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A two-phase approach to scheduling multi-category outpatient appointments – A case study of a women’s clinic

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Abstract

In this paper, we propose a two-phase approach for designing a weekly scheduling template for outpatient clinics providing multiple types of services. In many outpatient clinics, various service types are categorized to address the operational challenge of substantial changeover time between certain pairs of services. In the first phase of our approach, a mixed-integer program is formulated to assign service categories to clinic sessions during a week and determine the optimal number of appointments reserved for each service type in each clinic session. The objective in the first phase is to balance the workload of the providers among clinic sessions. In the second phase, a stochastic mixed-integer program is formulated for each clinic session to assign each contained appointment with a starting time based on several time-based performance measures. To solve the formulated stochastic program, we develop a Monte Carlo sampling based genetic algorithm. The two-phase approach is tested numerically with cases derived from a real women’s clinic. Our results demonstrate that the two-phase approach can efficiently find promising weekly appointment scheduling templates for outpatient clinics. In addition, our results suggest that the best suboptimal scheduling templates found become more sensitive to the weighting coefficients of the time-based measures as the provider workload increases.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, North Carolina Agricultural and Technical State University, 1601 East Market Street, Greensboro, NC, 27411, USA

    Xiuli Qu

  2. Department of Industrial and Manufacturing Engineering, North Dakota State University, 1410 14th Avenue N., Fargo, ND, 58102, USA

    Yidong Peng & Jing Shi

  3. Weldon School of Biomedical Engineering, Purdue University, 206 S. Martin Jischke Dr., West Lafayette, IN, 47907, USA

    Nan Kong

Authors
  1. Xiuli Qu
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  2. Yidong Peng
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  3. Nan Kong
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  4. Jing Shi
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Corresponding author

Correspondence to Nan Kong.

Appendices

Appendix A. A detailed description of the GA-MC procedure

Initialization

  • Step 0. Choose p, the population size of each generation, p c , the subpopulation size for crossover, β, the point mutation probability, n 1 and n 2, the Monte Carlo sample sizes, and g max, the iteration limit.

  • Step 1. Set the iteration index g = 0. Randomly generate p chromosomes x (0)(1), …, x (0)(p) to form the initial generation of the solutions.

  • Step 2. Generate a Monte Carlo sample of size n 1 to estimate the expectation of the weighted total cost of patient waiting time, provider idle time and provider overtime for each chromosome x (0)(i), and set w(i) to be the expectation of the weighted total cost for x (0)(i) for i = 1, …, p.

Iterative Generation of Chromosomes

  • Step 3. Selection, Crossover and Mutation Operations. Select p c chromosomes from the population of generation g using the roulette-wheel rule. Divide the selected p c chromosomes into p c /2 pairs, and execute a two-point crossover operation on each pair to generate p c new chromosomes. Mutate the newly generated chromosomes based on β.

  • Step 4. Forming the Next Generation of Chromosomes. Generate a Monte Carlo sample of size n 1 to estimate the expectation of the weighted total cost for each of the p c chromosomes newly generated in Step 3. Form the population of generation g + 1 by combining the p c new chromosomes and the (p – p c ) chromosomes in the population of generation g with the smallest w(i). Update {w(i)} with the expectation of the weighted total costs for the p c newly generated chromosomes.

  • Step 5. Let g = g + 1. If g < g max , go to Step 3; otherwise, go to Step 6.

Discovery of the Best Chromosomes in the Last Generation

  • Step 6. Final Monte Carlo Simulation. Generate a Monte Carlo sample of size n 2 to calculate the sample mean and sample standard error of the weighted total cost of patient waiting time, provider idle time and provider overtime for each chromosome x (g)(i), i = 1,…,p.

  • Step 7. Report the chromosome with the smallest sample mean and others with sample means not larger with statistical significance than the one with the smallest sample mean.

Appendix B. Parameter tuning for the GA-MC procedure

Table 8 Candidate algorithmic parameters tested for the GA-MC procedure
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Table 9 Weighted total cost of a chromosome estimated using each optional sample size n 2
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Fig. 1
figure 1

Convergence of the average objective value of the best combinations for four mutation rates

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Fig. 2
figure 2

Computational times and best objective function values found for 19 optional values of n 1

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Appendix C. Case study results for phase-I decisions

Table 10 Number of appointments reserved for each service type in Case 1 and the total service time
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Table 11 Number of appointments reserved for each service type in Case 2 and the total service time
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Table 12 Number of appointments reserved for each service type in Case 3 and the total service time
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Table 13 Number of appointments currently reserved for each service type in the studied women’s clinic and the total service time
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Appendix D: Case study results for phase-II decisions

Table 14 Best suboptimal weekly scheduling template found in Case 1
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Table 15 Best suboptimal weekly scheduling template found in Case 2
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Table 16 Best suboptimal weekly scheduling template found in Case 3
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Table 17 Scheduling template currently used in the studied women’s clinic and the simulated performance measures
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Qu, X., Peng, Y., Kong, N. et al. A two-phase approach to scheduling multi-category outpatient appointments – A case study of a women’s clinic. Health Care Manag Sci 16, 197–216 (2013). https://doi.org/10.1007/s10729-013-9223-5

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  • DOI: https://doi.org/10.1007/s10729-013-9223-5

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