Joint Strategy of Dynamic Ordering and Pricing for Competing Perishables with Q-Learning Algorithm

We use Machine Learning (ML) to study firms’ joint pricing and ordering decisions for perishables in a dynamic loop. The research assumption is as follows: at the beginning of each period, the retailer prices both the new and old products and determines how many new products to order, while at the end of each period, the retailer decides how much remaining inventory should be carried over to the next period. The objective is to determine a joint pricing, ordering, and disposal strategy to maximize the total expected discounted profit. We establish a decision model based on Markov processes and use the Q-learning algorithm to obtain a near-optimal policy. From numerical analysis, we find that (i) the optimal number of old products carried over to the next period depends on the upper quantitative bound for old inventory; (ii) the optimal prices for new products are positively related to potential demand but negatively related to the decay rate, while the optimal prices for old products have a positive relationship with both; and (iii) ordering decisions are unrelated to the quantity of old products. When the decay rate is low or the variable ordering cost is high, the optimal orders exhibit a trapezoidal decline as the quantity of new products increases.

Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures

In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature.