A surrogate-based robust optimization approach for the management of perishable products

An important challenge present in the retail setting is the handling of perishable goods, that is, those products for which there is a limited time to consume them. One example of all is food. It is clear that implementing improved management strategies is crucial since it can greatly decrease food waste by selling food prior to its sell-by date. Perishable retailers face the challenge of maximizing profitability and in addition trying to reduce food waste as well. This thesis focuses on the construction of a method for optimizing replenishment policies and the application of discounts for perishable products in a robust setting with respect to the parameters modeling the customers’ preferences. It has already been demonstrated in the literature that the application of discounts has the potential to contribute to reducing waste and increasing profitability. The setting is established within a robust framework that includes a multi-item environment with substitutable products with the objective to maximize the expected daily profit. A major challenge in the management of perishable goods is the uncertainty of demand, which makes planning and scheduling difficult. In our analysis, we consider a vertical differentiation setting for the substitutable products, where price is the determining factor when the products are of the same quality. A linear discrete demand model is used to estimate the utility of each product for each customer. A stochastic parameter that depends on the customer's valuation is employed, while the price and quality of the product are used to model the utility in a linear form. The parameter is assumed to be modeled by a Beta distribution. We consider products with given deterministic prices, qualities and costs, where each product faces a quality degradation as its residual life decreases. A thorough first phase of simulations has been instrumental in providing insight into the environment and the impact of changing parameters and products on profit. Following this phase, the optimization phase is initiated. The approach taken to optimize the policies involves the implementation of a metamodel. In particular, we adopt Kriging, a low-cost interpolation method that uses a stochastic process approach to construct a surrogate model of an expensive function. In our case, we refer to the proposed algorithm as the Efficient Global Robust Optimization algorithm. After an initialization phase, the next step is an iterative process in which the new sampling locations are selected using an adaptive sampling method. Given the nature of this problem as a worst-case robust configuration, we define a control variable space and an uncertain variable space. In this analysis, we refer to the order parameters and the discounting variables as the control variables. The parameters representing the Beta distribution of the uncertain parameter that models the utility, as well as the coefficient of variation on the distribution of consumers entering the store in some experiments, are considered to be uncertain variables. Two versions of the Expected Improvement Criterion are selected for sampling in the designated spaces. The significance of this work lies in the scarcity of literature dealing with the handling of perishable products in a worst-case, robust environment. This makes it a valuable contribution to the field. The results demonstrate the effectiveness of a metamodeling approach to the topic, as well as its adaptability in different settings.