pymprog库应用（一）工位规划--生产线平衡

问题描述

问题分析

设置不同的工位数，进行求解，评价工位平衡状态。

求解

设置工位数为5

求解得到：
工位1:[‘A’]
工位2:[‘B’]
工位3:[‘D’]
工位4:[‘C’, ‘E’, ‘F’, ‘I’]
工位5:[‘G’, ‘H’, ‘J’, ‘K’]
节拍时间:50.0
工位时间:
[45, 11, 50, 48, 41]
平衡率LBR: 78.00%
平衡损失率d: 22.00%
平滑性指数SI: 18.06
平衡状态: 差

设置工位数为3

求解得到：
工位1:[‘D’, ‘E’]
工位2:[‘A’, ‘B’, ‘C’]
工位3:[‘F’, ‘G’, ‘H’, ‘I’, ‘J’, ‘K’]
节拍时间:50.0
工位时间:
[65, 65, 65]
平衡率LBR: 100.00%
平衡损失率d: 0.00%
平滑性指数SI: 0.00
平衡状态: 优

平衡率最高时，工位划分如下。此时节拍为65，比50大很多。再考虑，工位数为4的情况。

设置工位数为4

求解得到：
工位1:[‘A’]
工位2:[‘D’]
工位3:[‘B’, ‘E’, ‘H’, ‘I’]
工位4:[‘C’, ‘F’, ‘G’, ‘J’, ‘K’]
节拍: 50.0
工位时间:
[45, 50, 50, 50]
平衡率LBR: 97.50%
平衡损失率d: 2.50%
平滑性指数SI: 2.50
平衡状态: 优

代码（生产线平衡）

import numpy as np
import matplotlib.pyplot as plt

plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号
plt.style.use('ggplot')


def _balance(t):
	#
	# 计算平衡状态
	#
	n = len(t)
	ct = max(t)
	lbr = sum(t) / (n * ct)
	d = 1 - lbr
	a = 0
	for i in t:
		a += pow((ct - i), 2)
	si = pow(a / n, 0.5)
	if d <= 0.1:
		cm = '优'
	elif d <= 0.2:
		cm = '良'
	else:
		cm = '差'
	return lbr * 100, d * 100, si, cm


def _bar(data, ct, xlabel, ylabel, xticks, setdpi, lbr):
	#
	# 绘制平衡图
	#
	index = np.arange(1, len(data) + 1)
	plt.grid(False)  # 不显示网格
	bar_width = len(data) / 10  # 条形图宽度
	plt.bar(index, data, width=bar_width, color='blue', alpha=0.6)  # 绘制条形图
	
	plt.ylim(0, 1.30 * max(data))  # 设置y轴范围
	ct = ct
	plt.plot([ct] * int(1.75 * len(data)), 'r--', alpha=0.4)
	# 图形属性设置及文字标注
	plt.xlabel(xlabel)  # 设置x轴的标签
	plt.ylabel(ylabel)  # 设置y轴的标签
	plt.xticks(range(1, len(xticks) + 1), xticks)  # 设置x轴的显示名称
	plt.title( "生产线平衡率LBR=")
	# 设置边框是否显示
	ax = plt.gca()
	ax.spines['top'].set_visible(False)
	ax.spines['right'].set_visible(False)
	
	plt.savefig("result.jpg", dpi=setdpi)
	plt.show()


def status(data, ct):
	#
	# 平衡状态
	#
	t = data
	ct = ct
	lbr, d, si, cm = _balance(t)
	xlabel = "工位"
	ylabel = "时间/s"
	xticks = []
	for i in range(1, len(t) + 1):
		xticks.append("工位%d" % i)
	setdpi = 720
	_bar(t, ct, xlabel, ylabel, xticks, setdpi, lbr)


def result(t):
	#
	# 输出结果
	#
	lbr, d, si, cm = _balance(t)
	print(str.format("平衡率LBR: {0:0.2f}%\n平衡损失率d: {1:0.2f}%\n平滑性指数SI: {2:0.2f}\n平衡状态: {3}", lbr, d, si, cm))

代码（pymprog数学模型）

from pymprog import *
import numpy as np
from ie.balance import result, status


def main():
	begin('assembly balance')
	job = np.load('a_datajob.npy').tolist()
	jobtime = np.load('a_datatime.npy').tolist()
	jobseqe = np.load('a_dataseq.npy').tolist()
	station = np.load('a_datastation.npy').tolist()
	ipo = iprod(job, station)
	x = var('x', ipo, kind=bool)
	ct = var('ct', kind=int)
	minimize(ct, 'cycle time')
	for i in job:  # 每个工序必须安排一个工位
		sum(x[i, k] for k in station) == 1
	
	for i, j in jobseqe:  # 工序顺序约束
		sum(k * x[j, k] - k * x[i, k] for k in station) >= 0
	
	for k in station:  # 工位时间约束
		sum(x[i, k] * jobtime[i] for i in job) <= ct
	
	def report():
		res = []  # 工序-工位
		for i in job:
			for j in station:
				if x[i, j].primal > 0:
					res.append([i, j])
		res.sort(key=lambda x: x[1])
		np.save('a_databalance.npy', res)
		st = []  # 工位-工序
		for i in station:
			temp = []
			for j in range(len(res)):
				if res[j][1] == i:
					temp.extend(res[j][0])
			st.append(temp)
		tm = []  # 工位-时间
		for s in st:
			temp = 0
			for j in s:
				temp += jobtime[j]
			tm.append(temp)
		for i in range(len(st)):
			print("工位{}:{}".format(i + 1, st[i]))
		print("节拍:",ct.primal)
		print("工位时间:\n", tm)
		result(tm)
		status(tm, ct.primal)
	
	
	solve()
	report()
	
	end()


if __name__ == "__main__":
	main()

代码（模型数据）

import numpy as np

job = "A,B,C,D,E,F,G,H,I,J,K".split(",")
jobtime = [45, 11, 9, 50, 15, 12, 12, 12, 12, 8, 9]
jobseq = [('A,B'), ('B,C'), ('C,F'), ('C,G'), ('F,J'),
          ('G,J'), ('D,E'), ('E,H'), ('E,I'), ('H,J'),
          ('I,J'), ('J,K')
          ]  # 不能有空格
station = range(1, 5)  # 设置工位数为3


def main():
	datajob = job
	datatime = {}
	dataseq = jobseq
	for i in range(len(job)):
		datatime[job[i]] = jobtime[i]
	
	for i in range(len(jobseq)):
		jobseq[i] = jobseq[i].split(',')
	
	np.save('a_datajob.npy', datajob)
	np.save('a_datatime.npy', datatime)
	np.save('a_dataseq.npy', dataseq)
	np.save('a_datastation.npy', station)
	
	a = np.load('a_datajob.npy')
	b = np.load('a_datatime.npy')
	c = np.load('a_dataseq.npy').tolist()
	d = np.load('a_datastation.npy')
	
	print("工序名称")
	print(a)
	print("工序时间")
	print(b)
	print("工序顺序")
	print(c)
	print("工位数")
	print(d)


if __name__ == "__main__":
	main()