Business Analytics for Decision Making

Steven Orla Kimbrough, Hoong Chuin Lau

• Publisher: Chapman and Hall/CRC
• Year: 2018
• ISBN:
  9781315360249
• Edition: 1
• Topic: Business
• Subtopic: Management
• Index: Business

Business Analytics for Decision Making, the first complete text suitable for use in introductory Business Analytics courses, establishes a national syllabus for an emerging first course at an MBA or upper undergraduate level. This timely text is mainly about model analytics, particularly analytics for constrained optimization. It uses implementations that allow students to explore models and data for the sake of discovery, understanding, and decision making.Business analytics is about using data and models to solve various kinds of decision problems. There are three aspects for those who want to make the most of their analytics: encoding, solution design, and post-solution analysis. This textbook addresses all three. Emphasizing the use of constrained optimization models for decision making, the book concentrates on post-solution analysis of models. The text focuses on computationally challenging problems that commonly arise in business environments. Unique among business analytics texts, it emphasizes using heuristics for solving difficult optimization problems important in business practice by making best use of methods from Computer Science and Operations Research. Furthermore, case studies and examples illustrate the real-world applications of these methods. The authors supply examples in Excel®, GAMS, MATLAB®, and OPL. The metaheuristics code is also made available at the book's website in a documented library of Python modules, along with data and material for homework exercises. From the beginning, the authors emphasize analytics and de-emphasize representation and encoding so students will have plenty to sink their teeth into regardless of their computer programming experience.

Part II

Optimization Modeling

Chapter 4
Simple Knapsack Problems

4.1 Introduction

4.2 Solving a Simple Knapsack in Excel

4.3 The Bang-for-Buck Heuristic

4.4 Post-Solution Analytics with the Simple Knapsack

4.4.1 Sensitivity Analysis

4.4.2 Candle Lighting Analysis

4.5 Creating Simple Knapsack Test Models

4.6 Discussion

4.7 For Exploration

4.8 For More Information

4.1 Introduction

We introduced the Simple Knapsack model and an example of it, the Eilon model, in Chapter 1. Our discussion here presumes familiarity with that material. We begin where the discussion in Chapter 1, in particular the discussion in §§1.2–1.3, left off.

4.2 Solving a Simple Knapsack in Excel

Recall that the Eilon model [45] has only 12 decision variables, which is quite small indeed. Even so, it affords a rich discussion that will apply in much larger cases. The model itself is fully specified in Table 4.1 (even ignoring the rightmost column to which we return soon) and implemented in Excel, as shown in Figure 4.1. The Excel file, Eilon-Omega_1987.xlsx, is available from the book’s Web site. The reader may easily reconstruct the implementation from Figure 4.1 with a small aliquot of information: (1) Cell C15 contains the formula =SUMPRODUCT(dvars,objectivecoeffs), which computes the objective function value for the current solution, and (2) Cell D16 contains the formula =SUMPRODUCT(dvars, constraint coeffs), which computes the LHS value for the current solution. With this setup, the Excel’s Solver tool can be used as indicated to solve the model to optimality. The pattern generalizes to larger models, subject to the limitation of Excel’s solver.

Variable No.	ci	wi	ci/wi
1	4.13	131	31.40
2	2890	119	24.29
3	577	37	15.59
4	1780	117	15.21
5	2096	140	14.97
6	2184	148	14.76
7	1170	93	12.58
8	780	64	12.19
9	739	78	9.47
10	147	16	9.19
11	136	22	6.18
12	211	58	3.64

TABLE 4.1: Specification of the Eilon Simple Knapsack model. b = 620.

FIGURE 4.1: Solving the Eilon Simple Knapsack model in Excel.

4.3 The Bang-for-Buck Heuristic

We saw, in the previous section, how the Eilon Simple Knapsack model is easily solved exactly to guaranteed optimality in Excel. Now we will explore how the model can be solved heuristically, that is, how we can reliably find a good although usually not optimal solution to the model. Why bother with a heuristic solution (method) since an exact solution (method) is available? There are at least two good reasons.

1. Exact solution methods are not always available or available at acceptable cost (either in time or computing resources). The Simple Knapsack model is among the most easily solved models with exact methods and even it will overwhelm these methods when it gets large enough. When this happens we have no choice but to rely on heuristic methods for solving the problem.

2. We will be using and exploring heuristics throughout this book. They are valuable and pervasive throughout business analytics. It is helpful to introduce and explore heuristics in contexts for which exact methods are available. And so we shall.

Microsoft Excel Solver, as we encountered it in the previous section, is limited to 200 decision variables htt­p:/­/suppo­rt.m­ic­rosoft­.com/k­b/75714 (accessed 2015-07-20); see also htt­p:­//w­ww.s­olve­r.c­om/s­tandard­-excel­-solver­-deal­ing-p­roble­m-size-­limits (accessed 2015-07-20)). This is small by current day problem standards. Other commercial solvers (including MATLAB’s, which we saw at work in Chapter 1) will work with much larger problems, but it will be handy to have a “good enough” (heuristic) solver of our own.

The bang-for-buck heuristic for Simple Knapsack problems is a reliable and excellent heuristic in practice and in theory [121]. It is intuitive, ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• List of Figures
• List of Tables
• I Starters
• II Optimization Modeling
• III Metaheuristic Solution Methods
• IV Post-Solution Analysis of Optimization Models
• V Conclusion
• A Resources
• Bibliography
• Index