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# Class_2b - EMSE 154 254 Applied Optimization Modeling...

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EMSE 154 - 254: Applied Optimization Modeling Lecture notes #2 Applied Optimization Modeling EMSE 154-254 Hern á n Abeledo Fall 2008 lass 2 Class 2 1

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EMSE 154 - 254: Applied Optimization Modeling Lecture notes #2 day: Today: P modeling LP modeling Typical LP constraints etwork models Network models 2
EMSE 154 - 254: Applied Optimization Modeling Lecture notes #2 modeling: LP modeling: ypical LP constraints: (see Chapter 2) Typical LP constraints: (see Chapter 2) Upper and lower bounds low constraints Flow constraints Simple resource constraints aterial balance constraints / flow conservation Material balance constraints / flow conservation Accounting constraints uality / Blending constraints (discussed last class) Quality / Blending constraints (discussed last class) 3

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EMSE 154 - 254: Applied Optimization Modeling Lecture notes #2 modeling: pper and lower bounds LP modeling: upper and lower bounds 1. Can’t sell more than 100 units of product 4 2. Need to send at least 20 units of product 6 4 sell 100 ust ship exactly 30 units of product 5 to client A d i bl 6 send 20 3. Must ship exactly 30 units of product 5 to client A ( fixed variable ) = 5, ship 30 A 4. Electricity can flow in either direction on a given cable. Can model electricity flow by a variable unrestricted in sign (eflow). The direction of flow is given by sign of variable’s value. 4 Need to declare eflow is_free , (otherwise, by default Mosel assumes variables to be nonnegative)
EMSE 154 - 254: Applied Optimization Modeling Lecture notes #2 modeling: ow constraints LP modeling: flow constraints Typically arise when there is some divisible item (water, traffic, etc) that is partitioned into different streams (or different streams that are joined) 1. Have a tank with 1000 liters and 3 customers to supply 2. I buy bricks from 3 suppliers and I need at least 5000 bricks + +≤ 12 3 1000 Supply Supply Supply need exactly 5000 bricks + +≥ 3 5000 Bricks Bricks Bricks 5 3. I need exactly 5000 bricks + += 3 5000 Bricks Bricks Bricks

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EMSE 154 - 254: Applied Optimization Modeling Lecture notes #2 modeling: ow constraints LP modeling: flow constraints 4. The factory has two water supplies, S1 and S2. Must pay for amount of water that arrives to factory. However, factory loses 1% of the water coming from S1 and 2% of the water at comes from S2. Factory needs 100,000 gallons of that comes from S2. Factory needs 100,000 gallons of water per day. One approach to modeling these constraints: Let Buy j = amount of water purchased from supplier j Get j = net amount of water received from supplier j + = = 12 1 100,000 0.99 * Get Get Get Buy 6 = 11 22 0.98 * Get Buy
EMSE 154 - 254: Applied Optimization Modeling Lecture notes #2 modeling: source constraints LP modeling: resource constraints Example: Each ton of chemical 1 uses 50 grams of catalyst and 1 kg of a fine chemical. Each ton of chemical 2 uses 130 grams of catalyst and 1.5 kg of the fine chemical. We can obtain 10 kg of catalyst per month and 200 kg of the fine chemical per month.

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## This note was uploaded on 01/02/2010 for the course EMSE 254 taught by Professor Hernanabeledo during the Fall '08 term at GWU.

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Class_2b - EMSE 154 254 Applied Optimization Modeling...

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