MDAB - Intro

MDAB - Intro

1. ELEMENTS

   • Objective function
   • Decision variables
     • Quantity
     • Of
       • Product
       • Service
     • To be produced
   • Constraints

2. GENERAL FORM

   • Max - Min
     • c1x1+c2x2+...+cnxn
       • c: objective function coefficient
   • Subject to
     • a11x1+a12x2+..+a1nxn <= b1
       • b: RHS
     • a21x1+a22x2+..+a2nxn <= b2
     • am1x1+am2x2+...+amnxn <= bn
     • all x1,..xn>=0

3. ASSUMPTION

   • Deterministic model
     • known with certainty
       • c: objective function coefficients
       • a: technical coefficients
       • b: RHS
   • Implications
     • Divisibility
       • variables are continuous
     • Proportionality
       • incrs decision variable x%, objective function incrs x%

4. LINEAR PROGRAMMING

   • Max
     • Profit
   • Min
     • Cost

5. SENSITIVITY ANALYSIS

   • Change objective function coefficient
     • change c
     • Reduced cost
       • how much c
       • improve
       • variable have positive value in optimal solution
     • Allowable incrs/dcrs
       • limit
       • c can be adjusted
       • optimal solution unchange
   • Change in constraints - RHS value
     • shadow price
       • if RHS incrs 1 unit
       • how much objective function incrs
     • Allowable incrs/dcrs
       • limit
       • b can adjust
       • shadow price unchange