M670_11 (Linear Programming)

# M670_11 (Linear Programming) - Linear Programming k MGMT...

This preview shows pages 1–12. Sign up to view the full content.

1 Linear Programming k MGMT 670: Business Analytics Krannert Graduate School of Management Purdue University

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Categories of Mathematical Models Descriptive : Understand the system Simulation, Regression Analysis, Time Series Analysis,… Prescriptive : Find the “optimal” solution Critical fractile, LP, Networks, IP, CPM, EOQ, NLP, … Model Quantitative Category Techniques
3 Prescriptive Mathematical Models § INPUTS Relate decision variables (controllable inputs) with fixed or variable parameters (uncontrollable inputs) § MODEL Frequently seek to maximize or minimize some objective function subject to constraints § OUTPUTS Optimal solution is the value of the decision variables that results in the most desirable objective value

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 Transforming Model Inputs into Output Uncontrollable Inputs (Environmental Factors) Controllable Inputs (Decision Variables) Output (Projected Results) Mathematical Model Unit price = \$100, Unit cost = \$30, Capacity = 50 Produce Profit = Revenue – Expenses Produce  50 Produce*=50 Profit* = 50×(100-30)=\$3500 * denotes optimal solution and optimal objective value
5 Steps in Formulating Linear Programming Models 1. Define decision variables 2. Express objective as a function of decision variables and known parameters 3. Formulate constraints to meet requirements and not exceed available capacity (using decision variables and known parameters)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6 An Example LP Problem Blue Ridge Hot Tubs produces two types of hot tubs: A and B. Processing requirements and contribution margins are: There are 200 pumps , 1566 hours of labor , and 2880 feet of tubing available for production. What production plan will maximize profit ? Product A Product B Pumps 1 1 Labor 9 hrs 6 hrs Tubing 12 feet 16 feet Unit Profit \$350 \$300
7 Formulating an LP Model 1. Define decision variables . 2. The objective Maximize Profit MAX

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
8 Formulating an LP Model (continued) 3. Formulate constraints (Pump) pumps required pumps available (Labor) (Tubing)
9 Feasibility versus Optimality § The constraints of an LP problem defines its feasible region . Any production plan for Product A and B that satisfies Pump, Labor and Tubing constraints is a feasible plan § The best point in the feasible region is the optimal solution to the problem. Among all feasible plans, the production plan that maximizes profit is the optimal plan.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
10 XB XA 250 200 150 100 50 0 0 50 100 150 200 250 tubing constraint 12XA + 16XB ≤ 2880 Feasible Region Constraints: Feasible Plans labor constraint 9XA + 6XB ≤ 1566 pump constraint XA + XB ≤ 200 (0, 200) (200, 0)
11 Objective: Profit § Objective function: MAX 350XA + 300XB § Some plans yield the same profit: (6,0) or (0,7) each yield a profit of 2100 § Plans that yield the same profit P .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/17/2011 for the course MGMT 670 taught by Professor Tawarmalani during the Spring '11 term at Purdue University.

### Page1 / 45

M670_11 (Linear Programming) - Linear Programming k MGMT...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online