Systems Analysis

Optimisation

  • Linear programming
  • Integer programming
  • Non-linear programming

 

Linear Programming

Typical process

  • Identify decision variables
  • Objective function
  • Split variables according to distinct segments for simplicity
  • Constraints:
  1. Supply
  2. Demand
  3. Pricing
  4. Material
  5. Machinery
  6. Production mixture
  7. Inventory

Supportive

  • Slack: <=
  • Surplus: >=
  • Binding constraint: contains optimal sol
  • Shadow price: O.C. of unit increase of constraint
  • Sensitivity studies: allowable range of the objective coefficients without changing optimal solution
  • Assumes: proportionality, additivity & continuity

Formulation

  • Decision var. in units
  • Objective function for problem
  • Constraints in inequalities

TORA solution

  • Formulate in canonical form: equalities & basic var. added
  • Tableau
  • Basic var. (bv):
  • Design var.:
  • Constraint values (cv):
  • Obj. value (-z): optimal when ALL -ve

Integer Programming

Formulate

  • ALL decision var. = integers
  • Same as above
  • Constraints expressed in inequalities
  • Mathematical expressions

 

 

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