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        • Demand Concepts and Analysis >
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        • Adding Optimization to a Spreadsheet Model
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    • Cluster analysis using excel and excel miner
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​Formulating an Optimization Problem

​The key to the application of optimization is to be able to formulate the problem as a mathematical model.
Step 1: Identify decision variables.
In this problem there is only one set of decision variables, the quantity to be shipped from each supplier to each customer. Since there are five suppliers and four customers, there are four times five, or 20 decision variables in this problem.
Label or name the decision variables. In this example, A1, A2, A3, A4, B1, B2, B3, and so on. A$ represents the quantity shipped from supplier A to customer 4.
 
Step 2: Formulate the constraints. Constraints are formulated as functions of the decision variables.
In this example, there are 3 sets of constraints:
  • Limit the total amount shipped from each supplier based on their capacities:
A1+A2+A3+A4 <= 60
B1+B2+B3+B4 <= 50
C1+C2+C3+C4 <= 70
D1+D2+D3+D4 <= 40
E1+E2+E3+E4 <= 20
  • Make sure that the solution satisfies the demand:
A1+B1+C1+D1+E1 >= 75
A2+B2+C2+D2+E2 >= 25
A3+B3+C3+D3+E3 >= 35
A4+B4+C4+D4+E4 >= 65
  • Non-negativity constraints
 
Step 3: Formulating objective function
This is the mathematical expression that evaluates the quality of the solution. In optimization we want to find the best solution to our problem à where best means that the solution achieves the maximum or the minimum value of the objective function. For the transportation problem, best means a solution that minimizes the total cost of supplying the product needed to satisfy all the demand.
In this example, the objective function is the sum of the product of each cost times its corresponding decision variable.
Picture
Picture
​The above function will give us the total cost of transportation for our example.
 
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  • Home
  • Applied Analytics
    • Analytics for Decision Making >
      • What is Cluster Analysis
      • Data Reduction and Unsupervised Learning
      • Preparing Data and Measuring Dissimilarities
      • Hierarchical and k-Means Clustering
      • Defining Output Variables and Analyzing the Results
      • Using Historical Data to Model Uncertainty
      • Models with Correlated Uncertain Variables
      • Creating and Interpreting Charts
      • Using Average Values versus Simulation
      • Optimization and Decision Making
      • Formulating an Optimization Problem
      • Developing a Spreadsheet Model
      • Adding Optimization to a Spreadsheet Model
      • What-if Analysis and the Sensitivity Report
      • Evaluating Scenarios and Visualizing Results to Gain Practical Insights
      • Digital Marketing Application of Optimization
      • Advanced Models for Better Decisions
      • Business Problems with Yes/No Decisions
      • Formulation and Solution of Binary Optimization Problems
      • Metaheuristic Optimization
      • Chance Constraints and Value At Risk
      • Simulation Optimization
    • Analytics for Marketing >
      • Marketing Analytics and Customer Satisfaction
      • Customer Satisfaction
      • Measurements and Scaling Techniques – Introduction
      • Primary Scales of Measurement
      • Comparative Scaling
      • Non-Comparative Scaling
      • Experiment Design: Controlling for Experimental Errors
      • A/B Testing: Introduction
      • A/B Testing: Types of Tests
      • ANOVA – Introduction
      • Example -Inspect Spray and Tooth Growth
      • Logit Model - Binary Outome and Forecastign linear regression
      • Text Summarization
      • Social media Microscope
      • N-Gram - Frequcy Count and phase mining
      • LDA Topic Modeling
      • Machine-Learned Classification and Semantic Topic Tagging
    • Data Engine >
      • Understanding The Growth Of Data
      • Evaluating Methods Of Data Access
      • Communication journey
      • Data Journey
      • Planning for data visualisation
      • Visualisation Component
      • Content Connection and Chart Legitibility
    • Customer Insights >
      • Introduction
      • What is Descriptive Analytics?
      • Survey Overview
      • Net Promoter Score and Self-Reports
      • Survey Design
      • Passive Data Collection
      • Media Planning
      • Data Visualization
      • Causal Data Collection and Summary
      • Asking Predictive Questions
      • Regression Analysis
      • Data Set Predictions
      • Probability Models
      • Results and Predictions
      • Perspective Analytics (Maximize Revenue and Market Structure Competitions)
    • Analytics for Advance Marketing >
      • Visualisation and statistics (Political Advertising,Movie Theater and Data Assembly)
      • Excel Analysis of Motion Picture Industry Data
      • Displaying Conditional Distributions
      • Analyzing Qualitative Variables
      • Steps in Constructing Histograms
      • Common Descriptive Statistics for Quantitative Data
      • Regression-Based Modeling
      • Customer Analytics
      • Illustrating Customer Analytics in Excel
      • Customer Valuation Excel Demonstration
  • Soft Skills
    • Adaptability
    • Confidence
    • Change Management
    • Unlearning and Learning
    • Collaboration and Teamwork
    • Cultural Sensitivity
  • Marketing
  • Finance
  • Economics
    • Introduction to Managerial Economics >
      • Basic Techniques
      • The firm: Stakeholders, Objectives and Decision Issues
      • Demand and Revenue Analysis >
        • Demand Estimation and Forecasting
        • Demand Elasticity
        • Demand Concepts and Analysis >
          • Formulation and Solution of Binary Optimization Problems
      • Scope of Managerial Economics
    • Prodution and Cost Analysis >
      • Production Function
      • Estimation of Production and Cost Functions
      • Cost Concepts and Analysis I
      • Cost Concepts and Analysis II
    • Pricing Decisions >
      • Pricing strategies >
        • Adding Optimization to a Spreadsheet Model
      • Market structure and microbes barriers to entry
      • Pricing under pure competition and pure monopoly
      • Pricing under monopolistic and oligopolistic competition
    • Narendra Modi Development Model of Gujarat
  • JBDON Golf
    • Digital Marketing Application of Optimization
  • Let's Talk
  • MBA Project Sharing
  • About Us
    • Good Read >
      • IIMC says PepsiCo CEO Indra Nooyi was an average student
      • India’s middle class figures in Fortune’s Top Ten list of those who matter
      • The Start-Up of you.
      • BUYING AND MERCHANDISING
      • HUMAN RESOURCE MANAGEMENT
      • Do You Suffer From Decision Fatigue?
      • New Page
      • About social media and web 2.0
      • Building Your Own Start-up Technology Company, Part 1
      • Building Your Own Start-up Technology Company, Part 2
      • Building Your Own Start-up Technology Company, Part 3
      • Building Your Own Start-up Technology Company, Part 4
      • Renewable energy is no longer alternative energy
      • What Makes an Exceptional Social Media Manager?
      • The Forgotten Book that Helped Shape the Modern Economy
      • Home
      • How to Think Creatively
      • A Lighthearted Looks at Project Management and Sports Analogies
      • Why Trust Matters More Than Ever for Brands
  • CET Knowledge Zone
    • Tips From JBIMS Students >
      • Prasad Sawant
      • Chandan Roy
      • Ram
      • Ashmant Tiwari
      • Rajesh Rikame
      • Ami Kothari
      • Ankeet Adani
      • Sonam Jain
      • Marketing Analytics and Customer Satisfaction
      • Mitesh Thakker
      • Tresa Sankoorikal
    • Speed Techniques
    • CET Workshops
  • Untitled
  • New Page
    • Cluster analysis using excel and excel miner
    • Chance Constraints and Value At Risk
    • Adding Uncertainty to a Spreadsheet Model
  • Adidas