In this module, you will gather some additional resources to help you understand linear programming in a more detailed manner. You have learned how to formulate a linear programming model on a spreadsheet to represent a variety of managerial problems and then how to use a solver to find an optimal solution for this model. You might think that this would finish the story about linear programming: Once the manager learns the optimal solution, the manager would immediately implement this solution and then turn the attention to other matters. However, this is not the case. The enlightened manager demands much more from linear programming, and linear programming has much more to offer, which you will discover in this module. An optimal solution is only optimal with respect to a particular mathematical model that provides only a rough representation of the real problem. A manager is interested in much more than just finding such a solution. The purpose of a linear programming study is to help guide management’s final decision by providing insights into the likely consequences of pursuing various managerial options under a variety of assumptions about future conditions. Most of the important insights are gained while conducting analysis after finding an optimal solution for the original version of the basic model. This analysis is commonly referred to as what-if analysis because it involves addressing some questions about what would happen to the optimal solution if different assumptions were made about future conditions. Spreadsheets play a central role in addressing these what-if questions.

This assessment is a graded quiz based on the modules covered this week.

In this module, you will learn how non-integer solutions are not always practical when you formulate a linear programming model and solve it. When only integer solutions are practical or logical, it is sometimes assumed that non-integer solution values can be “rounded off” to the nearest feasible integer values. This method would cause little concern if, for example, x1 = 7,000.7 pages (A4) were rounded off to 7,000 pages (A4) because pages (A4) cost only a few rupees a piece. However, if you are considering the production of a big container ship and x1 = 7.4 container ship, rounding off could affect profit (or cost) by millions of rupees. In this case, you need to solve the problem so that an optimal integer solution is guaranteed.

In this module, you will be introduced to a common type of problem where, instead of how-much decisions, the decisions to be made are yes-or-no decisions. A yes-or-no decision arises when a particular option is being considered and the only possible choices are yes, go ahead with this option, or no, decline this option. You will also learn about binary variables, which is a natural choice of a decision variable for a yes-or-no decision, and whose only possible values are 0 and 1. When representing a yes-or-no decision, a binary decision variable is assigned a value of 1 for choosing yes and a value of 0 for choosing no. Finally, you will gain insights into a special type of integer programming model known as the binary integer programming (BIP) model. A general integer programming model is simply a linear programming model except for also having constraints that some or all of the decision variables must have integer values (0, 1, 2, . . .). A BIP model further restricts these integer values to be only 0 or 1.

This assessment is a graded quiz based on the modules covered this week.

Networks arise in numerous settings and in a variety of guises. Transportation, electrical, and communication networks pervade our daily lives. Network representations also are widely used for problems in such diverse areas as production, distribution, project planning, facilities location, resource management, and financial planning-to name just a few examples. In fact, a network representation provides such a powerful visual and conceptual aid for portraying the relationships between the components of systems that it is used in virtually every field of scientific, social, and economic endeavour.This module introduces you to the network optimization problems that have been particularly helpful in dealing with managerial issues. This module also focuses on the nature of these problems and their applications rather than on the technical details and the algorithms used to solve the problems. It discusses an especially important type of network optimization problem called a minimum-cost flow problem. A typical application involves minimizing the cost of shipping goods through a distribution network. Thus, this problem is similar to a transportation problem except now there are some intermediate points (e.g., warehouses) in the distribution network. Finally, you will learn about the maximum flow problems, which are concerned with such issues as how to maximize the flow of goods through a distribution network.

In this module, you will learn about two special types of linear programming model formulations- transportation and assignment problems. You will examine how they form a part of a larger class of linear programming problems known as network flow problems and represent a popular group of linear programming applications. You will also gain insights into how these problems have special mathematical characteristics that have enabled management scientists to develop very efficient, unique mathematical solution approaches to them. These solution approaches are variations of the traditional simplex solution procedure. Finally, this module will focus on model formulation and solution by using Excel and carrying out sensitivity analysis.

This assessment is a graded quiz based on the modules covered this week.

In this module, you will learn about the basics of non-linear programming and its solution in Excel. You will also learn how different business processes behave in a non-linear manner. For instance, the price of a bond is a non-linear function of interest rates, and the price of a stock option is a non-linear function of the price of the underlying stock. This module will give you an insight into how the marginal cost of production often decreases with the quantity produced, and the quantity demanded for a product is usually a non-linear function of the price. These and many other non-linear relationships are present in many business applications. A non-linear optimization problem is an optimization problem in which at least one term in the objective function or a constraint is non-linear.

In this module, you will learn about the implementation of non-linear optimization in Excel with the help of case studies. Non-linear programming problems are given a separate name because they are solved in a different manner than linear programming problems. In fact, their solution is considerably more complex than that of linear programming problems, and it is often difficult, if not impossible, to determine an optimal solution, even for a relatively small problem. In linear programming problems, solutions are found at the intersections of lines or planes; although there may be a very large number of possible solution points, the number is finite, and a solution can eventually be found. However, in non-linear programming, there may be no intersection or corner points; instead, the solution space can be an undulating line or surface, which includes virtually an infinite number of points. For a realistic problem, the solution space may be like a mountain range, with many peaks and valleys, and the maximum or minimum solution point could be at the top of any peak or at the bottom of any valley. What is difficult in non-linear programming is determining if the point at the top of a peak is just the highest point in the immediate area (called a local optimal) or the highest point of all (called the global optimal).

In this module, you will learn how to run the Naïve Bayes classification method for numeric predictors. You will also learn about advanced model performance evaluation tools like lift charts.

In this module, you will learn how to run the k nearest neighbor method (KNN) for multiple categorical variable classification. You would be introduced to the concept of dummy variables, how to create them in R, and how to run KNN method if such variables are there in the dataset.

This assessment is a graded quiz based on the modules covered this week.

In this module, you will be introduced to the advanced concept of the decision tree, that is, pruning, to overcome the problem of overfitting in the decision tree.

In this module, you will learn how to calculate the weight associated with input nodes to node j using the backpropagation process and gradient descent function.

Course Wrap-Up Video