Carandang, Angelou M.
#109 Brgy. Sta.Teresita Sto. Tomas Batangas
+639157821098
anjocarandang@gmail.com
OBJECTIVES:
To be able to help for the growth of your company, in your competitive organization by
using my skills, apply my further knowledge and wide
Revised Simplex
Simplex in Matrix Review
A = matrix for the constraint coefficients
B = A matrix but only columns for the basic variables
b = column of constraint RHS
c = row vector of objective function coefficients
CB = objective function coefficients o
Integer Programming
1
Integer Programming (IP)
Variables are restricted to integer values
Pure IP if all variables are integers
Mixed IP if not all variables are integers
Binary Integer Programming (BIP) if the
variable values can only be 1 or 0
Doesnt a
Branch and Bound
Branch and Bound
Developed by Land and G. Doig in 1960
Method in solving mixed and pure IP problems
Most efficient general purpose solution procedure for integer linear
problems
General steps:

Ignore the integer constraints and solv
Goal Programming
Goal Programming
Involves multiple (sometimes conflicting) objectives
May be impossible to find a feasible solution that will optimize
all objectives
GP seeks a compromise solution based on the relative
importance of each objective
Mu
Cutting Plane Method
Cutting Plane Method
Uses Gomorian Cuts
Made by Ralph E. Gomory
Cuts the noninteger region of the basic variables
All coefficients and the RHS of the basic variable row must be
integers
Cutting Plane Method
Given the optimal tabl
Clarifications on (Revised) Dual Simplex
Although commonly used for minimization
problems, this can be used for max problems
as well to remove infeasibility
For the minimum ratio test, the denominator
(B1A) must be negative
Once infeasibility is remov
Duality
Weak Duality
Assume the primal is a max problem
Let x be the Z value for the primal and y for the dual
For each iteration, X Y
Y is always equal or better than x but not necessarily feasible
Y is only feasible once it is equal to X
The feasible re
Introduction to Operations
Research
1
What is Operations Research?
Discipline of applying advanced analytical
methods to help make better decisions
Science of Better
Scientific approach to decision making
Seeks to best design and operate a system
Usu
DP
Applications
WorkForce Size
Workforce model
For most Companies
workforce varies from time to time depending on
project needs
hiringfiring strategies from time to time in order to
maintain & satisfy demand
Optimal scenario: one with minimum cost
Dyna