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Lecture Operations management: Creating value along the supply chain (Canadian edition) - Chapter 14S

Chapter 14 supplement - Linear programming. This chapter includes contents: Model formulation, graphical solution method, linear programming model solution, solving linear programming problems with excel, sensitivity analysis. | Supplement 14-1 Robert S. Russell, Bernard W. Taylor III, Ignacio Castillo, Navneet Vidyarthi CHAPTER 14 SUPPLEMENT Linear Programming OPERATIONS MANAGEMENT: Creating Value Along the Supply Chain, Canadian Edition 1 Lecture Outline Model Formulation Graphical Solution Method Linear Programming Model Solution Solving Linear Programming Problems with Excel Sensitivity Analysis Supplement 14-2 2 Linear Programming (LP) A model consisting of linear relationships representing a firm’s objective and resource constraints A mathematical modeling technique which determines a level of operational activity in order to achieve an objective, subject to restrictions called constraints Supplement 14-3 3 Types of LP Supplement 14-4 4 Types of LP Supplement 14-5 5 Types of LP Supplement 14-6 6 LP Model Formulation Decision variables symbols representing levels of activity of an operation Objective function linear relationship for the objective of an operation most frequent business objective is to . | Supplement 14-1 Robert S. Russell, Bernard W. Taylor III, Ignacio Castillo, Navneet Vidyarthi CHAPTER 14 SUPPLEMENT Linear Programming OPERATIONS MANAGEMENT: Creating Value Along the Supply Chain, Canadian Edition 1 Lecture Outline Model Formulation Graphical Solution Method Linear Programming Model Solution Solving Linear Programming Problems with Excel Sensitivity Analysis Supplement 14-2 2 Linear Programming (LP) A model consisting of linear relationships representing a firm’s objective and resource constraints A mathematical modeling technique which determines a level of operational activity in order to achieve an objective, subject to restrictions called constraints Supplement 14-3 3 Types of LP Supplement 14-4 4 Types of LP Supplement 14-5 5 Types of LP Supplement 14-6 6 LP Model Formulation Decision variables symbols representing levels of activity of an operation Objective function linear relationship for the objective of an operation most frequent business objective is to maximize profit most frequent objective of individual operational units (such as a production or packaging department) is to minimize cost Constraint linear relationship representing a restriction on decision making Supplement 14-7 7 LP Model Formulation Max/min z = c1x1 + c2x2 + . + cnxn subject to: a11x1 + a12x2 + . + a1nxn (≤, =, ≥) b1 a21x1 + a22x2 + . + a2nxn (≤, =, ≥) b2 : an1x1 + an2x2 + . + annxn (≤, =, ≥) bn xj = decision variables bi = constraint levels cj = objective function coefficients aij = constraint coefficients Supplement 14-8 Constraints 8 Highlands Craft Store Supplement 14-9 Labor Clay Revenue Product (hr/unit) (lb/unit) ($/unit) Bowl 1 4 40 Mug 2 3 50 There are 40 hours of labor and 120 pounds of clay available each day Decision variables x1 = number of bowls to produce x2 = number of mugs to produce Resource Requirements 9 Highlands Craft Store Supplement 14-10 Maximize Z = $40 x1 + 50 x2 Subject to x1 + 2x2 40 hr (labor constraint) 4x1 + 3x2 120 lb .