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Main example - production planning

Develop a monthly buying and production plan to optimize profit in the first half of 2003. Solve a linear programming problem with 96 variables and constraints for raw oil purchasing, consumption, storage, and production. Ensure quality and storage capacity compliance.

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Main example - production planning

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  1. Main example - production planning

  2. Raw oil price (monthly basis) [NOK/ton] Sales price (one product): 1500 NOK/ton Storage cost: 50 NOK/ton per month Storage capacity: 1000 ton (for each raw oil) Main example - production planning

  3. Raw oil type Hardness VEG 1 8.8 VEG 2 6.1 OIL 1 2.0 OIL 2 4.2 OIL 3 5.0 Main example - production planning • Product quality is defined by “hardness” • quality window

  4. Production capacity: [ton/month] • “vegetable oil”: max 200 • “non-vegatable oil”: max 250 Main example - production planning There is 500 ton in every storage tank at the start (end of Dec.) There should be 500 ton in every storage tank at the end (end of June). Problem formulation: Find the buying and production strategy (on a monthly basis) that maximizes profit during the first half of 2003.

  5. Mathematical formulation - prod. planning Problem formulation: Find the buying and production strategy (on a monthly basis) that maximizes profit during the first half of 2003.

  6. Problem formulation: Find the buying and production strategy (on a monthly basis) that maximizes profit during the first half of 2003. Mathematical formulation - prod. planning • Unknown variables: • Monthly purchase of raw oil • (6 months x 5 raw oils=30 variables) • Monthly consumption of raw oil • (6 months x 5 raw oils=30 variables) • ----------------- • Stored raw oil (on a monthly basis) • (6 months x 5 raw oil storage tanks=30 variables) • Monthly production (6 months x 1 product=6 variables)

  7. Linear objektive function + 144 linear inequalities Problem formulation: Find the buying and production strategy (on a monthly basis) that maximizes profit during the first half of 2003. Mathematical formulation - prod. planning Objective function: Sales income - All costs (eq.7) Production capacity constraints 12 inequalities (eq.8,9) Quality constraints 12 inequalities (eq.10,11) Storage capacity constraints 30 inequalities (eq.16) The variables cannot be negative 90 inequalities (eq.17,18,19)

  8. 41 linear equations Problem formulation: Find the buying and production strategy (on a monthly basis) that maximizes profit during the first half of 2003. Mathematical formulation - prod. planning Mass balance production 6 equalities (eq.12) Mass balance storage tanks 30 equalities (eq.13) Final storage requirement in each storage tank 5 equalities (eq.15)

  9. Problem formulation: Find the buying and production strategy (on a monthly basis) that maximizes profit during the first half of 2003. Mathematical formulation - prod. planning • Problem formulation: • Linear objective function • 144 linear inequalities • 41 linear equalities • 96 unknown variables • This is a medium-sized • linear programming problem (LP-problem)

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