mathematical concepts applied to operations management

MATHEMATICAL CONCEPTS APPLIED TO OPERATIONS MANAGEMENT IN

20 SLIDES

© North Delta College 2015

Mathema'cs applied to Opera'ons Management 1

SUMMARY PART 1: BUSINESS PROCESSES A) DefiniFons/Examples PART 2: PROCESS RE-‐ENGINEERING A) Process Re-‐Engineering B) Examples C) ERP projects (Enterprise Resources Planning) PART 3: MODELLING BUSINESS ORGANISATIONS A) A business organisaFon seen as a MathemaFcal Space B) The T&P layer PART 4: MATHEMATICAL PART A) Layered spaces B) Examples C) Changes & DisrupFons


PART 1: BUSINESS PROCESSES

Axiom 1: A business process is the accomplishment of a repeFFve work by an employee inside a company in order to achieve a given funcFonality


PROCESSES AND TASKS

Remark: This work is generally formally codified by management so that the individual employee's thinking doesn't come into the equaFon. His individual intelligence is only used

to perform the work.

Axiom 2: Each process is made up of tasks

that can be performed either: 1)  Linearly

2) by mulF-‐tasking

Axiom 3: ulFmately a business organisaFon, seen as a profit generaFng enFty is nothing more than the set of all its processes. A

process-‐machine.

Example: Order-‐Intake process

Process: order-‐intake

Task 1: OI Clerk receives order from customer over email or phone

Task 2: OI Clerk enters order in the computer system

Task 3: OI clerk sends confirmaFon to OI Department Manager

Task 4: OI clerk acknowledges receipt of order to the client


PART 1: BUSINESS PROCESSES

Order Receipt

Order Entry

Internal Confirma'on

Order Acknowledgement

PART 2: PROCESS RE-‐ENGINEERING

Business processes form chains inside the organisaFon. Each process leads to one or more other processes.

Process re-‐engineering intends to re-‐design these internal chains of processes in order to fulfill the business needs of the organisaFon and in view of course of improving them. Among the targeted objecFves, we could have: gain of Fme, increased efficiency, cost cuang etc...


DefiniFon

THE PROBLEM: Company Kamera has hundreds of reports reaching management every month. These reports are produced by Finance department but the data originally comes from MIS department. For this reason when a problem occurs in the report, each department blames the other for the

mistake and no soluFon is found.

THE SOLUTION: The process engineer could create a data owner inside either department. A person in charge of checking accuracy of data and cleaning it if necessary in order to streamline the reporFng process. MIS would sFll provide the data, but the data owner would check and amend it first before Finance

proceeds with the reporFng.

This is a perfect example of process re-‐engineering.


PART 2: PROCESS RE-‐ENGINEERING Example: creaFng a data owner inside a department

ERP projects (Enterprise Resources Planning)

The IT systems in many organisaFons prior to an ERP are generally products of historic factors rather than raFonal ones. They ocen use

different plaeorms and are mutually incompaFble.

The principal objecFve of an ERP project is precisely to put ALL the IT systems of the organisaFon into one common roof, from the general

ledger of accounFng, to order-‐intake or procurement. All the processes of the organisaFon are under different computer screens but the same

socware.



Why is an ERP a process re-‐engineering?

An ERP project is an example of process re-‐engineering.

Why? Because in order to put all the processes of an organisaFon under a common IT plaeorm, the project manager has to re-‐design these processes, re-‐arrange them and amend the structure of the process-‐

chain.

The process-‐chain structure has therefore been re-‐engineered acer an ERP.



Benefits of an ERP

There are many benefits of undertaking an ERP project.

1) Beher accuracy of data. Less mistakes. 2) Beher reporFng system and therefore beher visibility

over the business 3) A more customer friendly IT system for the internal

users 4) a more efficient and reliable way of working for the office clerks cuang therefore on unnecessary costs.



A business organisaFon seen as a MathemaFcal Space

Once a process is completed, it impacts on following processes. These subsequent processes are either at the same hierarchical level inside the

company or levels below.

The set of all processes forms therefore organisaFonal layers of hierarchy inside the company. These layers are disFnct and ordered. A given layer is made up of

processes within the same horizontal level.

Furthermore the whole organisaFon as a profit-‐making enFty can be seen as the total sum of its business processes.


PART 3: MODELLING BUSINESS ORGANISATIONS

OrganisaFonal layers -‐ Picture

It is therefore possible to draw a picture of the organisaFonal structure of any company. Many big companies have 4, 5 or more layers.

Layer 1: strategic layer Layer 2: upper managerial layer Layer 3: lower managerial layer

Layer 4: work layer



Layer 1

Layer 2

Layer 3

Layer 4

The T&P layer

The actual process re-‐engineering project takes place on its own transverse layer: the T&P layer. Because it is transverse this layer is THE engine of

change inside the organisaFon.

In any case, this layer where the project manager sits is situated between the lower managerial and the work layer.

Thus the real happening of any organisaFon is in between the lower managerial and the work layer.



Lower Management Layer T&P Layer

Worker/Clerk Layer

Layered spaces

From the study of business organisaFons we want to introduce a new mathemaFcal object: a layered space.


PART 4: MATHEMATICAL PART

Cells

DefiniFon: the most fundamental unit in a layered space is the cell. The whole space is made up of cells.

Property: each cell has the following ahributes: 1) Individual Energy

2) Momentum

Property: each cell can communicate to other cells. This is called impulse. Every impulse has a sender and a receiver. Impulses go only one way, from the sender to the receiver

and not the reverse.



Layered spaces

DefiniFon: impulses can be either horizontal or downward verFcal.

Property: Cells which are in the same line of horizontal impulses form a layer.

Property: Every cell belongs to a parFcular layer whose consFtuent cells remain fixed. Some layers are below others.



Example – Business OrganisaFons

A business organisaFon is a layered space. The consFtuent cells are the

business processes.

Example: a business organisaFon with 4 layers

Layer 1: leadership Layer 2: upper management Layer 3: lower management

Layer 4: workers & office clerks



Example – Society as a whole

A given human society can also be seen as a layered space. The component cells are the individual persons making up

the society.

Some socieFes can be seen as a 4 layer space.

Layer 1: priests / intellectuals Layer 2: warriors/ aristocracy

Layer 3: business people Layer 4: workers



EvoluFon in Fme

The layered space would remain staFc in Fme if there were not transverse, invisible layers permeaFng the whole space and allowing it to move forward.

In the case of business organisaFons, it is the T&P layer

Without it there would be no change or progress.



T&P Layer

Changes

As we have seen layers are in a hierarchical order from top to bohom. The transverse layers allow the whole system to remain dynamic and not just

responsive to the environment. However real change happens only when 2 or more layers collide at a given moment in Fme.

In the case of business organisaFons this happens during major re-‐engineering projects like ERPs.



DisrupFon

A disrupFon occurs when all the layers collide at the same Fme.

Acer the turmoil, you get a new layered space with a new structure. In our societal example, we could take the Zoroastrian revoluFon in ancient

Persia or more recently the French RevoluFon.



mathematical concepts applied to operations management

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bymulftasking axiom3