So far in this specialization, we have focused on descriptive and predictive analytics. For managerial decisions that have limited numbers of alternatives, the tools that we have discussed up to this point might be sufficient. However, for decision problems that have a very large, or perhaps infinite number of possible courses of action, we need something different. This is why in this module we introduce optimization, the key tool in prescriptive analytics. Optimization has been defined as the process of selecting the values of decision variables that minimize or maximize some quantity of interest. Optimization is started in the area of operations management, but it is now used in all areas of business. Optimization models are prescriptive because their outcome is a recommendation of what to do. For example, in logistics, an optimization model can recommend where to build a facility, or how to manage inventory or how to route delivery tracks. In finance, optimization can be used to find diversified investment portfolios that maximize returns, and limit risks. Optimization is a very rich area, and the subject of many research articles and books in this module we will narrow our scope to linear models, which will help you tackle many business problems. Optimization models consist of three major elements, decision variables, an objective function, and constraints. Decision variables are the unknowns for which the optimization process will find the best values. Depending on the context, decision variables could represent quantities to produce, quantities to ship from one warehouse to a customer, or the amount of money to spend in various types of digital ads. The objective of an optimization model is to either minimize or maximize a function. Typically, models are set up to maximize a function of revenue or to minimize a function of cost. Constraints are restrictions or limitations that are either related to technical and practical considerations or they're imposed by managerial policies. For instance, the capacity of a truck represents a physical constraint while requiring that 10% of an advertising budget to be spent in YouTube ads is a managerial policy. The difficulty with solving optimization problems is determined by the interaction of the three major elements. For most models, the difficulty increases with the number of decision variables and constraints. The process of building an optimization model consists of translating a problem description into mathematical functions that are based on the decision variables. The transportation problem is a classic in the optimization literature and we're going to use it to illustrate these ideas. In the transportation problem, there is a set of suppliers and a set of customers. For the sake of simplicity, we are going to assume that there is only one type of product that needs to be sent from suppliers to customers. Suppliers have limited quantities of the product to meet the customer demands. There's a cost associated with sending one unit of product from each supplier to each customer. In this example, we have five suppliers and four customers and therefore, there are 20 transportation processes. The input data for this problem consists of three sets of values, the supply, the demand and the transportation process. A solution to the problem is a set of shipments that meets all the demand and does not exceed the supply. For example, in the solution supplier A sends 50 units of product to customer 4. Supplier B sends 20 units to customer 2 and 20 units to customer 3. The solution is feasible because it satisfies all the demands while staying within the capacity limits of its supplier. Now we need to know how good this feasible solution is. Measuring the quality of a solution is the role of the objective function. In the transportation problem, the Objective Function is the Total Cost. To calculate the total cost all we need to do is to multiply the amount being shipped by the shipment cost and add up all these values. The total cost for this solution is 1,085. How does this solution compare to others? Is this a solution with minimal cost? Well, we don't know, but optimization provides the answers to these questions. An important feature of optimization models is that, often, the same model can be reinterpreted to be used in more than one setting or industry. For instance, rental car companies sometimes find themselves in situations where their inventory of cars is unbalanced. There may be an excess of certain types of cars in some locations and a deficit in others. In terms of the transportation mall, the locations with excess cars can be interpreted as supply locations. And the locations with deficits can be interpreted as demand locations. A transportation model can help a rental car company decide how to move cars from one location to another. The cost could reflect not only distance from one location to another, but also the transportation mode that is used to transfer the vehicles, because they could be driven or moved on a truck to preserve the mileage of the car. Optimization is a very exciting field within data analytics for business. There are applications of optimization everywhere. I am sure that you will start identifying optimization problems in your everyday life, once you learn the basics of optimization in this course.