{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T03:47:19Z","timestamp":1774324039304,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T00:00:00Z","timestamp":1668038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Azienda Ospedaliero Universitaria Policlinico Vittorio Emanuele Catania","award":["59762022008"],"award-info":[{"award-number":["59762022008"]}]},{"name":"Azienda Ospedaliero Universitaria Policlinico Vittorio Emanuele Catania","award":["PIACERI 2020\/22\u2013GOSPEL\/59722022261"],"award-info":[{"award-number":["PIACERI 2020\/22\u2013GOSPEL\/59722022261"]}]},{"name":"University of Catania","award":["59762022008"],"award-info":[{"award-number":["59762022008"]}]},{"name":"University of Catania","award":["PIACERI 2020\/22\u2013GOSPEL\/59722022261"],"award-info":[{"award-number":["PIACERI 2020\/22\u2013GOSPEL\/59722022261"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This research deals with the same-day chemotherapy outpatient scheduling problem that is recognized as a leading strategy to pursue the objective of reducing patient waiting time. Inspired by a real-world context and different from the other studies, we modeled a multi-stage chemotherapy ward in which the pharmacy is located away from the treatment area and drugs are delivered in batches. Processes in oncology wards are characterized by several sources of uncertainty that increase the complexity of the problem; thus, a stochastic approach was preferred to study the outpatient scheduling problem. To generate effective appointment schedules, we moved in two directions. First, we adopted a late-start scheduling strategy to reduce the idle times within and among the different stages, namely medical consultation, drug preparation and infusion. Then, since the problem is NP-hard in the strong sense, we developed a hybrid harmony search metaheuristic whose effectiveness was proved through an extended numerical analysis involving another optimization technique from the relevant literature. The outcomes from the numerical experiments confirmed the efficacy of the proposed scheduling model and the hybrid metaheuristic algorithm as well.<\/jats:p>","DOI":"10.3390\/a15110424","type":"journal-article","created":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T21:33:02Z","timestamp":1668115982000},"page":"424","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Hybrid Harmony Search for Stochastic Scheduling of Chemotherapy Outpatient Appointments"],"prefix":"10.3390","volume":"15","author":[{"given":"Roberto Rosario","family":"Corsini","sequence":"first","affiliation":[{"name":"DICAR Department, University of Catania, 95125 Catania, Italy"}]},{"given":"Antonio","family":"Costa","sequence":"additional","affiliation":[{"name":"DICAR Department, University of Catania, 95125 Catania, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6940-6939","authenticated-orcid":false,"given":"Sergio","family":"Fichera","sequence":"additional","affiliation":[{"name":"DICAR Department, University of Catania, 95125 Catania, Italy"}]},{"given":"Vincenzo","family":"Parrinello","sequence":"additional","affiliation":[{"name":"U.O. Qualit\u00e0 e Rischio Clinico, Azienda Ospedaliero, Universitaria \u201cPoliclinico-Vittorio Emanuele\u201d, 95125 Catania, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1080\/07408170802165880","article-title":"Appointment scheduling in health care: Challenges and opportunities","volume":"40","author":"Gupta","year":"2008","journal-title":"IIE Trans."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.ejor.2018.11.028","article-title":"Generating outpatient chemotherapy appointment templates with balanced flowtime and makespan","volume":"275","author":"Hesaraki","year":"2019","journal-title":"Eur. J. Oper. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2103","DOI":"10.1016\/j.compbiomed.2013.10.012","article-title":"Algorithms for scheduling of chemotherapy plans","volume":"43","author":"Sevinc","year":"2013","journal-title":"Comput. Biol. Med."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4280","DOI":"10.1287\/mnsc.2018.3150","article-title":"Managing appointment booking under customer choices","volume":"65","author":"Liu","year":"2019","journal-title":"Manag. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e380","DOI":"10.1200\/JOP.2014.001545","article-title":"Patients prefer chemotherapy on the same day as their medical oncology outpatient appointment","volume":"10","author":"Lau","year":"2014","journal-title":"J. Oncol. Pract."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1007\/s10729-018-9462-6","article-title":"Chemotherapy appointment scheduling and daily outpatient\u2013nurse assignment","volume":"23","author":"Benzaid","year":"2020","journal-title":"Health Care Manag. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1191\/1078155203jp105oa","article-title":"Next-day chemotherapy scheduling: A multidisciplinary approach to solving workload issues in a tertiary oncology center","volume":"9","author":"Dobish","year":"2003","journal-title":"J. Oncol. Pharm. Pract."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1188\/17.CJON.250-253","article-title":"Acuity-Based Scheduling: Outcomes in Ambulatory Oncology Centers","volume":"21","author":"Edwards","year":"2017","journal-title":"Clin. J. Oncol. Nurs."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sadki, A., Xie, X., and Chauvin, F. (2011, January 24\u201327). Appointment scheduling of oncology outpatients. Proceedings of the 2011 IEEE International Conference on Automation Science and Engineering, Trieste, Italy.","DOI":"10.1109\/CASE.2011.6042417"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1080\/19488300.2012.665155","article-title":"Chemotherapy operations planning and scheduling","volume":"2","author":"Turkcan","year":"2012","journal-title":"IIE Trans. Healthc. Syst. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Heshmat, M., Nakata, K., and Eltawil, A. (2017, January 21\u201323). Modified formulation for the appointment scheduling problem of outpatient chemotherapy departments. Proceedings of the 2017 4th International Conference on Industrial Engineering and Applications (ICIEA), Nagoya, Japan.","DOI":"10.1109\/IEA.2017.7939205"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.orhc.2014.02.002","article-title":"Scheduling patient appointments via multilevel template: A case study in chemotherapy","volume":"3","author":"Condotta","year":"2014","journal-title":"Oper. Res. Health Care"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7177","DOI":"10.1080\/00207543.2014.988891","article-title":"Improvement of chemotherapy patient flow and scheduling in an outpatient oncology clinic","volume":"53","author":"Liang","year":"2015","journal-title":"Int. J. Prod. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10729-014-9313-z","article-title":"Acuity-based nurse assignment and patient scheduling in oncology clinics","volume":"19","author":"Liang","year":"2016","journal-title":"Health Care Manag. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bouras, A., Masmoudi, M., Saadani, N.E.H., and Bahroun, Z. (2017, January 5\u20137). A three-stage appointment scheduling for an outpatient chemotherapy unit using integer programming. Proceedings of the 2017 4th International Conference on Control, Decision and Information Technologies (CoDIT), Barcelona, Spain.","DOI":"10.1109\/CoDIT.2017.8102714"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.cie.2018.07.033","article-title":"Solving the patient appointment scheduling problem in outpatient chemotherapy clinics using clustering and mathematical programming","volume":"124","author":"Heshmat","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.orhc.2018.10.003","article-title":"A mental workload based patient scheduling model for a Cancer Clinic","volume":"20","author":"Huggins","year":"2019","journal-title":"Oper. Res. Health Care"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s10729-014-9268-0","article-title":"Dynamic optimization of chemotherapy outpatient scheduling with uncertainty","volume":"17","author":"Carter","year":"2014","journal-title":"Health Care Manag. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1108\/IJHCQA-10-2017-0187","article-title":"Chemotherapy scheduling template development using an optimization approach","volume":"32","author":"Huang","year":"2019","journal-title":"Int. J. Health Care Qual. Assur."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/j.ejor.2020.03.026","article-title":"Minimizing bed occupancy variance by scheduling patients under uncertainty","volume":"286","author":"Ridder","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"106281","DOI":"10.1016\/j.cie.2020.106281","article-title":"A stochastic programming approach to the physician staffing and scheduling problem","volume":"142","author":"Marchesi","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s10729-016-9380-4","article-title":"Chemotherapy appointment scheduling under uncertainty using mean-risk stochastic integer programming","volume":"21","author":"Alvarado","year":"2018","journal-title":"Health Care Manag. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1080\/19488300.2016.1189468","article-title":"A stochastic programming approach to reduce patient wait times and overtime in an outpatient infusion center","volume":"6","author":"Castaing","year":"2016","journal-title":"IIE Trans. Healthc. Syst. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1287\/mnsc.2018.3218","article-title":"Data-driven appointment-scheduling under uncertainty: The case of an infusion unit in a cancer center","volume":"66","author":"Mandelbaum","year":"2020","journal-title":"Manag. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s10696-018-9326-x","article-title":"Daily outpatient chemotherapy appointment scheduling with random deferrals","volume":"32","author":"Garaix","year":"2020","journal-title":"Flex. Serv. Manuf. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1002\/nav.21952","article-title":"A stochastic programming approach for chemotherapy appointment scheduling","volume":"68","author":"Demir","year":"2021","journal-title":"Nav. Res. Logist. (NRL)"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Corsini, R.R., Costa, A., and Fichera, S. (2021, January 23\u201327). Comparing production control policies in two-product supply chain dynamics. Proceedings of the 2021 IEEE 17th International Conference on Automation Science and Engineering (CASE), Lyon, France.","DOI":"10.1109\/CASE49439.2021.9551581"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Corsini, R.R., Fichera, S., and Costa, A. (2022). Assessing the Effect of a Novel Production Control Policy on a Two-Product, Failure-Prone Manufacturing\/Distribution Scenario. Selected Topics in Manufacturing, Springer.","DOI":"10.1007\/978-3-030-82627-7_1"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Corsini, R.R., Costa, A., Fichera, S., Pluchino, A., and Parrinello, V. (2022, November 05). System Design of Outpatient Chemotherapy Oncology Departments through Simulation and Design of Experiments. Available online: https:\/\/www.tandfonline.com\/doi\/citedby\/10.1080\/17509653.2022.2134223?scroll=top&needAccess=true.","DOI":"10.1080\/17509653.2022.2134223"},{"key":"ref_30","first-page":"289","article-title":"Solving operational problems in outpatient chemotherapy clinics using mathematical programming and simulation","volume":"398","author":"Heshmat","year":"2019","journal-title":"Ann. Oper. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s10479-009-0624-2","article-title":"Scheduling preparation of doses for a chemotherapy service","volume":"178","author":"Mazier","year":"2010","journal-title":"Ann. Oper. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/19488300.2016.1226212","article-title":"Studying nurse workload and patient waiting time in a hematology-oncology clinic with discrete event simulation","volume":"6","author":"Baril","year":"2016","journal-title":"IIE Trans. Healthc. Syst. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s10729-006-9005-4","article-title":"Optimization of surgery sequencing and scheduling decisions under uncertainty","volume":"10","author":"Denton","year":"2007","journal-title":"Health Care Manag. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s10878-017-0211-4","article-title":"The medical laboratory scheduling for weighted flow-time","volume":"37","author":"Li","year":"2019","journal-title":"J. Comb. Optim."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Corsini, R.R., Costa, A., Fichera, S., and Pluchino, A. (2022, November 05). A Configurable Computer Simulation Model for Reducing Patient Waiting Time in Oncology Departments. Available online: https:\/\/www.tandfonline.com\/doi\/citedby\/10.1080\/20476965.2022.2030655?scroll=top&needAccess=true.","DOI":"10.1080\/20476965.2022.2030655"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1023\/A:1018976827443","article-title":"Scheduling a two-stage hybrid flow shop with parallel machines at the first stage","volume":"69","author":"Gupta","year":"1997","journal-title":"Ann. Oper. Res."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Birge, J.R., and Louveaux, F. (2011). Introduction to Stochastic Programming, Springer Science & Business Media. [2nd ed.].","DOI":"10.1007\/978-1-4614-0237-4"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1016\/j.cie.2013.01.004","article-title":"A dual encoding-based meta-heuristic algorithm for solving a constrained hybrid flow shop scheduling problem","volume":"64","author":"Costa","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1016\/j.engappai.2013.05.008","article-title":"A survey on applications of the harmony search algorithm","volume":"26","author":"Manjarres","year":"2013","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_40","first-page":"1","article-title":"A survey of harmony search algorithm","volume":"70","author":"Metwally","year":"2013","journal-title":"Int. J. Comput. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1080\/03052150500211895","article-title":"The harmony search heuristic algorithm for discrete structural optimization","volume":"37","author":"Lee","year":"2005","journal-title":"Eng. Optim."},{"key":"ref_42","first-page":"643","article-title":"Global-best harmony search","volume":"198","author":"Omran","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Komaki, M., Sheikh, S., and Teymourian, E. (2014, January 9\u201312). A Hybrid Harmony Search algorithm to minimize total weighted tardiness in the permutation flow shop. Proceedings of the 2014 IEEE Symposium on Computational Intelligence in Production and Logistics Systems (CIPLS), Orlando, FL, USA.","DOI":"10.1109\/CIPLS.2014.7007154"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.eswa.2017.08.018","article-title":"An innovative framework for designing genetic algorithm structures","volume":"90","author":"Dao","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Fichera, S., Costa, A., Corsini, R.R., and Parrinello, V. (2021). Application of lean techniques and simulation to improve efficiency of oncology department. Int. J. Serv. Oper. Manag., 1\u201325.","DOI":"10.1504\/IJSOM.2021.10037906"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1177\/003754970107600201","article-title":"A new heuristic optimization algorithm: Harmony search","volume":"76","author":"Geem","year":"2001","journal-title":"Simulation"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/11\/424\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:14:02Z","timestamp":1760145242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/11\/424"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,10]]},"references-count":46,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["a15110424"],"URL":"https:\/\/doi.org\/10.3390\/a15110424","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,10]]}}}