Dynamic Matching Problem Research Articles

Designing Service Menus for Bipartite Queueing Systems

Designing Fair and Incentive-Compatible Matching Systems Many service systems face the challenge of dynamically matching customers who have heterogeneous preferences with an available pool of service providers in a fair and equitable manner. The first come, first served (FCFS) service discipline offers a straightforward and fair approach to allocate arriving customers to available servers and manage congestion. However, FCFS may limit the ability of service providers to reach an efficient allocation based on the individual preferences of customers and the characteristics of servers. In “Designing Service Menus for Bipartite Queuing Systems,” Caldentey, Hillas, and Gupta develop a queueing framework to address this dynamic matching problem. Their proposed methodology enables service providers to offer a menu of different service classes, each served by a distinct pool of servers. By thoughtfully designing this menu, a service provider can encourage self-interested customers to select service classes in a way that optimizes the trade-off between quality of matching and waiting time delays.

Online acceptance probability approximation in peer-to-peer transportation

Crowdsourced transportation by independent suppliers (or drivers) is central to urban delivery and mobility platforms. While utilizing crowdsourced resources has several advantages, it comes with the challenge that suppliers are not bound to assignments made by the platforms. In practice, suppliers often decline offered service requests, e.g., due to the required travel detour, the expected tip, or the area a request is located. This leads to inconveniences for the platform (ineffective assignments), the corresponding customer (delayed service), and also the suppliers themselves (non-fitting assignment, less revenue). Therefore, the objective of this work is to analyze the impact of a platform approximating and incorporating individual suppliers’ acceptance behavior into the order dispatching process and to quantify its impact on all stakeholders (platform, customers, suppliers). To this end, we propose a dynamic matching problem where suppliers’ acceptances or rejections of offers are uncertain. Suppliers who accept an offered request are assigned and reenter the system after service looking for another offer. Suppliers declining an offer stay idle to wait for another offer, but leave after a limited time if no acceptable offer is made. Every supplier decision reveals only their acceptance or rejection information to the platform, and in this paper, we present a corresponding mathematical model and an approximation method that translates supplier responses into updated approximations of the likelihood of a specific supplier to accept a specific future offer and use this information to optimize subsequent offering decisions. We show via a computational study based on crowdsourced food delivery that online approximation and incorporating individual supplier acceptance estimates into order dispatching leads to overall more successful assignments, more revenue for the platform and most of the suppliers, and less waiting for the customers to be served. We also show that considering individual supplier behavior can lead to unfair treatment of more agreeable suppliers.

How (Not) to Eat a Hot Potato

We consider a dynamic matching problem where players are repeatedly assignedtasks and can choose whether to accept or reject them. Players prefer to avoidcertain tasks (“hot potatoes”) while other tasks give a positive payoff (“sweet pota-toes”). There are frictions in the matching process in that players may not bematched to desirable tasks even if one is available. Both under the optimal mecha-nism and in decentralized settings, players may accept hot potatoes if this reducesfrictions in the matching process. We quantify the welfare loss due to matchingfrictions and show that, unlike losses due to more conventional frictions, it does notvanish when the cost of handling hot potatoes grows large.

Social-Aware UAV-Assisted Mobile Crowd Sensing in Stochastic and Dynamic Environments for Disaster Relief Networks

In this paper, we consider a social-aware unmanned aerial vehicle (UAV) assisted mobile crowd sensing (MCS) system for disaster relief networks, and investigate how to recruit suitable UAVs to perform sensing tasks in stochastic and dynamic environments (both UAVs and tasks arrive stochastically). We formulate the task assignment problem into a dynamic matching problem, and propose a multiple-waitlist based task assignment (MWTA) algorithm to find the stable matching in time-varying environment. We prove that MWTA can achieve the dynamic stability containing the strategy-proofness, efficiency, and envy-freeness. Simulation results demonstrate the performance improvement of our proposed scheme compared with the traditional matching algorithm applied to deterministic matching model in stochastic setting.

Multi-Hop Cooperative Caching in Social IoT Using Matching Theory

It is envisioned that the Internet of Things (IoT) will provide promising opportunities to users, manufacturers, and service providers with a wide applicability in many fields. By employing social networking and device-to-device (D2D) communications in the IoT, the resulting social IoT can potentially provide services more effectively and efficiently. This paper focuses on content sharing among smart objects (devices) in the social IoT with D2D-based cooperative coded caching. Generally, complete content items or coded fragments are allowed to be delivered via multi-hop cooperative D2D communications. First, aiming at maximizing the overall success rate of multi-hop-based content sharing, the interplay between coding parameter optimization and wireless resource allocation is investigated by considering both physical and social characteristics. Moreover, a Roth and Vande Vate-based distributed scheme is proposed to solve the dynamic matching problem between the content helpers and content requesters. Numerical results demonstrate that the proposed scheme can achieve a good tradeoff between system performance and computational complexity.

Caching Meets Millimeter Wave Communications for Enhanced Mobility Management in 5G Networks

One of the most promising approaches to overcoming the uncertainty of millimeter wave (mm-wave) communications is to deploy dual-mode small base stations (SBSs) that integrate both mm-wave and microwave ( $\mu \text{W}$ ) frequencies. In this paper, a novel approach to analyzing and managing mobility in joint mmwave– $\mu \text{W}$ networks is proposed. The proposed approach leverages device-level caching along with the capabilities of dual-mode SBSs to minimize handover failures and reduce inter-frequency measurement energy consumption. First, fundamental results on the caching capabilities are derived for the proposed dual-mode network scenario. Second, the impact of caching on the number of handovers (HOs), energy consumption, and the average handover failure (HOF) is analyzed. Then, the proposed cache-enabled mobility management problem is formulated as a dynamic matching game between mobile user equipments (MUEs) and SBSs. The goal of this game is to find a distributed HO mechanism that, under network constraints on HOFs and limited cache sizes, allows each MUE to choose between: 1) executing an HO to a target SBS; 2) being connected to the macrocell base station; or 3) perform a transparent HO by using the cached content. To solve this dynamic matching problem, a novel algorithm is proposed and its convergence to a two-sided dynamically stable HO policy for MUEs and target SBSs is proved. Numerical results corroborate the analytical derivations and show that the proposed solution will significantly reduce both the HOF and energy consumption of MUEs, resulting in an enhanced mobility management for heterogeneous wireless networks with mm-wave capabilities.

Dynamic Matching of Dual-mode Electro-mechanical Transmission (EMT) Based on the Optimal Motor Efficiency

Abstract Energy and environment has been the problem which is the most concerned by all over the world. Hybrid electric vehicle (HEV), which has the virtue of low exhaustion and low consumption, is the optimal choice to solve these problems at present. As an innovative power-split transmission (PST) technology, electro-mechanical transmission (EMT) is widely applied in military and civilian vehicles. In this paper, the dynamic matching problem of a dual-mode EMT is studied and a dynamic matching model is developed. A multi-objective optimization model is built to improve the motor energy utilization ratio through optimizing the design parameters. Sensitivity of the design parameters for dynamic matching performance are analyzed by design of experiments (DOE). Finally, the feasible region of the optimal parameters where the dynamic matching model get the optimal evaluation index is obtained.

Dynamic Matching in a Two-Sided Market

We consider an intermediary's problem of dynamically matching demand and supply of heterogeneous types in a periodic-review fashion. More specifically, there are two disjoint sets of demand and supply types. There is a reward associated with each possible matching of a demand type and a supply type. In each period, demand and supply of various types arrive in random quantities. The platform's problem is to decide on the optimal matching policy to maximize the total discounted rewards minus costs, given that unmatched demand and supply will incur waiting or holding costs, and will be carried over to the next period with abandonments. This problem applies to many emerging settings in the sharing economy and also includes many classic problems, e.g., assignment/transportation problems, as special cases. For this dynamic matching problem, we provide sufficient and robustly necessary conditions (which we call modified Monge conditions) only on matching rewards such that the optimal matching policy follows a priority hierarchy among possible matching pairs: if some pair of demand and supply types is not matched as much as possible, all pairs that have strictly lower priority down the hierarchy should not be matched. The modified Monge condition generalizes the Monge sequence condition, discovered by Gaspard Monge in 1781, that guarantees a static and balanced transportation problem to be solved by a greedy algorithm. We show the modified Monge conditions are satisfied by vertically and unidirectionally horizontally differentiated types, for which quality and distance determine priority, respectively. As a result of the priority property, the optimal matching policy boils down to a match-down-to threshold structure (instead of matching as much as possible in the greedy algorithm) when considering a specific pair of demand and supply types, along the priority hierarchy.

Matching with Dynamic Ordinal Preferences

We consider the problem of repeatedly matching a set of alternatives to a set of agents with dynamic ordinal preferences. Despite a recent focus on designing one-shot matching mechanisms in the absence of monetary transfers, little study has been done on strategic behavior of agents in sequential assignment problems. We formulate a generic dynamic matching problem via a sequential stochastic matching process. We design a mechanism based on random serial dictatorship (RSD) that, given any history of preferences and matching decisions, guarantees global stochastic strategyproofness while satisfying desirable local properties. We further investigate the notion of envyfreeness in such sequential settings.

Flexibility measure analysis of supply chain

This paper is intended to explore a new method of measuring supply chain flexibility from two dimensions (resources and time) when the supply chain is coordinated. Under the assumptions that the node enterprises’ marginal costs increase with their outputs, firstly this paper analyses the coordination problem of a supply chain with buyback contract, then formulates the resource allocation with the entropy concept in the case of supply chain coordination, puts forward the concepts of resource output elasticity and time output elasticity, analyses the resources’ dynamic matching problem from the two dimensions of resource and time in order to respond to the change of market demand. Finally, based on the above discussion, this paper proposes a method of measuring supply chain flexibility by integrating the resource flexibility and time flexibility. The method not only considers the resources and time required to respond the market’s change, but also takes into account the coordination relationship between the node enterprises.

The Day Care Assignment: A Dynamic Matching Problem

We study the problem of centralized allocation of children to public day care centers, illustrated by the case of Denmark. Our framework applies to problems of dynamic matching in which there is entry and exit of agents over time; for example, the school choice problem once student mobility is taken into account. We show that there does not exist any mechanism that is both stable and strategy-proof. We also show that the well-known Top Trading Cycles mechanism is neither Pareto efficient nor strategy-proof. Finally, a mechanism in which parents sequentially choose menus of schools is both strategy-proof and Pareto efficient. (JEL C73, D82, I21)

Dynamic matchings and quasidynamic fractional matchings. I

AbstractThis paper presents and solves in polynomial time the dynamic matching problem, an integer programming problem which involves matchings in a time‐expanded infinite network. The initial model is a finite directed graph G = (V, E) in which each edge has an associated real‐valued weight and an integral distance. We wish to “match” vertices over an infinite horizon, and we permit vertex i in period p to be matched to vertex j in period r if and only if there is an edge e = (i, j) of E with distance r‐p or else an edge e = (j, i) of E with distance p‐r. Equivalently, we construct a “dynamic graph” in which there is an edge incident to vertex i‐p and to vertex j‐r in the above cases. The weight of this matched edge in the dynamic (time‐expanded) graph is the weight of e. The dynamic matching problem is to determine a matching M in the dynamic graph such that M has a maximum long‐run average weight per period. We show that the infinite horizon dynamic matching problem is linearly transformable to the finite horizon Q‐matching problem, which is shown to be solvable in polynomial time in Part II of this paper.

Dynamic matchings and quasidynamic fractional matchings. II

AbstractConsider a directed graph G in which every edge has an associated real‐valued distance and a real‐valued weight. The weight of an undirected circuit of G is the sum of the weights of the edges, whereas the distance of an undirected circuit is the sum of the distances of the forward edges of the circuit minus the sum of the distances of the backward edges. A trivial circuit is a two‐edge circuit in which one edge of G appears twice on the circuit. A quasidynamic fractional matching (or Q‐matching) is a collection of vertex‐disjoint circuits such that each circuit is either trivial or else it is an odd circuit whose distance is nonzero. The G‐matching problem is to find a Q‐matching that maximizes the sum of the weights of its circuits. The Q‐matching problem generalizes both the matching problem and the fractional matching problem. Moreover, the dynamic matching problem, which is a matching problem on an infinite dynamic (time‐expanded) graph, is linearly transformable to the Q‐matching problem, as shown in Part I of this paper. In this paper we solve the Q‐matching problem by generalizing Edmonds' blossom algorithm. In fact, all of the major components of the blossom algorithm‐including alternating trees, augmentations, shrinking, and expanding‐are appropriately generalized to yield a running time that is proportional to that for the weighted matching problem. Furthermore, if all edge distances are equal to zero, this new algorithm reduces to the blossom algorithm.