Optimization+I E10 - Optimization I Rob Leachman Leachman...

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Optimization I ob eachman Rob Leachman E10, Spring, 2010 February 1, 2010 Feb. 1, 2010 E10 Optimization I Prof. Leachman 1
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hat is Optimization What is Optimization • Calculation of how best to operate or configure a ystem system – Decision variables ( A for what we can adjust ) – Objective function ( B for what’s best ) – Constraints on variables ( C for how are we constrained ) • Mathematical methods of optimization – Calculus: Functional characterization of possible decisions and economic consequences – Search: Enumeration and evaluation of alternative decisions • Directed search (always move to a better alternative) •S topping rule: Proof of optimality without evaluating every Feb. 1, 2010 E10 Optimization I Prof. Leachman 2 pp g p y g y alternative
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ventory Replenishment Problem Inventory Replenishment Problem • Demand for a good occurs at a steady rate D per unit time and must be met from on-hand inventory. e replenish inventory by ordering in batches It We replenish inventory by ordering in batches. It takes L units of time from the time we place a replenishment order until the order arrives. • When we order, we buy the good at a cost of c per unit. In addition, there is a fixed replenishment cost A per order (regardless of how small or large the order is). • We have to finance and store on-hand inventory. his costs er unit per unit time Feb. 1, 2010 E10 Optimization I Prof. Leachman 3 This costs h per unit per unit time.
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et up the Optimization Model Set up the Optimization Model • Understand the problem. • What do we have to decide (A)? – When to order, how much to order Q • What’s best (B)? – We have to worry about the ordering cost and the inventory holding cost. We want to minimize costs. • How are we constrained (C)? – We have to meet the demand, i.e., we have to keep the inventory from running out. yg – We must place an order when the inventory falls to level L*D (and there is no reason to place an order before then). Feb. 1, 2010 E10 Optimization I Prof. Leachman 4
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odel set- p (cont ) Model set up (cont.) Figure 1. Inventory Level vs. Time - =200, D=1,000 Q 200, D 1,000 250 150 200 ry Level 50 100 Invent o 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ime Feb. 1, 2010 E10 Optimization I Prof. Leachman 5 Time
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odel set- p (cont ) Model set up (cont.) • If we order a very large batch, we delay spending A again, but we have to pay h on a large inventory (which gets worked off at rate D ) we order a small batch we pay nasma l l • If we order a small batch, we pay h on a small inventory, but we will have to pay A
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Optimization+I E10 - Optimization I Rob Leachman Leachman...

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