Dynamic pricing and inventory control for multiple products in a retail chain

The biggest problems in the retail industry are related to price allocation to keep the product attractive to the market, without allowing arbitrage, together with adequate inventory control involving substitution and complementarity. The above objectives gains relevance if the uncertain behavior of the market is taken into account. Most of the existing literature addresses each of the above problems independently or as a combination of some of them and not as a whole that is related to each other. In this research, we present a model that allows setting optimal dynamic pricing and inventory policies in each period in which a planning horizon is divided. When assigning the price, the model avoids the presence of arbitrage, by allowing the use of fixed price policies (same price for the product in the stores) and/or variable price policies (different prices for the product in the stores). When making replenishments, it allows having an adequate quantity of each product, since it incorporates substitution and complementarity between them. The market demand in each store is represented by a probability distribution that is a function of the market by means of a seasonality parameter, price sensitivity, price and inventory, subject to a set of restrictions. We find that demand has uncertainty in the seasonality parameter and in the price sensitivity, due to variations outside the historical data with which it is calculated. To handle this uncertainty, we use a Robust Stochastic Optimization formulation, which we solve in an approximate way, using a scenario generation technique. We show computational experiments applied to a case with industrial data. The results show the advantages of using this methodology, allowing managers to make the right decisions and thus improve operating results.