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A supply chain network design for blood and its products using genetic algorithm: A case study of Turkey

  • *Corresponding author: Gokhan Agac

    *Corresponding author: Gokhan Agac 

This study was produced from researcher Gokhan Agac's doctoral thesis

Abstract Full Text(HTML) Figure(12) / Table(16) Related Papers Cited by
  • In the paper, a novel mathematical model for blood supply chain network and a variant of Genetic Algorithm for the problem are proposed. The proposed mathematical model is developed using Mixed-integer nonlinear programming. The model is designed as a location, allocation, and routing problem that includes determining locations of local blood centers, assigning transfusion and blood donation centers to predetermined local blood centers, and routing between them. Eventually, a case study is conducted in the Eastern Black Sea Region of Turkish Red Crescent to illustrate the practicality and validity of the proposed model.

    Mathematics Subject Classification: Primary: 90C11, 90C27.

    Citation:

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  • Figure 1.  Basic models based on blood supply chain. (a) single center model, (b) multiple independent centers model and (c) coordinated multiple centers model

    Figure 2.  Proposed BSCN model

    Figure 3.  Representation of the TRBC on the map

    Figure 4.  Solution of the model with BARON

    Figure 5.  Boxplots of the comparing algorithms

    Figure 6.  The representation of the model network structure

    Figure 7.  The hierarchical representation of the model structure

    Figure 8.  LBC sequence representation. (a) capacity levels corresponding to the LBCs and (b) shipment coefficients corresponding to the LBCs

    Figure 9.  TCs and BDCs sequence representation

    Figure 10.  Vehicle sequence representation

    Figure 11.  Representation of vehicle assignment to LBC

    Figure 12.  Representation of a vehicle's route. (a) first route (b) simplified route

    Table 1.  The classification of the studies related to BSCN

    Study Problem Type Echelon Network Type Model Type Objective Function Product Type** Solution Approach Application Data Application Location
    Or and Pierskalla [73] Location-allocation-routing Distribution SC IP MinC WB Heuristic Case Study USA
    Jacobs et al. [50] Allocation Distribution SC IP MinD WB Exact Case Study USA
    Şahin et al. [85] Location-allocation Distribution SC MIP, IP MinDD WB Exact Case Study Turkey
    Doerner et al. [27] Routing Distribution SC MIP MinC WB Exact, Heuristic Case Study Austria
    Cetin and Sarul [17] Location-allocation Distribution SC INLP MinC, MinD, MinCV WB Exact Random Data -
    Zahiri et al. [102] Location-allocation Collection * MINLP MinC WB Exact Random Data -
    Arvan et al. [9] Location-allocation Integrated SC MILP MinC, MaxRS WB, PLT, PLS, RBC Exact Random Data -
    Mobasher et al. [67] Routing Collection * MILP MaxCB WB Heuristic Case Study USA
    Şahinyazan et al. [87] Location-routing Collection * MIP MinC, MaxCB WB Heuristic Case Study Turkey
    Zahiri et al. [105] Location-allocation Collection * MILP MinC WB Exact Case Study Iran
    Chaiwuttisak et al. [18] Location-allocation Integrated SC ILP MinD, MinDD, MaxCB WB Exact Case Study Thailand
    Cheraghi et al. [23] Location-allocation Integrated SC MILP MinC WB Exact Random Data -
    Mouatassim et al. [70] Routing Distribution * MILP MinC WB Exact Case Study Morocco
    Heidari-Fathian and Pasandideh [45] Location-allocation-inventory Integrated SC MIP MinC WB Exact Random Data -
    Kaveh and Ghobadi [58] Allocation Distribution SC ILP MinDD WB Meta-heuristic Case Study Iran
    Kazemi et al. [60] Inventory-routing Integrated SC MIP MinC WB Exact Case Study Iran
    Ramezanian and Behboodi [83] Location-allocation-inventory Integrated SC MILP MinC WB Exact Case Study Iran
    Zahiri and Pishvaee [103] Location-allocation Integrated SC MINLP MinC, MinUD WB, PLT, PLS, RBC Exact Case Study Iran
    Heidari-Fathian and Pasandideh [46] Location-allocation-inventory Integrated SC MIP MinC, MinDB, MinEI WB, PLT, PLS, RBC Heuristic Random Data -
    Osorio et al. [75] Location-allocation Integrated CMC MILP MinC WB, PLT, PLS, RBC Heuristic Case Study Colombia
    Özener and Ekici [76] Routing Collection * ILP MaxCB WB Heuristic Random Data -
    Zahiri et al. [104] Allocation-inventory-routing Integrated SC MINLP MinC, MaxRS WB, PLT, PLS, RBC Meta-heuristic Random Data -
    Bruno et al. [14] Location-allocation Integrated SC IP MinC WB Exact Case Study Italy
    Hamdan and Diabat [42] Location-allocation-inventory Integrated SC MIP MinC, MinDT, MinDB RBC Exact Case Study Jordan
    Mohamed et al. [68] Location Integrated SC MIP MinC WB Exact Case Study Turkey
    Samani et al. [36] Location-allocation-inventory Integrated SC MILP MinC, MaxRS, MaxCB WB, PLT, PLS, RBC Exact Case Study Iran
    Araújo et al. [7] Allocation-inventory Integrated SC ILP MinC WB, PLT, RBC Exact Case Study Portugal
    Kaya and Ozkok [59] Location-allocation-routing-inventory Distribution CMC MINLP MinC WB Exact, Heuristic Case Study Turkey
    Yaghoubi et al.[99] Location-allocation-inventory Integrated * MIP MinC, MinS PLT Exact Case Study Iran
    Karadağ et al. [54] Location-allocation Integrated SC MILP MinD WB Exact Case Study Turkey
    This study Location-allocation-routing Integrated CMC MINLP MinC WB, PLT, PLS, RBC Meta-heuristic Case Study Turkey
    Notes: SC, single center; CMC, coordinated multiple centers; IP, integer programming; ILP, integer linear programming; INLP, integer nonlinear programming; MIP, mixed-integer programming; MILP, mixed-integer linear programming; MINLP, mixed-integer nonlinear programming; MinC, minimizing cost; MinCV, minimizing coefficient of variance; MinD, minimizing distance; MinDB, minimizing amount of defective blood; MinDD, minimizing demand-weighted distance; MinDT, minimizing delivery time; MinEI, minimizing environmental impacts; MinUD, minimizing unsatisfied demand; MaxCB, maximizing amount of collected bloods; MaxRS, maximizing remaining shelf life; MaxSI, maximizing total social impacts; PLT, platelet; PLS, plasma; RBC, red blood cell; WB, whole blood.
    * Network type could not be determined since the proposed model does not contain RBC (or main blood center).
    ** The whole blood is also taken for studies that do not specify single product type in their studies.
     | Show Table
    DownLoad: CSV

    Table 2.  The parameters and levels for the experiments

    Level Parameter
    Number of population Number of iteration Crossover rate Mutation rate
    1 20 250 0.6 0.05
    2 30 500 0.7 0.1
    3 40 750 0.8 0.2
    4 50 1000 0.9 0.3
     | Show Table
    DownLoad: CSV

    Table 3.  The distribution of the parameters according to $ L_{16}(4^4) $

    Number of experiment Parameter Observation
    Number of population Number of iteration Crossover rate Mutation rate Mean Standard deviation
    1 20 250 0.6 0.05 2, 488, 350 176, 760
    2 500 0.7 0.1 2, 387, 633 208, 211
    3 750 0.8 0.2 2, 297, 514 215, 127
    4 1000 0.9 0.3 2, 240, 570 201, 131
    5 30 250 0.7 0.2 2, 424, 464 171, 962
    6 500 0.6 0.3 2, 400, 807 297, 907
    7 750 0.9 0.05 2, 151, 286 224, 764
    8 1000 0.8 0.1 2, 131, 026 198, 773
    9 40 250 0.8 0.3 2, 310, 707 284, 917
    10 500 0.9 0.2 2, 210, 203 237, 160
    11 750 0.6 0.1 2, 160, 792 257, 404
    12 1000 0.7 0.05 2, 086, 162 211, 818
    13 50 250 0.9 0.1 2, 367, 584 298, 232
    14 500 0.8 0.05 2, 219, 789 243, 224
    15 750 0.7 0.3 2, 181, 113 254, 553
    16 1000 0.6 0.2 2, 056, 323 251, 595
     | Show Table
    DownLoad: CSV

    Table 4.  Taguchi response table for S/N

    Level Number of population Number of iteration Crossover rate Mutation rate
    1 -127.46 -127.64 -127.17 -127.01
    2 -127.17 -127.29 -127.14 -127.13
    3 -126.86 -126.89 -127.05 -127.06
    4 -126.92 -126.60 -127.06 -127.22
    Delta (Best-Worst) 0.59 1.03 0.13 0.21
     | Show Table
    DownLoad: CSV

    Table 5.  Validation of parameter values

    Mean Standard deviation t p
    Prediction 2, 025, 206 213, 267 -0.68 0.5
    Observation 1, 999, 730 209, 084
     | Show Table
    DownLoad: CSV

    Table 6.  The location information of the facilities

    Facility type Display code Location Facility type Display code Location
    LONGITUDE (X) LATITUDE (Y) LONGITUDE (X) LATITUDE (Y)
    RBC RBC 39.71436918 41.00504666 TC TC$_{21}$ 39.12385941 40.18857810
    TC TC$_1$ 39.62491751 41.00717196 TC TC$_{22}$ 38.70773077 40.94959852
    TC TC$_2$ 39.59401846 41.01671678 TC TC$_{23}$ 38.24460983 40.93993863
    TC TC$_3$ 40.04374981 40.91651238 TC TC$_{24}$ 38.38883020 40.91321157
    TC TC$_4$ 40.27007461 40.94276502 TC TC$_{25}$ 38.38326663 40.91365446
    TC TC$_5$ 40.13169676 40.91158188 TC TC$_{26}$ 38.41151834 40.90588272
    TC TC$_6$ 39.70023394 40.99953269 TC TC$_{27}$ 38.38979244 40.91223964
    TC TC$_7$ 39.70139265 41.00128976 TC TC$_{28}$ 38.34879756 40.90906126
    TC TC$_8$ 39.72576320 40.99493331 TC TC$_{29}$ 38.44433784 40.91330177
    TC TC$_9$ 39.72798407 41.00819209 TC TC$_{30}$ 38.97944927 41.03708900
    TC TC$_{10}$ 39.69852269 40.98711849 TC TC$_{31}$ 38.42622757 40.29882320
    TC TC$_{11}$ 39.70712185 41.00531789 TC TC$_{32}$ 38.82866621 41.00373905
    TC TC$_{12}$ 39.76861954 40.99249988 TC TC$_{33}$ 41.29930258 41.35125468
    TC TC$_{13}$ 39.27011490 41.04767326 TC TC$_{34}$ 41.81862652 41.18207775
    TC TC$_{14}$ 40.94366312 41.17991369 TC TC$_{35}$ 41.68003678 41.35487479
    TC TC$_{15}$ 40.51333487 41.03050129 TC TC$_{36}$ 41.42846972 41.40415302
    TC TC$_{16}$ 40.51444530 41.02836460 TC TC$_{37}$ 42.34782100 41.25702095
    TC TC$_{17}$ 40.57150930 41.03764941 BDC BDC$_1$ 38.34259629 40.91140047
    TC TC$_{18}$ 40.72704792 41.09021972 BDC BDC$_2$ 39.47874248 40.45892159
    TC TC$_{19}$ 39.46682811 40.46151134 BDC BDC$_3$ 40.51563889 41.02773936
    TC TC$_{20}$ 39.43600282 40.12571111 BDC BDC$_4$ 41.82027541 41.18059400
     | Show Table
    DownLoad: CSV

    Table 7.  The comparison of Genetic Algorithm with CPLEX solver

    Sample number Number of facilities Number of vehicles CPLEX GA (best) GA (mean)
    LBC TC BDC Total cost CPU (s) Total cost CPU (s) Total cost CPU (s)
    1 2 2 2 5 198, 796 0.23 198, 796 23.06 198, 796 26.95
    2 3 3 2 5 198, 941 0.33 198, 941 25.25 198, 941 25.80
    3 4 4 2 5 199, 143 0.52 199, 143 27.33 199, 143 27.78
    4 4 4 4 5 199, 189 0.98 199, 189 30.87 199, 189 32.16
    5 5 5 2 5 200, 617 0.77 199, 102 27.96 199, 102 31.68
    6 5 5 5 10 199, 307 87.70 199, 307 37.31 199, 310 55.71
    7 6 6 2 10 198, 863 4.25 198, 863 42.06 198, 863 45.52
    8 6 6 4 10 199, 031 1, 015.94 199, 031 46.60 199, 034 51.02
    9 6 6 6 10 199, 179 27, 225.25 199, 179 43.24 199, 215 51.72
    10 8 8 4 10 199, 698 4, 281.73 199, 698 54.84 199, 792 60.48
    11 8 8 6 10 265, 159 27, 590.64 265, 182 64.23 265, 564 73.38
    12 10 10 2 10 200, 280 218.47 200, 243 51.10 200, 357 52.83
    13 10 10 6 15 n/a $>$ 43, 200 265, 847 70.67 266, 997 74.01
    14 12 12 6 15 n/a $>$ 43, 200 273, 661 90.25 275, 997 95.95
    15 12 12 10 20 n/a $>$ 43, 200 354, 205 97.34 414, 955 96.18
     | Show Table
    DownLoad: CSV

    Table 8.  The difference of Genetic Algorithm with CPLEX solver

    Sample number Difference (%)*
    GA (best)-CPLEX GA (mean)-CPLEX
    Total cost CPU (s) Total cost CPU (s)
    1 0.00 9, 926.09 0.00 11, 617.39
    2 0.00 7, 551.52 0.00 7, 718.18
    3 0.00 5, 155.77 0.00 5, 242.31
    4 0.00 3, 050.00 0.00 3, 181.63
    5 -0.76 3, 531.17 -0.76 4, 014.29
    6 0.00 -57.46 0.00 -36.48
    7 0.00 889.65 0.00 971.06
    8 0.00 -95.41 0.00 -94.98
    9 0.00 -99.84 0.02 -99.81
    10 0.00 -98.72 0.05 -98.59
    11 0.01 -99.77 0.15 -99.73
    12 -0.02 -76.61 0.04 -75.82
    13 $-$ -99.84 $-$ -99.83
    14 $-$ -99.79 $-$ -99.78
    15 $-$ -99.77 $-$ -99.78
    * Difference (%) = 100 x (The GA solution value - # solver solution value) / # solver solution value.
     | Show Table
    DownLoad: CSV

    Table 9.  The comparison of Genetic Algorithm with general Variable Neighborhood Search algorithm-based heuristic

    Types of cost
    Genetic Algorithm (GA) Opening and operating Transportation Holding Vehicle usage Total CPU (s)
    Best 159, 442 112, 738 13, 893 1, 140, 000 1, 571, 879 927.25
    Worst 526, 883 226, 549 13, 893 1, 980, 000 2, 449, 378 1, 122.74
    Median 309, 633 164, 626 13, 893 1, 440, 000 1, 984, 623 941.19
    Mean 317, 829 168, 007 13, 893 1, 500, 000 1, 999, 730 964.48
    Variable Neighbor Search (VNS)
    Best 161, 876 105, 516 13, 893 1, 740, 000 2, 245, 926 1, 018.68
    Worst 1, 337, 112 158, 127 13, 893 2, 160, 000 3, 644, 573 1, 337.99
    Median 1, 184, 488 129, 645 13, 893 1, 980, 000 3, 243, 514 1, 122.81
    Mean 980, 311 129, 349 13, 893 1, 999, 355 3, 122, 909 1, 137.10
    Difference (GA-VNS) (%)
    Best 1.53 -6.41 0.00 52.63 42.88 9.86
    Worst 153.78 -30.20 0.00 9.09 48.80 19.17
    Median 282.55 -21.25 0.00 37.50 63.43 19.30
    Mean 208.44 -23.01 0.00 33.29 56.17 17.90
     | Show Table
    DownLoad: CSV

    Table 10.  The experimental results for the model cost

    Experiment Number Opening and Operatinga Transportationb Holdingc Vehicle Usaged Total
    Cost Dev. (%) Cost Dev. (%) Cost Dev. (%) Cost Dev. (%) Cost Dev. (%)
    1 159, 442 49.83 184, 487 9.81 13, 893 0.00 1, 440, 000 4.00 1, 797, 822 10.10
    2 161, 876 49.07 188, 854 12.41 13, 893 0.00 1, 620, 000 8.00 1, 984, 623 0.76
    3 314, 499 1.05 170, 627 1.56 13, 893 0.00 1, 500, 000 0.00 1, 999, 020 0.04
    4 526, 883 65.78 164, 626 2.01 13, 893 0.00 1, 560, 000 4.00 2, 265, 402 13.29
    5 374, 259 17.75 145, 537 13.37 13, 893 0.00 1, 440, 000 4.00 1, 973, 689 1.30
    6 238, 188 25.06 153, 448 8.67 13, 893 0.00 1, 440, 000 4.00 1, 845, 529 7.71
    7 485, 627 52.80 190, 813 13.57 13, 893 0.00 1, 620, 000 8.00 2, 310, 334 15.53
    8 376, 692 18.52 163, 574 2.64 13, 893 0.00 1, 440, 000 4.00 1, 994, 160 0.28
    9 309, 633 2.58 136, 925 18.50 13, 893 0.00 1, 320, 000 12.00 1, 780, 451 10.97
    10 312, 066 1.81 160, 938 4.21 13, 893 0.00 1, 500, 000 0.00 1, 986, 897 0.64
    11 302, 814 4.72 159, 142 5.28 13, 893 0.00 1, 620, 000 8.00 2, 095, 849 4.81
    12 376, 692 18.52 154, 468 8.06 13, 893 0.00 1, 440, 000 4.00 1, 985, 054 0.73
    13 448, 137 41.00 149, 263 11.16 13, 893 0.00 1, 560, 000 4.00 2, 171, 294 8.58
    14 374, 259 17.75 120, 105 28.51 13, 893 0.00 1, 260, 000 16.00 1, 768, 257 11.58
    15 238, 188 25.06 185, 642 10.50 13, 893 0.00 1, 380, 000 8.00 1, 817, 723 9.10
    16 462, 256 45.44 182, 570 8.67 13, 893 0.00 1, 680, 000 12.00 2, 338, 720 16.95
    17 312, 066 1.81 124, 103 26.13 13, 893 0.00 1, 320, 000 12.00 1, 770, 063 11.48
    18 233, 321 26.59 137, 845 17.95 13, 893 0.00 1, 440, 000 4.00 1, 825, 059 8.73
    19 309, 633 2.58 207, 211 23.33 13, 893 0.00 1, 680, 000 12.00 2, 210, 737 10.55
    20 228, 935 27.97 226, 549 34.84 13, 893 0.00 1, 980, 000 32.00 2, 449, 378 22.49
    21 247, 440 22.15 196, 938 17.22 13, 893 0.00 1, 620, 000 8.00 2, 078, 272 3.93
    22 233, 321 26.59 172, 210 2.50 13, 893 0.00 1, 440, 000 4.00 1, 859, 424 7.02
    23 453, 004 42.53 203, 909 21.37 13, 893 0.00 1, 500, 000 0.00 2, 170, 807 8.56
    24 305, 247 3.96 189, 739 12.94 13, 893 0.00 1, 800, 000 20.00 2, 308, 880 15.46
    25 383, 511 20.67 160, 549 4.44 13, 893 0.00 1, 380, 000 8.00 1, 937, 953 3.09
    26 448, 137 41.00 130, 815 22.14 13, 893 0.00 1, 320, 000 12.00 1, 912, 845 4.34
    27 159, 442 49.83 205, 838 22.52 13, 893 0.00 1, 560, 000 4.00 1, 939, 174 3.03
    28 302, 814 4.72 158, 651 5.57 13, 893 0.00 1, 440, 000 4.00 1, 915, 358 4.22
    29 305, 247 3.96 112, 738 32.90 13, 893 0.00 1, 140, 000 24.00 1, 571, 879 21.40
    30 235, 754 25.82 199, 319 18.64 13, 893 0.00 1, 740, 000 16.00 2, 188, 967 9.46
    31 233, 321 26.59 170, 779 1.65 13, 893 0.00 1, 320, 000 12.00 1, 737, 994 13.09
    Best 305, 247 1.05 112, 738 1.56 13, 893 0.00 1, 140, 000 0.00 1, 571, 879 0.04
    Worst 228, 935 65.78 226, 549 34.84 13, 893 0.00 1, 980, 000 32.00 2, 449, 378 22.49
    Median 161, 876 25.06 188, 854 12.41 13, 893 0.00 1, 620, 000 8.00 1, 984, 623 8.58
    Mean 317, 829 24.63 168, 007 13.65 13, 893 0.00 1, 500, 000 8.77 1, 999, 730 8.36
    a The opening and operating cost of LBC includes cost of cabinet purchasing and head personnel.
    b The transportation cost includes transportation cost per km multiplied by the total distance.
    c The holding cost includes cabinet electricity consumption and its maintenance fee.
    d The vehicle usage cost includes car rental and driver fees.
     | Show Table
    DownLoad: CSV

    Table 11.  The model cost for different working time and maximum distance, transportation cost, and holding cost

    Working time and distance Opening and operating cost Transportation cost Holding cost Vehicle usage cost Total cost
    8 h & 500 km Mean 317, 829 168, 007 13, 893 1, 500, 000 1, 999, 730
    Median 161, 876 188, 854 13, 893 1, 620, 000 1, 984, 623
    8 h & 750 km Mean 306, 867 174, 133 13, 893 1, 505, 806 2, 000, 700
    Median 228, 935 168, 238 13, 893 1, 560, 000 1, 971, 067
    10 h & 500 km Mean 313, 278 168, 233 13, 893 1, 292, 903 1, 788, 308
    Median 161, 876 225, 149 13, 893 1, 380, 000 1, 780, 918
    10 h & 750 km Mean 184, 463 165, 015 13, 893 1, 170, 968 1, 534, 339
    Median 235, 754 153, 802 13, 893 1, 140, 000 1, 543, 449
    Transportation cost
    $ \beta=0.5 $ Mean 307, 307 93, 014 13, 893 1, 538, 710 1, 952, 925
    Median 445, 704 79, 676 13, 893 1, 440, 000 1, 979, 273
    $ \beta=1 $ Mean 317, 829 168, 007 13, 893 1, 500, 000 1, 999, 730
    Median 161, 876 188, 854 13, 893 1, 620, 000 1, 984, 623
    $ \beta=2 $ Mean 326, 816 339, 072 13, 893 1, 530, 968 2, 210, 749
    Median 383, 511 326, 897 13, 893 1, 500, 000 2, 224, 301
    Holding cost
    $ \theta=0.5 $ Mean 340, 404 179, 822 6, 947 1, 556, 129 2, 083, 302
    Median 459, 823 147, 412 6, 947 1, 500, 000 2, 114, 181
    $ \theta=1 $ Mean 317, 829 168, 007 13, 893 1, 500, 000 1, 999, 730
    Median 161, 876 188, 854 13, 893 1, 620, 000 1, 984, 623
    $ \theta=2 $ Mean 349, 580 170, 421 27, 787 1, 461, 290 2, 009, 078
    Median 473, 942 181, 336 27, 787 1, 320, 000 2, 003, 065
     | Show Table
    DownLoad: CSV

    Table 12.  The comparison matrix for different working time and maximum distance, transportation cost, and holding cost

    Comparison type Groups t test
    t p
    Working time and maximum distance 8 h & 500 km * 8 h & 750 km -0.02 0.99
    8 h & 500 km * 10 h & 500 km 4.30 0.00
    8 h & 500 km * 10 h & 750 km 10.65 0.00
    8 h & 750 km * 10 h & 500 km 3.99 0.00
    8 h & 750 km * 10 h & 750 km 9.67 0.00
    10 h & 500 km * 10 h & 750 km 6.53 0.00
    Transportation cost $ \beta=0.5 $ * $ \beta=1 $ -0.88 0.38
    $ \beta=0.5 $ * $ \beta=2 $ -4.49 0.00
    $ \beta=1 $ * $ \beta=2 $ -3.67 0.00
    Holding cost $ \theta=0.5 $ * $ \theta=1 $ -1.61 0.11
    $ \theta=0.5 $ * $ \theta=2 $ 1.45 0.15
    $ \theta=1 $ * $ \theta=2 $ -0.18 0.86
     | Show Table
    DownLoad: CSV

    Table 13.  The capacity levels for each LBC and opening and operating costs of each LBC

    Product
    Capacity level Red blood cells Platelet Plasma Opening and operating cost
    $ N_j = 1 $ 120 48 280 73, 878.44
    $ N_j = 2 $ 294 54 352 76, 311.80
    $ N_j = 3 $ 720 96 384 85, 564.00
     | Show Table
    DownLoad: CSV

    Table 14.  The capacities for each vehicle and holding costs for blood products

    Product Vehicle capacity Holding cost
    Red blood cells 250 16.70
    Platelet 75 90.26
    Plasma 250 47.43
     | Show Table
    DownLoad: CSV

    Table 15.  The mean of yearly demand for each

    Product Transfusion centers
    TC$_1$ TC$_2$ TC$_3$ TC$_4$ TC$_5$ TC$_6$ TC$_7$ TC$_8$ TC$_9$ TC$_{10}$ TC$_{11}$ TC$_{12}$ TC$_{13}$ TC$_{14}$ TC$_{15}$ TC$_{16}$ TC$_{17}$ TC$_{18}$ TC$_{19}$
    Red blood cells 17 17 2 3 3 7 15 18 7 16 60 80 9 13 3 23 82 1 16
    Platelet 3 3 1 1 0 1 1 1 1 2 16 23 1 1 1 1 17 0 1
    Plasma 3 3 1 1 1 4 4 1 2 11 27 75 1 2 1 3 22 1 6
    Product Transfusion centers
    TC$_{20}$ TC$_{21}$ TC$_{22}$ TC$_{23}$ TC$_{24}$ TC$_{25}$ TC$_{26}$ TC$_{27}$ TC$_{28}$ TC$_{29}$ TC$_{30}$ TC$_{31}$ TC$_{32}$ TC$_{33}$ TC$_{34}$ TC$_{35}$ TC$_{36}$ TC$_{37}$
    Red blood cells 4 1 1 11 1 5 1 3 59 34 5 4 4 4 18 1 4 2
    Platelet 0 0 0 3 1 1 1 1 5 4 1 0 0 1 2 0 0 0
    Plasma 1 1 1 6 1 1 1 1 7 9 3 1 1 1 5 0 1 0
     | Show Table
    DownLoad: CSV

    Table 16.  Other parameter values about product transportation

    The annual usage cost for the vehicle is 60, 000
    The transportation cost per km is 0.32
    Product delivery/collection time for each LBC and TC is 0.25 hour
    The maximum distance for each vehicle is less than or equal to 500 Km
    The maximum transportation time for each vehicle is less than or equal to 8 hours
    The number of shipments for each vehicle are 83 tours
     | Show Table
    DownLoad: CSV
  • [1] U. Abdulwahab and M. Wahab, Approximate dynamic programming modeling for a typical blood platelet bank, Computers and Industrial Engineering, 78 (2014), 259-270. 
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