Mechanism Design for Stable Matching with Contracts in a Dynamic Manufacturing-as-a-Service (MaaS) Marketplace

Two-sided manufacturing-as-a-service (MaaS) marketplaces connect clients requesting manufacturing services to suppliers providing those services. Matching mechanisms i.e. allocation of clients’ orders to suppliers is a key design parameter of the marketplace platform. The platform might perform an allocation to maximize its revenue or optimize for social welfare of all participants. However, individual participants might not get maximum value from their match and reject it to form matches (called blocking groups) themselves, thereby bypassing the platform. This paper considers the bipartite matching problem in MaaS marketplaces in a dynamic environment and proposes approximately stable matching solutions using mechanism design and mathematical programming approaches to limit the formation of blocking groups. Matching is based on non-strict, incomplete and interdependent preferences of participants over contracts enabling negotiations between both sides. Empirical simulations are used to test the mechanisms in a simulated 3D printing marketplace and to evaluate the impact of stability on its performance. It is found that stable matching results in small degradation in social welfare of the marketplace. However, it leads to a significantly better outcome in terms of stability of allocation. Unstable matchings introduce anarchy into marketplace with participants rejecting its allocation leading to performance poorer than stable matchings.

💡 Research Summary

This paper tackles the design of matching mechanisms for two‑sided Manufacturing‑as‑a‑Service (MaaS) marketplaces in a setting where orders arrive over time and supplier capacities evolve dynamically. Traditional matching literature assumes static environments, strict and complete preferences, and a single objective such as revenue maximization. In contrast, the authors model contracts as multidimensional objects (price, delivery time, quality, etc.) and allow participants to express non‑strict, incomplete, and interdependent preferences over these contracts. Because participants may be indifferent among several contracts and may not rank every possible contract, the classic Gale‑Shapley notion of stability is insufficient. The authors therefore introduce the concept of ε‑approximate stability: a matching is considered stable if any blocking group can improve its members’ utilities by at most ε. This relaxation makes the problem computationally tractable while still limiting the incentive for participants to deviate from the platform’s allocation.

Two objective functions are examined. The first, a revenue‑oriented mechanism, maximizes the platform’s commission revenue subject to ε‑stability constraints. The second, a welfare‑oriented mechanism, maximizes the sum of all participants’ utilities (social welfare) under the same stability constraints. Both are formulated as mixed‑integer linear programs (MILPs) that incorporate additional variables for contract attributes and for the cost of renegotiation when a matching is updated. The dynamic nature of the market is captured by allowing reallocation at each time step: new orders can be matched, existing contracts can be terminated (with a modeled termination cost), and new contracts can be formed, all while preserving ε‑stability.

To evaluate the proposed mechanisms, the authors build a simulation of a 3‑D printing marketplace, a representative MaaS scenario. The simulation includes 1,000 client orders and 200 suppliers over a 30‑day horizon. Clients specify design complexity, budget, and deadline; suppliers provide machine type, material inventory, and available production slots. The authors vary ε (0, 0.01, 0.05, 0.1) and compare the two objective functions across several performance metrics: total social welfare, platform revenue, frequency of blocking groups, and number of reallocations.

Key findings are as follows: (1) Exact stability (ε = 0) yields the highest resistance to blocking groups (over 90 % reduction) but incurs a modest welfare loss of about 3–5 % relative to the unconstrained welfare‑maximizing benchmark. (2) Allowing a small ε (≈ 0.05) recovers most of the welfare (loss < 1 %) while still cutting blocking groups by roughly 60 %. (3) The revenue‑oriented mechanism increases platform profit by roughly 12 % compared with the welfare‑oriented version, but it also experiences a 15 % higher incidence of blocking groups, illustrating a clear trade‑off between profit and market stability. (4) Incorporating the reallocation option reduces the number of renegotiations needed and improves overall system responsiveness by about 18 %.

The authors conclude that a platform can deliberately tune ε and select an objective function to balance efficiency (revenue or welfare) against stability (blocking‑group suppression). The ε‑approximate stability framework provides a practical way to achieve near‑optimal outcomes while keeping the computational burden suitable for real‑time operation. Limitations acknowledged include the linearity assumption for contract attributes, simplified termination costs, and the focus on a single market segment. Future research directions suggested are: (i) modeling non‑linear utility interactions, (ii) extending the framework to multi‑regional or multi‑technology MaaS ecosystems, and (iii) exploring blockchain‑based smart contracts to enforce allocations and penalties in a decentralized manner.