Introduction to Operations Management

Components of an effective operations/manufacturing system

1. educated/knowledgable(int the task at hand, of cource) and flexible workforce
2. consistent, continuous focus on quality
3. effective assets/resource management

Reasons For Global Operations

• low labour costs, and labour law
• access to expertise
• access to capacity
• specialist/subcntractors-achieve exonoies of scale
• Access to raw material
• tax regime
• accessing local markets
• quality
• technology and assets, assets is financial(money) techinial, expert people etc.

Reason Against Global Operations

• labour law
• risks(of supply, delays, environment, tax regimes changing…)
• loss of control of product quality
• changes in cost structures
• supply chain complexity
• trade tariffs
• loss of local expertise

Operations Management Decisions

• Design of products and service: what do we offer? how can we design these?
• Quality how do we define it(i.e. policies and standards); responsibolty allocation
• Process desingn, determining capacity requirements: our products- what do they require? what equipment and tech we will need and how much of it?
• Location strategy/supply chain design: where we should locate new facilities(manufacturing and also distribution - e.g supermarket/warehouses etc); what are the criteria for our choices?
• Layouts of facilities: how we could arrange the facility/its layout i.e. to maximise throughput or/and use of space: size of the facility(capacity)
• Human reasource and job design/allocation: how to design the work environment. how much outputs whorls we expect from a given work allocation scheme?
• Supply chain management : make or buy decision? supplier selection and order/demand allocation to suppliers(model risks)?
• Inventory Management: how much inventory of each SKU(Stock keeping unit) we should have? when we reorder?
• Scheduling: which jobs to perform next? Do we need overtime or how much of flexible workforce we require?
• Maintenance: how do we embed realiablity into our processess? who is responsible?

Parabola Line

Example
we have a function to descript a process of throwing a ball like this:

$$ h=-4.9t^2+10t+2 $$

Questions

1. When it kicks the ground?
2. How high it goes?

Solutions
Q1:

• h=0

  $$ -4.9t^2+10t+2=0 $$
  $$t = \frac{-10 \pm \sqrt{10^2-4(-4.9)2}}{2(-4.9)}.$$

Q2:

• Derivation

  $$ \frac{dh}{dt} $$
  $$ h’=-9.8t+10 $$
  $$ h’=0, then\ t = \frac{10}{9.8} $$

Q1:

• Newton Raphson Method

  $$ x_0=init\ guess $$
  then we try:
  Point:$$(x,h(x_0))$$
  A straight line: $$ y-h(x_0)=h’(x_0)(x-x_0) $$
  then we got: $$y=0,x=x_1$$
  $$ -h(x_0)=h’(x_0)(x_1-x_0) $$
  $$ x_1=x_0-\frac{h(x_0)}{h’(x_0)} $$
  $$ x_2=x_1-\frac{h(x_1)}{h’(x_1)} $$
  $$ ……. $$

Q2:

• Gradient Descent

  $$ h’(t)=-9.8t+10 $$
  $$ h^{‘’}(t)=-9.8 $$
  $$ t_0=2 $$
  $$ t_1=2- \frac{-9.8(2)+10}{-9.8}=1.02$$
  $$ h=-4.9(1.02)^2+10(1.02)+2=7.1 $$
  $$ …… $$

Newton Raphson Method && Gradient Descent

• may not
• if this guess is not good, then may never convince

Local vs Global Optimal

• global maxium & global minum
• local maxium & local minum