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Busm 360

by: Hali Nepsha

Busm 360 BUSM 360

Hali Nepsha

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About this Document

these notes briefly cover chapter 19 linear programing model.
Production/ Operations Management
Dr. Raida Abuizam
Class Notes
operations, Managment, BUSM, 360, CH, 19, notes, Linear, programming
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This 2 page Class Notes was uploaded by Hali Nepsha on Wednesday October 12, 2016. The Class Notes belongs to BUSM 360 at Purdue University Calumet taught by Dr. Raida Abuizam in Fall 2016. Since its upload, it has received 6 views. For similar materials see Production/ Operations Management in Business at Purdue University Calumet.

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Date Created: 10/12/16
Linear Programing ch 19 Oct. wed 12 Linear Programming Model The goal maximization or minimization Decision variables Amounts either inputs or outputs Constraints Limitations restrict available alternatives Parameters Numerical values Linear Programming Assumptions Linearity Impact decision variables is linear in constraints & objective function Divisibility Non-integer values decision variables acceptable Certainty Values parameters known & constants Non-negativity Negative values decision variables unacceptable Linear Programming model: Maximize (or Minimize) Z = c x +1c 1 + c 2 2 . . 3 3 x n n subject to: a 11+1a x +12 2 + . 13. 3 a 1n n  b 1 a 21+1a x +22 2 + . 23.3a x 2n n  b 2 a31 +1a x +32 2 + . 33.3a x 3n n  b3 : : : : : am1 +1a x +m2 x2+ . .m3 3 x mn n  b m x 1,x2, 3, . .n. Linear programming has two parts: 1.)setting up model 2.)solving model Solving the Model -graphical technique -using Microsoft excel solver Graphical linear programming: method used for finding optimal solutions two decision variable problem. o Set up objective function & constraints in mathematical format o Plot constraints o Identify the feasible solution space o Plot the objective function o Determine the optimum solutions Slack and surplus:  Slack: when the values of the decision variables are substituted into a < constraint, and the resulting value is less than the right side value  Surplus: when the values of decision variables are substituted into a > constraint and the resulting value exceeds the right side value  Binding Constraint: a constraint that forms the optimal corner point of the feasible solution space. Sensitivity Analysis: Assessing impact of potential changes to numerical values of linear programming model There are 3 types potential changes: 1.) Objective function coefficients 2.) Right-hand values of constraints 3.) Constraint coefficients Objective Function coefficients  Consider how changes in objective function coefficients might affect optimal solution  Range of optimality for each coe. Provides range val. Over which current solution will remain optimal  Mangers should focus on those objectives coefficients that have narrow range optimality & coe. Near endpoints of range Right-Hand Sides  Consider how a change in right-hand side for constraint might affect feasible region & might cause change in optimal solution  Improvement in value optimal solution per unit increase in right-hand side called dual price  Range feasibility is range over which dual price applicable  RHS increases, other constraints will become binding & limit change in value of objective function


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