# American Institute of Mathematical Sciences

August & September  2019, 12(4&5): 1501-1513. doi: 10.3934/dcdss.2019103

## Multi-machine and multi-task emergency allocation algorithm based on precedence rules

 1 School of Information Science and Technology, Agricultural University of Hebei, Baoding 071000, China 2 Graduate School, Agricultural University of Hebei, Baoding 071000, China 3 School of Agricultural Mechanization, Agricultural University of Hebei, Baoding 071000, China 4 University College of Southeast Norway, Kongsberg, 3603 Vestfold, Norway 5 School of Foreign Language, Hebei University of Technology, Tianjin 300401, China

* Corresponding author: Guifa Teng

Received  July 2017 Revised  December 2017 Published  November 2018

Aiming at the problems of asymmetric information and unreasonable emergency allocation schemes in the current cross-regional emergency operation, the emergency deployment process of multi-machine and multi-task is analyzed, and the emergency allocation model with the goal of minimizing the allocation cost and loss is established in the paper. Emergency allocation algorithm based on rule of nearest-distance-first, which allocate machinery for the nearest farmland firstly, and emergency allocation algorithm based on rule of max-ability-first, by which machinery with maximum ability to farmland is allocated firstly, are proposed. The operational data of farmland and agricultural machinery generated randomly are calculated and analyzed. The results show that when the amount of agricultural machinery is sufficient, the algorithm based on the maximum contribution capacity priority is better. When the agricultural machinery is insufficient, the calculation results of the emergency allocation algorithm based on the nearest distance priority are better. When the number of farmland is not more than 30, the average operation time of the two algorithms in this paper is not more than 3.8 seconds, and both two algorithm have good performance.

Citation: Fan Zhang, Guifa Teng, Mengmeng Gao, Shuai Zhang, Jingjing Zhang. Multi-machine and multi-task emergency allocation algorithm based on precedence rules. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1501-1513. doi: 10.3934/dcdss.2019103
##### References:

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##### References:
Schematic diagram of emergency allocation of agricultural machinery
Flow Chart of Emergency Allocation Algorithm with Rules of Short-Distance First
Flow Chart of Emergency Allocation Algorithm with Rules of Max-Ability First
The basic information of emergent farmland.
 N0 Areas/hm$^{2}$ Longitude Latitude F$_{1}$ 0.333 114.413521 36.531836 F$_{2}$ 0.267 114.613724 36.452427 F$_{3}$ 0.433 114.682483 36.436548 F$_{4}$ 0.400 114.653451 36.675132 F$_{5}$ 0.333 114.533785 36.511864 F$_{6}$ 0.533 115.020156 36.672432
 N0 Areas/hm$^{2}$ Longitude Latitude F$_{1}$ 0.333 114.413521 36.531836 F$_{2}$ 0.267 114.613724 36.452427 F$_{3}$ 0.433 114.682483 36.436548 F$_{4}$ 0.400 114.653451 36.675132 F$_{5}$ 0.333 114.533785 36.511864 F$_{6}$ 0.533 115.020156 36.672432
The basic information of available agricultural machinery
 N0 Type of machinery Longitude Latitude M$_{1}$ 1 114.527263 36.495766 M$_{2}$ 1 114.323553 36.475637 M$_{3}$ 2 114.876027 36.301018 M$_{4}$ 2 115.162425 36.420928 M$_{5}$ 3 115.235720 36.442845 M$_{6}$ 3 114.593689 36.5024681 M$_{7}$ 1 115.299793 36.368265 M$_{8}$ 1 114.599927 36.573633 M$_{9}$ 2 114.852262 36.496237 M$_{10}$ 2 114.873121 36.552312 M$_{11}$ 3 115.014362 36.495874 M$_{12}$ 3 115.06645 36.530413
 N0 Type of machinery Longitude Latitude M$_{1}$ 1 114.527263 36.495766 M$_{2}$ 1 114.323553 36.475637 M$_{3}$ 2 114.876027 36.301018 M$_{4}$ 2 115.162425 36.420928 M$_{5}$ 3 115.235720 36.442845 M$_{6}$ 3 114.593689 36.5024681 M$_{7}$ 1 115.299793 36.368265 M$_{8}$ 1 114.599927 36.573633 M$_{9}$ 2 114.852262 36.496237 M$_{10}$ 2 114.873121 36.552312 M$_{11}$ 3 115.014362 36.495874 M$_{12}$ 3 115.06645 36.530413
the types information of agricultural machinery
 Working ability Operating fuel Types hm$^{2}$/h consumption L/h 1 3.5 0.47 2 5.4 0.67 3 7.2 1
 Working ability Operating fuel Types hm$^{2}$/h consumption L/h 1 3.5 0.47 2 5.4 0.67 3 7.2 1
Comparison results of two algorithms
 Losses/ Cost/ Total Completion Algorithm Yuan Yuan distances/Km ratio /% NDF 0.00 14537.50 652.30 100% MAF 0.00 14239.50 627.50 100%
 Losses/ Cost/ Total Completion Algorithm Yuan Yuan distances/Km ratio /% NDF 0.00 14537.50 652.30 100% MAF 0.00 14239.50 627.50 100%
the comparison of emergent allocation schemes with insufficient agricultural machinery
 No Losses/yuan Cost/yuan Total distances/Km NDF MAF NDF MAF NDF MAF 1 2534.50 2647.50 11304.40 11935.30 475.50 509.50 2 2741.50 2928.50 12126.10 12763.45 495.20 517.50 3 2495.00 2613.50 11465.50 12021.20 488.50 526.10 4 2839.50 3325.00 11867.50 12574.20 499.60 523.50 5 2864.00 2985.50 10457.20 11064.60 469.50 503.80 6 2930.50 3073.00 12629.50 12317.50 536.50 514.70 7 2205.00 2365.50 10522.70 10213.40 468.20 425.50 8 3359.50 3516.50 12625.50 11921.90 558.50 512.60
 No Losses/yuan Cost/yuan Total distances/Km NDF MAF NDF MAF NDF MAF 1 2534.50 2647.50 11304.40 11935.30 475.50 509.50 2 2741.50 2928.50 12126.10 12763.45 495.20 517.50 3 2495.00 2613.50 11465.50 12021.20 488.50 526.10 4 2839.50 3325.00 11867.50 12574.20 499.60 523.50 5 2864.00 2985.50 10457.20 11064.60 469.50 503.80 6 2930.50 3073.00 12629.50 12317.50 536.50 514.70 7 2205.00 2365.50 10522.70 10213.40 468.20 425.50 8 3359.50 3516.50 12625.50 11921.90 558.50 512.60
The comparison of emergent deployment schemes with adequate agricultural machinery
 No Losses/yuan Cost/yuan Total distances/Km NDF MAF NDF MAF NDF MAF 1 0.00 0.00 13247.20 13046.50 557.40 521.30 2 0.00 0.00 12646.30 12453.60 510.80 487.60 3 0.00 0.00 13527.70 13407.50 583.90 561.40 4 0.00 0.00 14216.50 14003.50 619.40 596.20 5 0.00 0.00 14639.70 14522.00 648.50 617.30 6 0.00 0.00 13257.90 13153.60 540.50 527.60 7 0.00 0.00 13863.50 13597.50 572.40 551.50 8 0.00 0.00 14739.50 14586.80 635.20 617.90
 No Losses/yuan Cost/yuan Total distances/Km NDF MAF NDF MAF NDF MAF 1 0.00 0.00 13247.20 13046.50 557.40 521.30 2 0.00 0.00 12646.30 12453.60 510.80 487.60 3 0.00 0.00 13527.70 13407.50 583.90 561.40 4 0.00 0.00 14216.50 14003.50 619.40 596.20 5 0.00 0.00 14639.70 14522.00 648.50 617.30 6 0.00 0.00 13257.90 13153.60 540.50 527.60 7 0.00 0.00 13863.50 13597.50 572.40 551.50 8 0.00 0.00 14739.50 14586.80 635.20 617.90
the comparison of average operation time among the two Algorithms
 Number of Average Operation Time/S Increasing Ratio Farmland NCG NDF MAF IR$_{1}$ IR$_{2}$ 6 3.185 2.214 2.345 30.49% 26.37% 10 4.257 2.624 2.648 38.36% 37.80% 15 5.368 3.215 3.198 40.11% 40.42% 30 6.463 3.524 3.699 45.47% 42.77%
 Number of Average Operation Time/S Increasing Ratio Farmland NCG NDF MAF IR$_{1}$ IR$_{2}$ 6 3.185 2.214 2.345 30.49% 26.37% 10 4.257 2.624 2.648 38.36% 37.80% 15 5.368 3.215 3.198 40.11% 40.42% 30 6.463 3.524 3.699 45.47% 42.77%
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