278. Cheatsheet

279. Linear Programming

Function
Type		 Method Example
Maximization to
Minimization
Constraint
to
Equality Constraint
Slack Variable

Add slack variable :

is how much less is being used than the maximum limit of 6
Surplus Variable

Add slack variable :

is the amount above the minimum required level 6

280. Integer Programming

Function
Type		 Method Example
At least of the items in

Produce at least 3 products:
At most of the items in

Open at most 2 facilities:
Exactly of the items in

Choose exactly one location:
If , then
If project A is done, project B must also be done
If , then
Projects A and B are mutually exclusive
If , then
If project A is selected, neither project B nor C can be selected
If , then at least
items in must be selected
You have a main server represented by . If it is down or not used (), then at least backup servers (in set ) must be activated
At least of
constraints satisfied
Enforce any of the constraints by relaxing up to of them
Fixed (Setup) Costs
If facility is used (), then allow production up to ; else
Balanced Flow
Each node receives and sends exactly units of flow. If , this is a TSP or assignment
Unbalanced Flow

Each node has net inflow minus outflow equal to :

  • : demand
  • : supply
  • : transshipment
Subtours (MTZ)
Subtours (SEC)
For every subset of the nodes that has at least 2 nodes, the total number of arcs (or paths) within that subset — from node to node , where must be less than or equal to

281. Non-Linear Programming

Function
Type		 Example Linearization
Method		 Example
Binary Binary
Constraint
Binary Continuous
Constraint
Continuous Continuous
Constraint
Absolute Value
Max
Constraint
Min
Constraint
Max Min
Objective
Min Max
Objective
Min Min
Objective
Max Max
Objective

282. Algorithms

Algorithm Update Rule
Gradient
Descent
Newton’s
Method

Newton’s Method

Approximation Taylor
Expansion		 Newton
Update
Linear (1D)
Linear (nD)
Quadratic (1D)
Quadratic (nD)