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Multi-objective outpatient scheduling in health centers considering resource constraints and service quality: a robust optimization approach

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Abstract

Hospitals are among the largest and most sophisticated service organizations and the most critical service delivery units in the health system. Due to the high risk of hospital services, the services provided must be of acceptable quality. Also, patient scheduling and timely receiving of services in medical centers can lead to patient satisfaction. In this study, a patient admission scheduling is modeled in which it is assumed that the staff is not always available. To enhance the quality of healthcare services and increases patient satisfaction, in this research, mathematical modeling is presented, in which resource capacity and treatment sequence constraints are considered in the proposed model. Furthermore, the uncertainty in the service quality parameter is taken into account, which makes the model more realistic. In this regard, first, a robust optimization approach based on the Bertsimas and Sim model is applied. Then, due to its Np-hardness, the multi-objective particle swarm optimization algorithm is proposed. Finally, the quality of the proposed algorithm is examined by comparing its results with the GAMS solver and the NSGA-II algorithm in small and large-size instances, respectively. Results indicate the proper performance of the proposed algorithm.

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Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  • Abolos E, Carroli G, Egenia MM (2005) The tools and techniques of evidence-based medicine. Best Pract Res Clin Obstet Gynaecol 19:15–26

    Article  Google Scholar 

  • Amoozegar M, Eftekhari M (2011) Automatic model-based software performance optimization based on MOPSO. Comput Intell Electr Eng 2(2):1–11

    Google Scholar 

  • Anvaryazdi SF, Venkatachalam S, Chinnam RB (2020) Appointment scheduling at outpatient clinics using two-stage stochastic programming approach. IEEE Access 8:175297–175305

    Article  Google Scholar 

  • Barz C, Rajaram K (2015) Elective patient admission and scheduling under multiple resource constraints. Prod Oper Manag. https://doi.org/10.1111/poms.12395

    Article  Google Scholar 

  • Bazrafshan N, Lotfi M (2016) A multi-objective multi-drug model for cancer chemotherapy treatment planning: a cost-effective approach to designing clinical trials. Comput Chem Eng 87:226–233

    Article  Google Scholar 

  • Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805

    Article  MathSciNet  MATH  Google Scholar 

  • Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program 98(1–3):49–71

    Article  MathSciNet  MATH  Google Scholar 

  • Bolaji AL, Bamigbola AF et al (2022) A room-oriented artificial bee colony algorithm for optimizing the patient admission scheduling problem. Comput Biol Med 148:105850

    Article  Google Scholar 

  • Burdett RL, Kozan E, Sinnott M, Cook D, Tian Y-C (2017) A mixed integer linear programing approach to perform hospital capacity assessments. Expert Syst Appl 77:170–188

    Article  Google Scholar 

  • Cayirli T, Veral E (2003) Outpatient scheduling in healthcare: a review of literature. Prod Oper Manag 12(4):519–549

    Article  Google Scholar 

  • Clavel D, Mahulea C, Albareda J, Silva M (2018) Robust scheduling of elective patients under block booking by chance constrained approaches. Technical Report RR-18–01, Universidad de Zaragoza

  • Coello CC, Lechuga MS (2002) MOPSO: a proposal for multiple objective particle swarm optimization. Paper presented at the proceedings of the 2002 congress on evolutionary computation. CEC'02 (Cat. No. 02TH8600)

  • de la Maza M (1995) The Boltzmann selection procedure, lance chambers, editor, Practical handbook of genetic algorithms. New Frontiers, Volume II, CRC Press, 111–138

  • Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Paper presented at the International conference on parallel problem solving from nature

  • Dehghanimohammadabadi M, Rezaeiahari M, Keyser TK (2017) Simheuristic of patient scheduling using a table-experiment approach—Simio and Matlab integration application, 2017 Winter Simulation Conference (WSC), Las Vegas, NV, USA, 2929–2939

  • Fan X, Tang J, Yan C et al (2021) Outpatient appointment scheduling problem considering patient selection behavior: data modeling and simulation optimization. J Comb Optim 42:677–699

    Article  MathSciNet  Google Scholar 

  • Ferreira DC, Nunes AM, Marques RC (2020) Optimizing payments based on efficiency, quality, complexity, and heterogeneity: the case of hospital funding. Int Trans Oper Res 27:1930–1961

    Article  Google Scholar 

  • Hahn-Goldberg S, Carter MW, Beck JC (2014) Dynamic optimization of chemotherapy outpatient scheduling with uncertainty. Healthc Manag Sci 17:379–392

    Google Scholar 

  • Hakeem UR, Wan G, Zhan Y (2021) Multi-level, multi-stage lot-sizing and scheduling in the flexible flow shop with demand information updating. Int Trans Oper Res. https://doi.org/10.1111/itor.12645

    Article  MathSciNet  Google Scholar 

  • Hicks CR, Turner KV (1999) Fundamental concepts in the design of experiments, 5th edn. Oxford University Press, New York

    Google Scholar 

  • Issabakhsh M, Lee S, Kang H (2020) Scheduling patient appointment in an infusion center: a mixed integer robust optimization approach. Healthc Manag Sci. https://doi.org/10.1007/s10729-020-09519-z

    Article  Google Scholar 

  • Jain N, Nangia U, Jain J (2018) A review of particle swarm optimization. J Inst Eng (India) Series B 99(4):407–411

    Article  Google Scholar 

  • Jain V, Mohan U, Zacharia Z, Sanders NR (2022) Improving patient satisfaction and outpatient diagnostic center efficiency using novel online real-time scheduling. Oper Res Health Care 32:100338

    Article  Google Scholar 

  • Jiang B, Tang J, Yan C (2019) A comparison of fixed and variable capacity-addition policies for outpatient capacity allocation. J Comb Optim 37:150–182

    Article  MathSciNet  MATH  Google Scholar 

  • Kortbeek N, van der Velde M, Litvak N (2017) Organizing multidisciplinary care for children with neuromuscular diseases at the academic medical center, Amsterdam. Health Syst 6(3):209–225

    Article  Google Scholar 

  • Leeftink A, Vliegen I, Hans EW (2019) Stochastic integer programming for multi-disciplinary outpatient clinic planning. Healthc Manag Sci 22(1):53–67

    Google Scholar 

  • Li NLX, Zhang C, Kong N (2021) Integrated optimization of appointment allocation and access prioritization in patient-centred outpatient scheduling. Comput Ind Eng 154:107125

    Article  Google Scholar 

  • Lin CKY, Ling TWC, Yeung WK (2017) Resource allocation and outpatient appointment scheduling using simulation optimization. J Healthc Eng 2017:9034737

    Article  Google Scholar 

  • Liu L, Tang G, Fan B et al (2015) Two-person cooperative games on scheduling problems in outpatient pharmacy dispensing process. J Comb Optim 30:938–948

    Article  MathSciNet  MATH  Google Scholar 

  • Liu Q, Li X, Liu H, Guo Z (2020) Multi-objective metaheuristics for discrete optimization problems: a review of the state-of-the-art. Appl Soft Comput 93:106382

    Article  Google Scholar 

  • Lu T, Shih J, Kittipittayakorn C, Lian G (2013) Improving outpatient service quality in department of orthopedic surgery by using collaborative approaches, In: proceedings of the 2013 IEEE 17th international conference on computer supported cooperative work in design (CSCWD), Whistler, BC, 2013, pp 515–520

  • Maiyar LM, Thakkar JJ (2019) Environmentally conscious logistics planning for food grain industry considering wastages employing multi objective hybrid particle swarm optimization. Transp Res Part E Logist Transp Rev 127:220–248

    Article  Google Scholar 

  • McKight PE, Najab J (2010) Kruskal‐wallis test. The corsini encyclopedia of psychology, 1–1

  • Munavalli JR, Rao SV, Srinivasan A, van Merode G (2019) Integral patient scheduling in outpatient clinics under demand uncertainty to minimize patient waiting times. Health Inform J, 1460458219832044

  • Nasiri MM, Abdollahi M, Rahbari A, Salmanzadeh N, Meydani SS (2018) Minimizing the energy consumption and the total weighted tardiness for the flexible flowshop using NSGA-II and NRGA. J Ind Syst Eng 11:150–162

    Google Scholar 

  • Nikoofal Sahl Abadi N, Bagheri M, Assadi M (2018) Multiobjective model for solving resource-leveling problem with discounted cash flows. Int Trans Oper Res 25:2009–2030

    Article  MathSciNet  MATH  Google Scholar 

  • Parasuraman A, Zeithaml V, Berry LL (1988) A multiple item scale for measuring consumer perceptions of service quality. J Retail 64:12–40

    Google Scholar 

  • Rabbani M, Zhalechian M, Farshbaf-Geranmayeh A (2018) A robust possibilistic programming approach to multiperiod hospital evacuation planning problem under uncertainty. Int Trans Oper Res 25:157–189

    Article  MathSciNet  MATH  Google Scholar 

  • Rais A, Viana A (2011) Operations research in healthcare: a survey. Int Trans Oper Res 18:1–31

    Article  MathSciNet  Google Scholar 

  • Shehadeh KS, Cohn AEM, Jiang R (2020) A distributionally robust optimization approach for outpatient colonoscopy scheduling. Eur J Oper Res 283(2):549–561

    Article  MathSciNet  MATH  Google Scholar 

  • Shokoufi K, Zarei M (2017) Pareto-based multi-criteria evolutionary algorithm for parallel machines scheduling problem with sequence-dependent setup times. Int J Eng 30(12):1863–1869

    Google Scholar 

  • Sörensen K (2015) Metaheuristics—the metaphor exposed. Int Trans Oper Res 22:3–18

    Article  MathSciNet  MATH  Google Scholar 

  • Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21(5):1154–1157

    Article  MathSciNet  MATH  Google Scholar 

  • Su H, Wan G, Wang S (2019) Online scheduling for outpatient services with heterogeneous patients and physicians. J Comb Optim 37:123–149

    Article  MathSciNet  MATH  Google Scholar 

  • Taguchi G (1978) Off-line and on-line quality control systems. Proceedings of the international conference on quality control, Tokyo, October 1978

  • Tirkolaee EB, Goli A, Hematian M, Sangaiah AK, Han T (2019) Multi-objective multi-mode resource constrained project scheduling problem using Pareto-based algorithms. Computing 101(6):547–570

    Article  MathSciNet  MATH  Google Scholar 

  • Wang Y, Zhang Y, Tang J (2019) A distributionally robust optimization approach for surgery block allocation. Eur J Oper Res 273(2):740–753

    Article  MathSciNet  Google Scholar 

  • Wu X, Shen X, Zhang L (2018) Solving the planning and scheduling problem simultaneously in a hospital with a bi-layer discrete particle swarm optimization. Math Biosci Eng 16(2):831–861

    Article  MathSciNet  MATH  Google Scholar 

  • Yang Y, Luo S, Fan J et al (2019) Study on specialist outpatient matching appointment and the balance matching model. J Comb Optim 37:20–39

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran

    J. Behnamian & Z. Gharabaghli

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  1. J. Behnamian
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  2. Z. Gharabaghli
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Behnamian, J., Gharabaghli, Z. Multi-objective outpatient scheduling in health centers considering resource constraints and service quality: a robust optimization approach. J Comb Optim 45, 80 (2023). https://doi.org/10.1007/s10878-023-01000-1

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