Download PDFOpen PDF in browserOptimal Control of Dynamic Bipartite Matching ModelsEasyChair Preprint no. 25212 pages•Date: January 31, 2020AbstractA dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a stochastic process. Matched pairs leave the system and the others wait in the queues, which induces a holding cost. We model this problem as a Markov Decision Process and study the discounted cost and the average cost problem. We fully characterize the optimal matching policy for complete matching graphs and for the Nshaped matching graph. In the former case, the optimal policy consists of matching everything and, in the latter case, it prioritizes the matchings in the extreme edges and is of threshold type for the diagonal edge. In addition, for the average cost problem, we compute the optimal threshold value. For more general graphs, we need to consider some assumptions on the cost of the nodes. For complete graphs minus one edge, we provide conditions on the cost of the nodes such that the optimal policy of the Nshaped matching graph extends to this case. For acyclic graphs, we show that, when the cost of the extreme edges is large, the optimal matching policy prioritizes the matchings in the extreme edges. We also study the Wshaped matching graph and, using simulations, we show that there are cases where it is not optimal to prioritize to matchings in the extreme edges. Keyphrases: Dynamic matching models, Markov Decision Processes, optimal control
