**HOW TO OPTIMIZE PRICE?**

Price optimization utilizes data and mathematical analysis to determine the best price that will meet decision makers’ objectives such as maximizing profit. Pricing has significant importance for the companies since it defines the value of a product and affects customer’s willingness to pay. Price of a product determines the profit margin, therefore optimizing price can have a substantial contribution on companies’ profitability.

The project is conducted for a company having retail stores in several cities in Turkey. Customer groups are including business-to-consumer category. There are more than 4000 different product types.

**Methodology**

**Demand Forecasting**

The proposed methodology consists of two main steps, which are demand forecasting for next period and estimating price elasticity of demand for the products. Therefore, at first, we try to estimate what amount of a product will sell in next period. This part of the methodology is a classical forecasting problem. In this blog we will not go further in terms of explaining forecasting deeply. There are plenty of algorithms, methodologies to predict sales, we applied auto-forecasting process for more than 4000 products.

In order to yield accurate results, it is important to identify factors that have significant effect on sales. Features, also called exogenous variables, can vary on concept of the problems. We didn’t include *price* as exogenous variable in the forecasting model, which has major impact on sales. We exclude price from the model on purpose. If we add the price as a feature in the model, we must use it to predict next month’s sales. However, it is yet unknown what price should be used for the product. We need to know that how much the product will sell in next month without the effect of price because later we will add the price effect on the forecasting results and come up with an optimum price.

**Price elasticity of demand**

In the previous part we forecasted number of sales for the next period. Now we try to figure out how changes in price will affect the demand and subsequently predict how demand varies at different price points.

Before going further let us define price elasticity and how it contributes the proposed optimization model. Price elasticity of demand is a measurement of the change in sales of a product in relation to a change in its price. It shows how sensitive demand is to the price changes. In this regard some products show dramatic changes in sales over time due to price changes. These products are called **elastic** products. If price changes don’t have high impact on sales, it is called **inelastic** product.

In order to estimate price elasticity of products, we applied regression model with logarithmic transformation, which is log-log regression model. This model is efficacious while the price-demand relationship is nonlinear.

After performing a log-log model, the coefficient can be used to determine the impact of independent variables (X-price) on dependent variable (Y-demand), where and are the time components seasonality and trend respectively. The coefficients in a log-log model represent the elasticity of Y variable with respect to X variable. As we defined earlier, the coefficient is the estimated percent change in the dependent variable for a percent change in the independent variable.

Accuracy of is crucial point to estimate optimum price. We expect since the fact that increasing price leads to decrease in demand. Otherwise, optimum price of a product may enormously large.

After receiving price elasticity of each product, we can build price vs profit function graph. In the below formula when we substitute in, we receive a quadratic equation. It yields a concave graph where the corresponding x axis value to maximum y value gives the optimum price. As an example in table 3, optimum price for a product is 32.13 TL.

where is price, is last price of the product, is the predicted demand, is updated demand when we changed price from to, is price elasticity in terms of percent change, is the profit and is the cost of the product.

**Business Rules**

Business rules structures the methodology, the proposed results may be reformed by the business owners or market rules. For example, they may prefer specific rate of increasing and decreasing in prices. In this case they would prefer to choose among the prices near to optimum rather than applying exact optimum point.

**Test and Results**

Test process is necessary to verify result and observe the customer behaviors to price changes. Twenty stores were chosen as test and control groups, each has 10 number of stores. In test group price of the products have changed to estimated optimum price, and in control groups the prices remained the same. For two weeks test period, we reached 9% more profitability than control groups.

Zeynep Kezban TURGUT -Data Scientist