   Customer Behavior:
a.   Balking: Customer not joining the queue, because of queue length
b.   Jockeying: Switching between the queue, considering other queue will be treated faster
c.    Reneging: Leaving the queue ( which is also called as drop outs)

TRIZ (Theory of Inventive Problem Solving):
TRIZ is a problem-solving approach derived from the study of global invention patterns which was carried out by author Generic Altshuler in 1946. TRIZ is an acronym of ‘Teoriya Resheniya Izobretatelskikh Zadatch’ which is rendered as “Theory of Inventive Problem Solving” and often called as TIPS. TRIZ is a systematic approach for generating solutions in Problem solving even in finance, product, services, and manufacturing fields.
 
Altshuther screened over 200,000 patenst and observed that the most of the patents have very straight forward solution, only few had somewhat inventive solutions. Altshuter had extracted 40 inventive principles and those principles will serve as a hint to find the highly innovative solution to the business.
 
Concept of contradictions:
 
Problem lies in contradictions between two or more elements of interest. Increasing the quotient of desirable elements or reducing the quotient of Undesirable elements will lead to reduce the quotient of another one or more desirable elements or increase the quotient of undesirable elements. Sometimes we need the maximum and minimum quotient of the same element.
 
Some examples of contradictions:
 
Contradictions
More of Undesirable
Less of Desirable
More of Desirable
Increasing the strength of material , increases the weight
Increasing the capacity of the car, reduces mileage
Less of Undesirable
Reducing Variation in process, needs more effort and investment
Reducing the expense on material, leads to poor characteristics
More and less
Height of Rack in supermarket should be maximum to store more materials and also should be minimum for easy access of customers
 
While applying TRIZ to find inventive solution for the business problems, first and foremost things to do is to identify the contradicting statements as stated above. These are called as Technical contradictions.
 
Inventive principles:
 
Solutions are often straightforward by compromising one of the contradictions. But TRIZ provide us an ability to think to improve on both contradictions. By applying the inventive ideas, it has been proved that  Ideality i.e more of desirable and less of undesirable can be achieved at the same time. TRIZ principles are used in the many leading companies like Samsung, Xerox, IBM, LG, intel and so on.
 
Altshuter has developed a set of 40 inventive principles and later he also framed a matrix in which  he indicated 39 features ( which is also called as Engineering Parameters)in rows of desirable and columns of undesirable and the matrix is called as matrix of contradictions. Each cell points in the matrix points to the list of inventive principles which is more commonly used in order to resolve both contradictions and to achieve ideality.
 
Example:
 
For instance, now a days, all the Governments are facing challenge between economical crisis and pandemic risks due to the spread of COVID-19. If Lockdown is lifted, country will be in a good position to handle the economy, but will result in increasing the COVID-19 cases. They are looking for a solution to handle both and to strike a balance.
 
But in some fields or organization, they were able to overcome the spread and also helps in increasing the efficiency, cutting down some overheads such as travel allowance, Electricity bills, administration charges with the innovative ideas of working from Home, which was supported by lot of visual meeting medium, e-forms, e-signatures, remote access, Virtual machines etc. By which, the continuity of working for an organization or customer or on a project is carried out without the physical presence to generate  more revenue than before and at the same time reducing the risk of pandemic in their organization.
 
How I used TRIZ in my domain?
 
Background:
 
TRIZ has been used in the purchase of packaging machine which is one of its kind for our food product. I have morphed and simplified the terms for the better understanding and to maintain confidentiality.
 
We are into manufacturing of a food product which is available in different sizes (1x,2x,3x…..6x). Manufacturing of the products with varied size can be done by a single processing line  with the set up-time of 8 hours from one size to another and the packaging machine needs to be changed from smaller ( which can pack 1x, 2x and 3x) to bigger (4x, 5x and 6x) which is followed so far
 
As we are interested in buying a new packaging machine with more advanced features and accommodating HMI ,
A.   we need to buy two machines to cover all range of products, but it will increase the investment by double or
B.   we can buy universal machine which can pack all range of products, but the speed will get reduced for smaller products due to the design for maximum and investment also will be 1.7 times of budget of single machine or
C.   We can buy a standard machine which can pack the product sizes of 1x,2x and 3x. so we should drop plan of producing other bigger sizes.
 
Contradiction Statement:
To increase the packaging capability of wide range of products to meet demand of market with lesser set up time, we should increase our investment and/or reduce the packaging speed.
Desirable: Packaging capability, Packaging speed
Undesirable: Investment
 
Options
Packaging Capability
Investment
Packaging Speed
A
Wide (1x,2x,3x,4x,5x,6x)
High ( 2 times)
Standard
B
Wide (1x,2x,3x,4x,5x,6x)
Moderate (1.6 times)
Lesser than standard     (for 1x,2x and 3x)
C
Limited (1x,2x,3x)
Low (as per budget)
Standard (for 1x, 2x and 3x), Not feasible (4x,5x and 6x)
 
Ideality of Innovative idea,
Our interest is to pack wide range of products, with less investment and without compromising on speed.
 
 
Inventive principles applied:
Principle 1 : Segmentation. (Divide an object into independent parts)
Principle 16: If 100% of an object is hard to achieve by slightly less or slightly more, we can achieve it with same method which is considerably easier.
 
By combining above 2 principles, by dividing the standard machine with considerably spares for mechanical parts alone (which increases the cost by 3%), we will be able to cover a wide range from (1x to 5x), the solution was considered and accepted by machine maker  and order is placed for the same .  The machine going to be supplied is unique for the supplier and they have never adapted such flexibility before.

HAMMURABI CODE:
 
Hammurabi is the king who ruled from 1792 to 1750 BC in the middle east. The king, Hammuarbi enacted the code in 7.5 Feet Stele stone. It consists of 282 laws describing scaled punishments such as “an eye for an eye, a tooth for a tooth” based on the social groups and consequences of the committed mistakes. This code was found in 1901 and translation in to publication happened in 1902.
 
Hammurabi code is described as “the first code of conduct” which was passed about 4000 years ago. Being the King, who is leader of civilians, he was concerned about the welfare of people which is clearly depicted through his laws.
 
Hammurabi had taught few lessons through his code to the modern business leaders. It has featured some progressive precepts such as minimum wage’s law, innocent until proven guilty, fairness about graded punishment (Famous saying “an eye for an eye, a tooth for a tooth”). His codes of conduct are considered impossibly harsh and authoritative, but most leaders describe his concern as motivation towards the wellbeing of the society and his own civilians.
 
Hammurabi Code – skin in the game.
 
Mainlining the accountability
According to law number 232, if a Babylonian builder built a house with under quality materials which will apparently result in collapsing of the house will leads to death of owner, then builder will be put to death too. Builders build the Babylonian houses with high quality, because builders knew the consequences as default.
 
Risk Evaluation:
The King, Hammurabi encourage the builders to build the houses with more margin of safety to make the structure rigid not only during the predictable situations such as wind, storm, and rain but also in unpredictable situations like earthquake.
 
Incentive Management:
Builders are incented to build with better margin of safety but not cut the corners to pocket more money to the owners.
 
His code which is suggesting to have “one’s own skin in the game” thus entrusting a moral obligation for fair play, addresses the Business leaders of today to mainline the individual accountability, communicating the standards, Incentive management, Risk Management.
 
The issues concerned by the King Hammurabi are often the issues of modern business leaders. Now a days, Organizations are engaging the leaders to find the way of
 
1.   How to maintain employee accountability,
2.   Improving the Quality of execution,
3.   How to drive incentive system,
4.   Defining performance measure with clear KPI,
5.   Rewarding and Reprimanding – its not about punishment, about improvement,
6.   Employee fairness – Sustaining the employee’s morality.
 
 
Ways of Implanting the idea of having one’s own skin in an organization:
1.   Clear roles & Individual Accountability:
a.   When the roles and responsibility of the employees are ambiguous, people struggle to be accountable. Clear definition of the role through work instructions and SOP become a necessity.
b.   Measurable KPI with fair quotient of weightage.
c.    Assigning responsibility to the individuals with clear definition of his role.
d.   Removing confusions such as who is doing what, when, and how makes the person accountable for the successful execution and paves a way for success
 
2.   Team formation and owning the process:
a.   Form, Norm, Storm and perform as four stages of team formation. Leaders play an important responsibility to achieve the fourth stage of team formation.
b.   When team feels truly accountable, they will storm on the gaps, learn new roles and processes, teach to each other, find a way, bring synergy and makes more efficient team.
c.    Each member of the team will become responsible to seek information, give feedback and receive feedback and point out mistakes when it is needed.
 
3.   Autonomous and independent decision making:
a.   Listen to the multiple solutions and brainstorm, most of the problems will have multiple solution.
b.   Improve upon the team’s ideas, rather than imposing your own thoughts.
c.    Give them the freedom and support.
d.   By providing them the rights to take decision, team will increase their skills, confidence, and ownership.
 
 
4.   Communicating the standards:
Standard Operating Procedures:
SOPs are the documents which describes the actions to be taken under several circumstances, it also lays who, what, when and where for the important actions. It provides clear and concise guidelines.
SOP should be the document which is serving at higher level and the detailed instruction should be described in work instructions. The SOPs should be clear, simple, concise and continuously updated. Otherwise it results in instruction creep.
 
5.   Risk evaluation:
a.   Encourage people in assessing the possible failures of the process, get suggested on solutions to overcome the worst-case scenario.
b.   Engage the operational excellence or Business analyst in identifying the areas of risk and scope of improvement.
 
6.   Incentive Management:
a.   Incentive should not drive the process to fulfil what had been described.
b.   Fairness of evaluation is more important to keep employee’s morality high.
c.    Employee should be incented for their additional inputs, their creative and innovative initiatives.
 

Benford’s Law:
         Benford’s law is also called as the law of anamoulous number, law of first digit. This law is named after the physicist, Frank Branford who stated in 1938 and it describes the observation on the probability distribution of leading digits in many real time data sets.
         According to Benford, leading digit in any set of data most likely to be small. I.e the number of datum which starts with the digit 1 will be having the highest probability of around 30% , followed it the digit 2 will be having the second highest probability of 175 and so on, the probability of having 9 as the leading digit is the lowest as 5%.
         Benford’s law applies to the set of data if the logarithms of the number applies to the normal or uniform distribution, but not the number themselves.
         If a number x constrained to be between 1 and 9, set of data starts with digit 1  will be between 1 and 2, in similar way, x starts with digit 1 will be in the interval of [ Log 1, Log 2], and digit 2 will be in the interval [Log 2, Log 3] and so on

 
 
Picking a random number in a uniform manner on this line results 30% of time with leading digit 1.
 


Benford’s law application:
         This law applies to the large number of data with multiple orders of magnitude. Most of the data such as population of country, Account Balance,  Bills, Tax, data of tallest building heights in the world, COVID-19 spread.
 
         Of course , it will not apply to the set of data that has been divided and each data will be between 300  - 900 and are uniformly or normally distributed then the benfords law will not be applied there.
 
         In Business application, Benford’s law can be widely used in auditing the set of data. Based on the human plausible assumption , they will try to fabricate the figure  and distribute them uniformly. When it applied to the large set of data of multiple orders of magnitude, by simpliy finding the frequency of first digit, the data can be audited.
 
References:
        A movie released in 2016, The Accountant, a detective uses benford’s law to find the theft of funds.
         In US, criminal cases had been admitted with the evidence of benford’s law.
 
Benford’s law tested on COVID-19 affected cases:
 
         The distribution of COVID-19 as on today (19-May-2020) follows Benford’s law which is shown below.
Source: https://www.worldometers.info/coronavirus/#countries