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A stochastic risk-averse framework for blood donation appointment scheduling under uncertain donor arrivals

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Abstract

Blood is a key resource in all health care systems, usually drawn from voluntary donors. We focus on the operations management in blood collection centers, which is a key step to guarantee an adequate blood supply and a good quality of service to donors, by addressing the so-called Blood Donation Appointment Scheduling problem. Its goal is to employ appointment scheduling to balance the production of blood units between days, in order to provide a reasonably constant supply to transfusion centers and hospitals, and reduce non-alignments between physicians’ working times and donor arrivals at the collection center. We consider a two-phase solution framework taken from the literature, in which a deterministic linear programming model preallocates time slots to different blood types and a prioritization policy assigns the preallocated slots to the donors when they make a reservation. However, the problem is stochastic in nature and requires consideration of the uncertain arrivals of non-booked donors. In this work, to include the uncertain arrivals, we propose three stochastic counterparts of the preallocation model based on a risk-neutral objective and two risk-averse objectives, respectively, where the Conditional Value-at-Risk is considered as the risk measure in the last two methods. The resulting stochastic frameworks have been tested considering the historical data of one of the largest Italian collection centers, the Milan Department of the “Associazione Volontari Italiani Sangue” (AVIS). Results show the effectiveness of the stochastic models, especially the mean-risk one, and the need to include the uncertainty of arrivals in order to better balance the production of blood units.

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Author information

Authors and Affiliations

  1. Yeditepe University, Istanbul, Turkey

    Semih Yalçındağ & Seda Baş Güre

  2. Yeditepe University, Işık University, Istanbul, Turkey

    Seda Baş Güre

  3. DEIB, Politecnico di Milano, Milan, Italy

    Giuliana Carello

  4. CNR–IMATI, Milan, Italy

    Ettore Lanzarone

Authors
  1. Semih Yalçındağ
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  2. Seda Baş Güre
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  3. Giuliana Carello
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  4. Ettore Lanzarone
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Correspondence to Semih Yalçındağ.

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Appendix

Appendix

  • Table 4 shows the results for the RA model with only CV aR and of the RN model in the case OF1 and ε = 0.25 over the replications.

  • Tables 5 and 6 show the results for the mean-risk RA model with OF1, ε = 0 and α = {0.8, 0.9} over the replications.

  • Tables 7 and 8 show for the mean-risk RA model with OF1 and OF2, ε = 0 and α = {0.8, 0.9} over the replications.

  • Table 9 shows the variations between the total number of donations for each rolling day and its average amount over the entire rolling period for each model and replication.

  • Figure 9 shows the number of produced units on each rolling day (1st and 3rd replications) with OF1 and OF2 under the RA model with only CV aR and the RN model, and the corresponding values as in the historical data of AVIS Milan.

Table 4 Results of the RA model with only CV aR and of the RN model (OF1 and ε = 0.25): mean value ± half-width of the 95% CI over the replications. Symbol * denotes a solution associated with a non-null optimality gap < 3.7% in at least a repetition
Full size table
Table 5 Results for the mean-risk model with OF1, ε = 0 and α = 0.8: mean value ± half-width of the 95% CI over the replications
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Table 6 Results for mean-risk model with OF1, ε = 0 and α = 0.9: mean value ± half-width of the 95% CI over the replications
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Table 7 Results for mean-risk model with OF1 and OF2, ε = 0 and α = 0.8: mean value ± half-width of the 95% CI over the replications. Symbol * denotes a solution associated with a non-null optimality gap < 0.2% in at least a repetition
Full size table
Table 8 Results for mean-risk model with OF1 and OF2, ε = 0 and α = 0.9: mean value ± half-width of the 95% CI over the replications. Symbol * denotes a solution associated with a non-null optimality gap < 0.2% in at least a repetition
Full size table
Table 9 Variations between the total number of donations for a rolling day and its average amount over the entire rolling period for each model and replication; minimum, first quartile, median, third quartile and maximum values
Full size table
Fig. 9
figure 9

Numbers of produced blood units on each rolling day with OF1 and OF2 under the RA model with only CV aR and the RN model, and corresponding values as in the historical data of AVIS Milan: |S| = 50 for 1st replication (a); |S| = 100 for 1st replication (b); |S| = 50 (c) for 3rd replication; |S| = 100 for 3rd replication (d)

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Yalçındağ, S., Güre, S.B., Carello, G. et al. A stochastic risk-averse framework for blood donation appointment scheduling under uncertain donor arrivals. Health Care Manag Sci 23, 535–555 (2020). https://doi.org/10.1007/s10729-020-09508-2

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