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0571-3802

Deterministic models in operations research

Also listed as: מודלים דטרמיניסטיים בחקר ביצועים

Linear and integer programming, network flows and dynamic programming. The formal machinery behind design optimisation, scheduling and logistics.

Semester
Not fixed
Weekly hours
4h
Counts as
Faculty electives
Interest areas
Mechanical design

Comes after

  • Linear algebra

Opens up

  • Design optimisation research

What it covers

Topics

  • Linear programming, the simplex method and duality
  • Integer programming
  • Network flow problems
  • Transportation and assignment problems
  • Dynamic programming

Results worth carrying out

  • Linear program, standard form

    min  cTxs.t.Ax=b,    x0\min\; c^{\mathsf{T}}x \quad \text{s.t.} \quad Ax = b, \;\; x \ge 0
  • Strong duality

    max  bTy    s.t.    ATyc,cTx=bTy\max\; b^{\mathsf{T}}y \;\; \text{s.t.} \;\; A^{\mathsf{T}}y \le c, \qquad c^{\mathsf{T}}x^* = b^{\mathsf{T}}y^*
  • Bellman recursion

    Vt(s)=mina{c(s,a)+Vt+1 ⁣(f(s,a))}V_t(s) = \min_{a}\left\{ c(s,a) + V_{t+1}\!\left(f(s,a)\right) \right\}

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