Optimization+I E10

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

This preview shows pages 1–7. Sign up to view the full content.

Optimization I ob eachman Rob Leachman E10, Spring, 2010 February 1, 2010 Feb. 1, 2010 E10 Optimization I Prof. Leachman 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 21

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online