# A multi-unit combinatorial auction based approach for decentralized multi-project scheduling

## Abstract

In industry, many problems are considered as the decentralized resource-constrained multi-project scheduling problem (DRCMPSP). Existing approaches encounter difficulties in dealing with large DRCMPSP cases while respecting the information privacy requirements of the project agents. In this paper, we tackle DRCMPSP by formulating it as a multi-unit combinatorial auction (Wellman et al. in Games Econ Behav 35(1):271–303, 2001), which does not require sensitive private project information. To handle the hardness of bidder valuation, we introduce the capacity query which uses different item capacity profiles to efficiently elicit valuation information from bidders. Based on the capacity query, we adopt two existing strategies (Gonen and Lehmann in Proceedings of the 2nd ACM conference on electronic commerce, pp 13–20, 2000) for solving multi-unit winner determination problems to find good allocations of the DRCMPSP auctions. The first strategy employs a greedy allocation process, which can rapidly find good allocations by allocating the bidder with the best answer after each query. The second strategy is based on a branch-and-bound process to improve the results of the first strategy, by searching for a better sequence of granting the bids from the bidders. Empirical results indicate that the two strategies can find good solutions with higher quality than state-of-the-art decentralized approaches, and scale well to large-scale problems with thousands of activities from tens of projects.

### Keywords

Multi-project scheduling Multi-unit combinatorial auction Resource allocation## Notes

### Acknowledgements

This work was conducted within the Rolls-Royce@NTU Corporate Lab with support from the National Research Foundation (NRF) Singapore under the CorpLab@University Scheme.

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