{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T22:25:26Z","timestamp":1784067926201,"version":"3.55.0"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T00:00:00Z","timestamp":1712275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Cooperative alternatives need complex multi-criteria decision-making (MCDM) consideration, especially in resource allocation, where the alternatives exhibit interdependent relationships. Traditional MCDM methods like the Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) often overlook the synergistic potential of cooperative alternatives. This study introduces a novel method integrating AHP\/ANP with Shapley values, specifically designed to address this gap by evaluating alternatives on individual merits and their contributions within coalitions. Our methodology begins with defining problem structures and applying AHP\/ANP to determine the criteria weights and alternatives\u2019 scores. Subsequently, we compute Shapley values based on coalition values, synthesizing these findings to inform resource allocation decisions more equitably. A numerical example of budget allocation illustrates the method\u2019s efficacy, revealing significant insights into resource distribution when cooperative dynamics are considered. Our results demonstrate the proposed method\u2019s superiority in capturing the nuanced interplay between criteria and alternatives, leading to more informed urban planning decisions. This approach marks a significant advancement in MCDM, offering a comprehensive framework that incorporates both the analytical rigor of AHP\/ANP and the equitable considerations of cooperative game theory through Shapley values.<\/jats:p>","DOI":"10.3390\/a17040152","type":"journal-article","created":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T08:27:52Z","timestamp":1712305672000},"page":"152","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Resource Allocation of Cooperative Alternatives Using the Analytic Hierarchy Process and Analytic Network Process with Shapley Values"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7965-7165","authenticated-orcid":false,"given":"Jih-Jeng","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Computer Science & Information Management, SooChow University, No. 56 Kueiyang Street, Section 1, Taipei 100, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chin-Yi","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Business Administration, Chung Yuan Christian University, No. 200, Zhongbei Rd., Zhongli District, Taoyuan City 320, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"104930","DOI":"10.1016\/j.landusepol.2020.104930","article-title":"Optimal land-use allocation using MCDM and SWAT for the Hablehroud Watershed, Iran","volume":"100","author":"Arjomandi","year":"2021","journal-title":"Land Use Policy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2454","DOI":"10.1109\/TEM.2020.3015775","article-title":"A Cost Minimization Resource Allocation Model for Disaster Relief Operations With an Information Crowdsourcing-Based MCDM Approach","volume":"69","author":"Sarma","year":"2022","journal-title":"IEEE Trans. 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