Optimization of a Rural Portfolio Credit Granting System Using Improved TwoDimensional Strip Packing Grouping Delay Problem
Abstract
:1. Introduction
2. Problem Description and Mathematical Model
2.1. Problem Description
2.2. Simple Example
2.3. Mathematical Model
 (1)
 All rectangles must be packed into a strip box.
 (2)
 The sides of the rectangle must be parallel to the strip box, that is, rightangle filling.
 (3)
 The rectangle cannot be rotated.
 (4)
 Any two rectangles cannot overlap.
 (5)
 One size fits all must not be a requirement.
2.4. Lower Bound of Group Fairness
3. Branch and Bound Reverse Order Insert Algorithm
3.1. Deep Search Inverse Spanning Tree (DSRST)
3.2. Insert Spare Space (ISS)
3.3. Lag Pruning Operator (LPO)
3.4. Delay Equivalence and Dominance
3.5. Algorithm Flow
4. Numerical Experiment
4.1. Performance of Classical Test Instances
4.2. Performance of Improved Grouping Constraint Test Instances
4.3. Performance with Lag Factor
4.4. Global Sensitivity Analysis
5. Rural Portfolio Credit Case
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Symbol  Description  Meaning in Rural Portfolio Credit Scheduling Problem 

G_{k}  The group k (k = 1, 2, …, g, k ∈ N+)  Group k of portfolio credit project 
R_{ki}  The ith rectangle of Group k(i = 1, …, m_{k}, i ∈ N+)  The ith item of Group k 
h_{ki}  Height of the ith rectangle of Group k  Loan amount of the ith item 
l_{ki}  Length of the ith rectangle of Group k  Loan term of the ith item 
LSL_{ki}  The latest start length of the ith rectangle of Group k  Latest loan obtaining time for the ith item of Group k 
GHC_{k}  Height constraint of Group k  The total credit of Group k 
SL_{ki}  The start length of the ith rectangle in Group k  Scheduling start time for the ith item of Group k 
EL_{ki}  The end length of the ith rectangle in Group k  Scheduling end time for the ith item of Group k 
DL_{ki}  The scheduling delay length of the ith rectangle in Group k  Scheduling delay time for the ith item of Group k 
Rural Portfolio Credit  2SPGDP  

village  Group k  1  1  1  2  2 
loan item  Rectangle R_{ki}  1  2  3  1  2 
loan amount(million yuan)  Height h_{ki}  2  2  1  2  1 
loan term(year)  Length l_{ki}  2  1  2  2  2 
latest loan obtaining time (year)  Latest start length LSL_{k}  0.2  0.4  
village credit limit(million yuan)  Height Constraint GHL_{k}  4  3 

Test  BL  NFDH  BB  IBB  

L_{opt}  Time  L_{opt}  Time  L_{opt}  Time  L_{opt}  Time  
J1  29  362  21  419  18  733  18  615 
J2  24  46  18  13  22  1680  22  1640 
D1  60  60  52  680  52  1701  52  1680 
D2  54  40  47  15  45  855  45  792 
D3  138  820  131  17  143  2380  130  2330 
D4  233  46  245  15  236  1970  223  1920 
Kendell  140  66  210  30  140  956  140  934 
Test  Denote  Description 

Class 1  C1  H = 10, hj and lj at random in [1,10] 
Class 2  C2  H = 30, hj and lj at random in [1,10] 
Class 3  C3  H = 40, hj and lj at random in [1,35] 
Class 4  C4  H = 100, hj and lj at random in [1,35] 
Class 5  C5  H = 100, hj and lj at random in [1,100] 
Class 6  C6  H = 300, hj and lj at random in [1,100] 
Type 1  T1  h_{j} at random in [2/3 H, H]; l_{j} at random in [1, 1/2 H] 
Type 2  T2  h_{j} at random in [1, 1/2 H]; l_{j} at random in [2/3 H, H] 
Type 3  T3  h_{j} at random in [1/2 H, H]; l_{j} at random in [1/2 H, H] 
Type 4  T4  h_{j} at random in [1, 1/2 H]; l_{j} at random in [1, 1/2 H] 
Test  R_{S}  S_{min}  S_{avg}  S_{max}  

BL0  BB  IBB  BB  IBB  BB  IBB  BB  IBB  
C1  20  1  100  88  7  7  15  16  26  33 
40  0  100  82  12  12  31  32  56  56  
60  0  61  85  26  25  51  51  76  76  
80  0  71  75  39  39  66  67  96  103  
100  0  71  82  49  49  84  84  126  126  
C2  20  26  77  66  1  1  5  5  13  13 
40  58  42  36  1  1  4  4  12  12  
60  18  51  69  1  1  4  4  12  12  
80  16  58  71  1  1  4  4  12  12  
100  9  58  78  1  1  5  4  14  13  
C3  20  3  99  87  3  3  11  11  27  27 
40  0  100  76  8  8  24  25  46  46  
60  0  64  81  16  15  36  35  59  59  
80  0  71  80  24  24  48  48  76  76  
100  0  76  75  35  35  60  60  90  91  
C4  20  37  63  55  0  0  4  4  13  13 
40  46  54  43  0  0  4  4  9  10  
60  16  54  70  0  0  5  5  13  12  
80  15  61  69  1  1  5  5  16  19  
100  3  72  80  1  1  6  6  16  14  
C5  20  10  97  86  5  5  25  25  41  42 
40  0  100  84  11  11  25  25  48  49  
60  0  55  88  20  19  41  41  66  64  
80  0  63  79  28  27  52  52  79  82  
100  0  70  78  35  35  67  67  98  106  
C6  20  39  64  58  0  0  4  4  12  12 
40  68  32  27  0  0  4  4  12  12  
60  29  49  60  0  0  4  4  11  9  
80  29  52  52  1  1  4  4  15  17  
100  14  63  67  0  0  5  5  13  22  
T1  20  10  97  86  5  5  25  25  41  42 
40  0  100  90  25  25  58  59  103  103  
60  0  58  84  50  50  93  92  138  147  
80  0  59  81  77  77  122  122  165  163  
100  0  58  83  109  108  159  159  206  238  
T2  20  5  94  71  3  3  21  22  39  39 
40  0  99  85  25  25  51  51  75  75  
60  0  64  78  38  33  78  77  112  112  
80  0  69  84  60  55  107  106  158  158  
100  0  70  88  77  77  136  135  195  195  
T3  20  4  99  81  13  13  34  35  55  55 
40  1  99  81  45  45  73  74  105  105  
60  0  67  62  85  82  116  117  157  163  
80  0  68  68  118  118  154  154  187  187  
100  0  64  75  157  157  192  192  229  230  
T4  20  3  98  83  0  0  11  11  39  39 
40  0  100  72  2  2  27  28  99  99  
60  0  66  87  6  6  43  42  115  115  
80  0  76  86  16  10  58  58  118  118  
100  0  76  80  18  18  79  78  158  158 
LL  g  m_{k}  L_{p}  

Uniform  0.0039  0.2232  0.0240  0.4028 
Sobol  0.0059  0.2219  0.0214  0.3987 
G_{k}  i  Project  Amount  Total Loan Amount  Loan Term  Latest Obtaining Time  Village Credit 

1  1  Automatic irrigation equipment for planting  1  30  3  0.25  300 
1  2  Treatment of pig breeding wastes  1  50  5  0.25  
1  3  Personal business loans  33  65  2.5  0.1  
1  4  Personal consumption loans  142  92  1.5  0.1  
2  1  Meat intensive processing production line  1  45  3  0.25  300 
2  2  Egg incubator equipment  1  32  2  0.25  
2  3  Personal business loans  26  53  2.2  0.1  
2  4  Personal consumption loans  123  59  1.8  0.1  
3  1  Supporting facilities of “Hot Spring Village” featured health care center  1  100  8  0.25  300 
3  2  Greenhouse planting facilities  1  88  5  0.25  
3  3  Personal business loans  18  44  2.8  0.1  
3  4  Personal consumption loans  102  71  1.6  0.1  
4  1  Attached aquaculture equipment for abalone aquaculture  1  46  3  0.25  300 
4  2  Agricultural Products Wholesale Center Project  1  120  6  0.25  
4  3  Personal business loans  16  39  2  0.1  
4  4  Personal consumption loans  99  99  1.1  0.1  
5  1  Land fertility improvement project of fruit and vegetable base  1  69  2  0.25  300 
5  2  Low temperature finished grain storage construction project  1  110  8  0.25  
5  3  Personal business loans  18  45  2.4  0.1  
5  4  Personal consumption loans  102  77  1.3  0.1  
6  1  Irrigation and drainage pump station renovation project  1  50  4  0.25  300 
6  2  Photovoltaic power generation energy construction project  1  100  6  0.25  
6  3  Personal business loans  16  45  2.6  0.1  
6  4  Personal consumption loans  99  1020  1.9  0.1 
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Huang, H.; Li, Y. Optimization of a Rural Portfolio Credit Granting System Using Improved TwoDimensional Strip Packing Grouping Delay Problem. Systems 2022, 10, 193. https://doi.org/10.3390/systems10050193
Huang H, Li Y. Optimization of a Rural Portfolio Credit Granting System Using Improved TwoDimensional Strip Packing Grouping Delay Problem. Systems. 2022; 10(5):193. https://doi.org/10.3390/systems10050193
Chicago/Turabian StyleHuang, Huijun, and Yuzhong Li. 2022. "Optimization of a Rural Portfolio Credit Granting System Using Improved TwoDimensional Strip Packing Grouping Delay Problem" Systems 10, no. 5: 193. https://doi.org/10.3390/systems10050193