1 / 25

Business Analytics with Nonlinear Programming

This chapter delves into the intricacies of nonlinear programming (NLP) models, explaining their formulation, usage of Solver, sensitivity analysis, and practical recommendations within the context of big data. Through examples like optimizing investment portfolios and managing flood risks, the chapter explores the challenges and solutions offered by NLP in decision-making and optimization. With a focus on finding optimal solutions amidst multiple feasible areas, the chapter equips readers with the knowledge to navigate complex business relationships effectively.

mclegg
Download Presentation

Business Analytics with Nonlinear Programming

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 4 Business Analytics with Nonlinear Programming Beni AsllaniUniversity of Tennessee at Chattanooga Business Analytics with Management Science Models and Methods

  2. Chapter Outline • Chapter Objectives • Prescriptive Analytics in Action • Introduction: • Challenges to NLP Models • Local optimum versus global optimum • The solution is not always found at an extreme point • Multiple feasible areas • Example1: World Class furniture • Example2: Optimizing an Investment Portfolio • Exploring Big Data with Nonlinear Programming • Wrap up

  3. Chapter Objectives • Explain what are nonlinear programming models and why they are more difficult to solve than LP models • Demonstrate how to formulate nonlinear programming models • Show how to use Solver to reach solution for nonlinear programming models • Explain how to read the answer report and how to perform sensitivity analysis for nonlinear programming models • Offer practical recommendations when using nonlinear models in the era of big data

  4. Prescriptive Analytics in Action • Flood risk of Netherlands • Recommendation to increase protection standards tenfold • Expensive cost • To determine economically efficient flood protection standards for all dike ring areas • Minimize the overall investment cost • Ensure protection • Maintain fresh water supplies • Use of nonlinear programming model • Able to find optimal standard levels for each of 53 disk ring area • Only three of them need to be changed • Allow the government to effectively identify strategies and establish standards with a lower cost

  5. Introduction • Linear Programming • The objective function and constraints are linear equations • Both proportional and additive • Nonlinear Programming (NLP) • To deal with not proportional or additive business relationships • Same structure: objective function and a set of constraints • More challenging to solve • Necessity of using NLP • Difficult to use • But more accurate than linear programming

  6. Challenge to NLP Models • NLP Models • Represented with curved lines or curved surface • Complicated to represent relationship with a large number of decision variables

  7. Local Optimum versus Global Optimum Area of Feasible Solution with Local and Global Maximum

  8. The Solution Is Not Always Found at an Extreme Point Possible Optimal Solution For NLP Model

  9. Multiple Feasible Areas Multiple Areas of Feasible Solutions

  10. Challenge to NLP Models • Three Challenges NLP is Facing: • Local Optimum versus Global Optimum • The Solution Is Not Always Found at and Extreme Point • Multiple Feasible Areas • Solutions developed to deal with the challenges • Advanced heuristics such as genetic algorithms • Simulated annealing • Generalized reduced gradient (GRG) method • Quadratic programming • Barrier methods • However, these algorithms often are not successful

  11. Example1: World Class Furniture • Stores five different furniture categories • Economic Order Quantity (EOQ) model • Allow to optimally calculate the amount of inventory with the goal of minimizing the total inventory cost • Does not consider: • Storage capacity (200,000 cubic feet) • purchasing budget ($1.5 million)

  12. Formulation of NLP Models • Define decision variables • Formulate the objective function • Holding cost: • Ordering cost: • Total cost:

  13. Formulation of NLP Models

  14. Solving NLP Models with Solver • Step 1: Create an Excel Template

  15. Solving NLP Models with Solver • Step2: Apply Solver

  16. Solving NLP Models with Solver • Step3: Interpret Solver Solution • Objective Cell • Variable Cells • Constraints

  17. Sensitivity Analysis for NLP Models • Reduced Cost Reduced gradient • Shadow Price Lagrange multiplier • Valid only at the point of the optimal solution

  18. Example2:Optimizing an Investment Portfolio • Trade-off between return on investment and risk is an important aspect in financial planning • Smart Investment Services (SIS) designs annuities, IRAs, 401(k) plans and other products of investment • Prepare a portfolio involving a mix of eight mutual funds

  19. Investment Portfolio Problem Formulation • Define decision variables 2. Formulate objective function

  20. Investment Portfolio Problem Formulation

  21. Solving the Portfolio Problem The what-if template for this investment problem

  22. Solving the Portfolio Problem

  23. Exploring Big data with NLP • Volume • The availability of more data allows organization to explore, formulate and solve previously unsolvable problem • Variety and Velocity • Offer significant challenges for optimization models • Advanced software programs • Used to navigate trillions of permutations, variables and constraints • Such as Solver

  24. Wrap up • The NLP formulation shares the same with LP model • GRG algorithm is best suited for NLP models • A risk that the algorithm will result in a local optimum • Provide a good starting point in the trial template • Add a non-negativity constraint for decision variables • Pay close attention when selecting Solver parameters

  25. Wrap up

More Related