Lecture_3_Introduction_to_Linear_Programming_I

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Lecture 3: Introduction of Linear Programming-I Ankit Bansal Binghamton University abansal@binghamton.edu Ankit Bansal (BU) SSIE 553-Operations Research 1 / 14

Linear Programs (LPs) 1 LPs are optimization models with linear objective functions and constraints. 2 For the next few classes we will: Formulate LPs Solve LPs Ankit Bansal (BU) SSIE 553-Operations Research 2 / 14

Ingredients of an LP Model 1 Decision Variables 2 Objective Function 3 Constraints 4 Model parameters Objective function coefficients Constraint coefficients Right hand sides (Rhs) Ankit Bansal (BU) SSIE 553-Operations Research 3 / 14

LPs in words Following are some examples of LPs stated informally: 1 Maximize the production yield of pharmaceuticals subject to constraints on production parameters. 2 Minimize radiation absorption to healthy tissue subject to the requirement that cancer causing cells are destroyed. 3 Maximize advertising revenues on a broadcast network subject to a fixed schedule of commercial slots. Ankit Bansal (BU) SSIE 553-Operations Research 4 / 14

Simple Example 1 A surgical suite serves two types of surgeries: S1 and S2. 2 The surgeries require three resources: S1 requires R1 and R2. S2 requires R2 and R3. 3 Question: How many of each type of surgery should be planned for each day? 4 Note : R2 must be divided between S1 and S2. Ankit Bansal (BU) SSIE 553-Operations Research 5 / 14

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