﻿ 混流装配线车间内物料调度工位组划分优化法
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 同济大学学报(自然科学版)  2017, Vol. 45 Issue (8): 1191-1197.  DOI: 10.11908/j.issn.0253-374x.2017.08.013 0

### 引用本文

LI Aiping, ZHANG Yanhong, GUO Haitao, Xu Liyun. Station Groups Division of Material Dispatching System in Mixed-Model Assembly Line[J]. Journal of Tongji University (Natural Science), 2017, 45(8): 1191-1197. DOI: 10.11908/j.issn.0253-374x.2017.08.013.

### 文章历史

Station Groups Division of Material Dispatching System in Mixed-Model Assembly Line
LI Aiping, ZHANG Yanhong, GUO Haitao, Xu Liyun
Modern Manufacturing Technology Research Institute, Tongji University, Shanghai 201804, China
Abstract: In this study, an optimization method is proposed based on JIT, to divide station group and arrange the distribution vehicles. In order to eliminate case that assembly line production process was shut down due to material shortage, with the capacity of distribution vehicles and distribution time-window as the constraint, a model is developed, taking the full load ratio of distribution vehicles and station material requirement urgency as the optimization goal. Genetic algorithm is used to solve the model to optimize the total number of daily deliveries, which consequently give the plan of distribution of work station groups and vehicle scheduling. At last, the feasibility and effectiveness of this method was proved by the verification of example.
Key words: mixed-flow assembly line    material distribution    Just-in-time(JIT)    station groups division    full load ratio    genetic algorithm

1 问题描述

① 物料配送中心为单库存区域，配送车辆每趟配送绕装配线运行一周，每个消耗工位每趟只能被服务一次，途中无法调头返回；② 物料调度系统以及装配线无故障发生；③ 每位配送人员负责指定配送车辆；④ 初始状态时线边库存量为100%.

2 工位组划分模型构建

2.1 单次配送工位组划分方法及建模

 图 1 配送车辆配送任务示意图 Fig.1 Distribution vehicle distribution task diagram

 ${C_{O, i}} = \frac{{{H_i}}}{{{c_{t, i}}}} \cdot 60$ (1)

 ${\rm{R}}{{\rm{T}}_i} = \frac{{{E_i}-{M_{{\rm{IN, }}i}} \cdot {B_i}}}{{{C_{o, i}}}}$ (2)
 ${\rm{L}}{{\rm{T}}_i} = \frac{{{E_i}}}{{{C_{O, i}}}}$ (3)

 $T\_W = \left( {\left[ {{\rm{R}}{{\rm{T}}_1},{\rm{L}}{{\rm{T}}_1}} \right], \ldots ,\left[ {{\rm{R}}{{\rm{T}}_m},{\rm{L}}{{\rm{T}}_m}} \right]} \right)$ (4)

 ${T_{ij}} = \frac{{{d_{ij}}}}{v}$ (5)
 ${T_{{d_i}}} = \sum\limits_{j = 0}^m {\sum\limits_{i = 0}^m {{T_{ij}}{x_{iju}} + } } \sum\limits_{i = 1}^m {{T_s}{x_{iu}}}$ (6)

 ${\rm{R}}{{\rm{T'}}_i} = {\rm{R}}{{\rm{T}}_i}-{T_{{d_i}}}$ (7)
 ${\rm{L}}{{\rm{T'}}_i} = {\rm{L}}{{\rm{T}}_i}-{T_{{d_i}}}$ (8)
 $T\_{W'_i} = \left[{{\rm{R}}{{{\rm{T'}}}_i}, L{{{\rm{T'}}}_i}} \right]$ (9)

 ${\rm{L}}{{\rm{T}}_{\rm{u}}}{\rm{ = min(L}}{{\rm{T}}_i}{\rm{)}}$ (10)

 ${q_i} = {B_i} \cdot {G_i}$ (11)

 $\sum\limits_{i = 1}^m {{q_i}{x_{iu}} \le Q}$ (12)
 $M{_u} = \frac{{\sum\limits_{i = 1}^m {{q_i}{x_{iu}}} }}{Q}$ (13)

 ${E'_i} = {M_{{\rm{AX, }}i}} \cdot {B_i}-{\rm{L}}{{\rm{T}}_i} \cdot {C_{O, i}} + {q_i}$ (14)

 ${E_i} = {E'_i}-{\rm{L}}{{\rm{T}}_i} \cdot {C_{O, i}} + {q_i}$ (15)

 $\max \;{F_u} = \frac{{{M_u}}}{{{\rm{L}}{{\rm{T}}_u}}}$ (16)

2.2 优化模型求解

(1) 随机在父代个体中选择一个交叉区域，如父代M和父代N两个个体交叉区域位于两条直线之间，如图 2所示.

 图 2 遗传算法交叉第1步 Fig.2 Genetic algorithm crossing step 1

(2) 将父代N中的交叉区域放在父代M的前面，同理也将父代M中的交叉区域放在父代N的前面，得到父代M′和父代N′，如图 3所示.

 图 3 遗传算法交叉第2步 Fig.3 Genetic algorithm crossing step 2

(3) 为保证配送工位组中的任何一个消耗工位不被重复访问，将父代M′和父代N′中重复出现的基因删除，得到子代M和子代N，如图 4所示.

 图 4 遗传算法交叉第3步 Fig.4 Genetic algorithm crossing step 3

 图 5 遗传算法变异示意图 Fig.5 Genetic algorithm mutation

3 实例分析

 图 6 外装线消耗工位布局示意图 Fig.6 Layout of the assemble line

3.1 实例求解

 图 7 遗传算法种群适应度曲线 Fig.7 Genetic algorithm population fitness curve

 图 8 配送车辆配送时间窗甘特图 Fig.8 Gantt chart of distribution time window
3.2 结果分析

 图 9 优化前后配送车辆满载率对比图 Fig.9 Optimized comparison of full load ratio of distribution vehicles before and after

4 结束语

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