OptimizationReview(1,15)

# OptimizationReview(1,15) - Notes on Formulation of...

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590B intro 1 Notes on Formulation of Optimization Problems Leyla Ozsen Industrial Engineering Purdue University

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590B intro 2 Outline Conventions Formulation Rules Typical Constraint Forms
590B intro 3 Conventions I (generally) Use INDICES letters like i, j, k, (middle of alphabet) used as subscripts index items in sets with corresponding upper case letter (e.g, I, J, K) INPUTS lower case letters near beginning of alphabet DECISION VARIABLES upper case letters near end of alphabet

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590B intro 4 Indices, Inputs and Dec. Var INDICES used for enumerating items (e.g., demand nodes, candidate sites, scenarios, time periods) INPUTS you know these before you start the problem; either given or can readily compute them from other inputs demand values, distances, costs, probabilities, coverage distance, number of sites to locate, indicators of whether nodes are covered by others
590B intro 5 Indices, Inputs, and Dec. Var. DECISION VARIABLES these are what you want to know or what you must determine within the model along the way to determining what you really want to know locations of facilities, assignment of demand nodes to facilities, maximum distance, whether a node is covered

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590B intro 6 Objective function OBJECTIVE FUNCTION this is what you want to minimize or maximize may be a single decision variable (e.g., W for maximum distance between a node and the facility serving it as in P-center) more often will be a function of decision variables (e.g., the total number of facilities as in set covering, the total demand weighted distance as in P-median)
590B intro 7 Formulation rules 10 (or 11) rules of formulation

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590B intro 8 Rule 1 Clearly define all subscripts (at least in your own mind) and sets. For example: I: set of demand nodes indexed by i J: set of candidate sites indexed by j K: set of scenarios indexed by k T set of time periods indexed by t
590B intro 9 Rule 2 Clearly separate the definitions of indices and sets inputs (or parameters) decision variables

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10 Rule 3 In defining inputs or decision variables in words, if an index appears in the input or decision variable it should appear in the verbal definition as well
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## This note was uploaded on 10/08/2011 for the course IE 383 taught by Professor Leyla,o during the Spring '08 term at Purdue.

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OptimizationReview(1,15) - Notes on Formulation of...

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