# lecture2 - IND E 599 Intro to Optimization Models Lecture 2...

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IND E 599: Intro to Optimization Models Lecture 2: Building LP Models (Ch. 3), Interpreting and Using an LP solution (Ch. 6) Duality Prof. W. Art Chaovalitwongse

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Defining Objectives Common Objectives – Minimize cost – Maximize profit – Maximize utility – Maximize return on investment – Maximize net present value – Maximize customer satisfaction – Maximize probability of achieving a goal – Maximize reliability – Minimize the change in employment (hiring/ring) – Maximize robustness of a strategy or plan – Minimize makespan – others? Single Objective vs. Multiple/Conflicting Objectives Minimax Objectives Ratio Objectives
Multi-Objective Optimization

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Common Constraints Capacity constraints Demand constraints Balance constraints Flow constraints Bounding constraints (upper & lower bounds, also mini-max) Hard and soft constraints (use b + i and b - i to “soften” a constraint and penalize deviations - also goal programming) Use fuzzy set membership instead of soft constraints – and convert to LP using mini-max objective Chance constraints Either-or constraints (use binary variables) Logic constraints (Produce product 1 if product 2 is produced but neither products 3 or 4 are produced)
What to consider in building a good model Ease of understanding the model – state assumptions – clearly document the model – clearly define the decision variables – clearly state the objectives and constraints – document variations on model – include details such as units, sources of data Ease of detecting errors in the model – clerical errors and formulation errors – build modular formulations – if using substitutions and compact formulations, test equivalency in small problems – develop test cases that are scalable – verify that trends follow intuitive explanations – check for reasonable ranges on feasibility, boundedness – compare to historical solutions – get feedback from decision makers on reasonableness

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What to consider in building a good model Ease of computing the solution – consider tradeoffs between accuracy of model and computational time – test different solution techniques and compare – be alert to numerical error – debug a model as you would a computer program
Interpreting and using an LP (Chapter 6) Infeasible models Unbounded models Solvable models Sensitivity Analysis and Duality – Does the solution make sense? – What if capacity is increased/decreased -> RHS – What if costs are modified -> Cost coefficients – Compare to practical solutions

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Economic Interpretation of an LP Common terms relating to economic interpretations: – shadow prices, reduced costs, sensitivity analysis, duality Easiest interpretation when in the following form: How large a change in resource can be made without losing the “ shadow price ” interpretation?
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lecture2 - IND E 599 Intro to Optimization Models Lecture 2...

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