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【解】1线性规划数学模型车间基本生产工人工时计算如下S=27X22X8-2-4=4590人时/月按产量1%的工废实际可用时间4590/
1.1=4544每种设备月实际可利用工时如表C-2最后一列从表C-3中减去料废成本后每种排气管利润如下表所示12345678产品项目毛坯价格981049411210697104102料废成本
1.
962.
081.
882.
242.
121.
942.
082.04辅料消耗22222222动能消耗1010101010101010工具等消耗10131214158911管理费用
1.
4551.
0991.
211.
441.
1881.
22651.
3081.56税收
151614.
81716.
514.
515.
615.5售价
150160.
1149172166145.
6157.
8155.8利润元
11.
58511.
92113.
1113.
3213.
19210.
933513.
81211.7根据给定的条件及要求,设R,X2,…X8分别为第一种、第二种第八种排气管的月产量,月产量单位为1000根/月将目标函数取为每月的总产品利润,得出关于月计划的线性规划模型为max Z=
11.585%+
11.921x+
13.1lx+
13.32x+
13.192x+
10.9335x+
13.812x+
11.7x
234567841.9x,+
43.9X+
42.3x.+
47.8x+
46.5x+
39.7x+
49.2x+
45.744544工时约束94s
74.Ox+
4.5x+
4.8不+
5.8x+
5.2x+
4.0x+
4.6x+
5.641378设备工时约束4s
73.9X1+
4.5X+
4.3X+
5.0X+
4.9X+
4.4x+
5.1x+
4.8x
138623456785.9x+
5.8X+
5.7A\+
6.3儿+
6.5%+
6.Ox+
6.6x+
6.
442061973.5%+
3.0X+3・7%3+
4.0工4+
3.8/+
3.0X+
4.lx+
3.4x
69326785.8玉+
6.2%2+
5.77+
6.4X+
6.3x+
6.0x+
6.5x+
6.
245206745675.5%+
5.7X+
4.7%3+
6.0x+
5.9x+
5.2x+
6.2x+
5.
641382245675.9%+
3.8X+
4.0忍+4・1%4+3・7%5+
3.5x+
4.lx+
3.6713622674・1%]+4・0%2+
4.0X+
4.3%4+
4.2x+
3.8x+
4.3x+
4.3x
1370356782.5%+
2.9X+2JX+
3.0X+
3.0X+
2.5x+
3.1x+
2.8x
69323456782.8%+
2.9X+
2.1X+
3.2X+
3.0X+
2.5x+
3.2x+
3.0x6932345678x,10X-X=324x606X710%,工2,工3,工4,工5,%6,%7,422用WinQSB软件求解:Variable-X1X2X3X4X5X6X7X8Direction R.H.S.Maximize
11.
58511.
92113.
1113.
3213.
19210.
933513.
81211.7C
141.
943.
942.
347.
846.
539.
749.
245.7=4544C
244.
54.
85.
85.
244.
65.6=1378C
33.
94.
54.
354.
94.
45.
14.8=1386C
45.
95.
85.
76.
36.
566.
66.4=2061C
53.
533.
743.
834.
13.4=693C
65.
86.
25.
76.
46.
366.
56.2=2067C
75.
55.
74.
765.
95.
26.
25.6=
1382083.
93.
844.
13.
73.
54.
13.6=1362C
94.
1444.
34.
23.
84.
34.3=1370C
102.
92.733Z
53.
12.8=693C
112.
82.
92.
13.
232.
53.23=693C1210000000=10C1310-10000=3C140100000=5C1500000100=60C1600000010=10000LowerBound00000UpperBound RM M M M M M MVariableType Continuous Continuous Continuous ContinuousContinuousContinuousContinuousContinuous08:21:59Tuesday December142010Decision SolutionUnit Costor TotalReduced BasisAllowable AllowableVariableValue Profitcj ContributionCost StatusMin.疝Max.cj1X
110.
000011.
5850115.85000basic-M
12.98602X
23.
000011.
921035.76300basic-M
15.10053X
382.
773013.11001,
085.15500basic
12.0005M4X
4013.32000-
3.1795at bound-M
16.49955X
5013.19200-
1.2197at bound-M
14.41176X
6010.93350-
1.3707at bound-M
12.30427X
710.
000013.
8120138.12000basic-M
15.24858X
8011.70000-
2.4638at bound-M
14.1638Objective Function Max.=1J
74.8880Left HandRight HandSlack orShadow Allowable AllowableConstraint DirectionSide Side SurplusPrice Min.RHS Max.RHS=1C14,
544.
000000.3099L
254.20002C
2496.8106=1J
78.
0000881.
18930496.8107M3C
3459.4241=1,
386.
0000926.
57590459.4241M4C
4614.2064=2,
061.00001,
446.
79400614.2064M5C
5391.2603=
693.
0000301.
73970391.2603M6C
6613.4064=2,
067.00001,
453.
59400613.4064M7C
7523.1333=U
82.
0000858.
86670523.1333M8C
8422.4922=1,
362.
0000939.
50780422.4922M9C
9427.0922=1J
70.
0000942.
90780427.0922M10C
10288.1872=
693.
0000404.
81280288.1872M11C
11242.5234=
693.
0000450.
47660242.5234M12C
1210.0000=
10.00000-
1.
4010088.515513C
133.0000=
3.00000-
1.
6849077.938514C
1482.7730=
5.
000077.77300-M
82.773015C150=
60.
000060.000000M16C
1610.0000=
10.00000-
1.
4365076.8659X=10000,3000,82773,
0.0,0,10,0;Z=1374888元3月生产应如下按排第一〜第八种排气管分别按排10000,3000,82773,0,0,0,100,根月最大可获利润1374888元.结果分析41资源利用率如下表资源月可利用工时实际利用工时剩余资源实际利用率
1.平面铳床
1378496.
8106881.
1936.05%
2.卧铳床
1386459.
4241926.
5833.15%
3.组合钻
2061614.
20641446.
7929.80%
4.单面铳床
693391.
2603301.
7456.46%
5.攻丝床
2067613.
40641453.
5929.68%
6.精铳床
1382523.
1333858.
8737.85%7,扩孔钻床
1362422.
4922939.
5131.02%
8.摇臂钻床
1370427.
0922942.
9131.17%
9.去毛刺机
693288.
1872404.
8141.59%
10.清洗机
693242.
5234450.
4835.00%人工
454445440.
00100.00%结果表明,各种设备负荷都远没有达到饱和,而人工已经满负荷运转,所以应提高人工的有效工时2人工工时的影子价格等于
0.3099,所有设备的影子价格全等于零,因此人工工时是制约车间产量或利润增长的关键资源3将模型改为maxZ=
11.585%+
11.921尤2+13・11玉+
13.32%+
13.192/+
10.93354+
13.812~+1L7玉
41.9x+
43.9%+
42.3冬+
47.8%+
46.5x+
39.7x+
49.2x+
45.7x4544工时约束
74.0匹+
4.5%+
4.8项+
5.8X+
5.2X+
4.0x+
4.6x+
5.641378设备工时约束4671J•J Vz/
3.9%+
4.5X+
4.3%3+
5.0X+
4.9x+
4.4x+
5.1x+
4.
8413865.9X1+
5.8%+
5.7X+
6.3X+
6.5X+
6.0x+
2456734566.6x+
6.4x
20613.5X]+
3.0%2+3・7%3+
4.0%4+
3.8x+
3.0x+
4.1x+
3.4x
6937856785.8X]+
6.2々+5・7七+
6.4X+
6.3X+
6.0%+
6.5X+
6.2X
20675.5x,+
5.7X+
4.7X+
6.0x+
5.9x+
5.2x+
6.24567823456七+
5.6/
13825.9%+
3.8X+
4.0忍+
4.卜+
3.7X+
3.5X4-
4.1X+
3.6/
513624.1Xj+
4.0X+
4.0^+
4.3X+
4.2X245672345+
3.8X+
4.3X+
4.34《
1370672.5x,+
2.9x,+
2.7+
3.Ox+
3.0x+
2.54+
3.1为+
2.8/693乙,s,f Ju o
2.8x+
2.9x+
2.1%,+
3.2X+
3.0x+
2.5x+
3.2x+
3.046934s7JL4D1J U,O%]15,x5,x5,x3234忍215,x60,x10,4-6061%,/,工3,工4,工5,工6,工7,420用WinQSB软件求解,结果显示无可行解见下表Right HandShadow AddMore ThanAdd UpToConstraint DirectionSide PriceThis To RHS ThisToRHS1Cl4,
544.
000.2561,
639.504,
636.88=2C21,
378.000-
896.4016M=3C31,
386.000-
903.7013M=4C42,
061.000-1,
400.60M=5C56930-
344.9759M<二6C62,
067.000-1,
410.93M=7C7v=1,
382.000-
800.4016M8C81,
362.000-
967.651M<二9C91,
370.000-
936.7637M=10CIO6930-
409.9508M=11Cll=6930-
403.6258M12C
12150.8579—M-3=13C
1350.6818-
37.3462-
37.3462>二14C14=
52.2805-
38.7589-
38.758915C1530—M-3=16C16=150—M-1517C
17600.7696-M-
35.8753=18C18100-M-10=191cl9|[60|0|-M-
35.8753令所有产量为等式约束,给定一个较大的人工工时数,如9000小时,求解后显示工时的参数变化区间为
7516.4,M,见下表所示说明人工工时最少要加班7517—4544=2973小时设备时间有剩余Decision SolutionUnit Costor TotalReduced BasisAllowable AllowableVariableValue Profitcj ContributionCost StatusMin.cj Max.cj[XI
15.000011~
5850173.77500basic M M2X
25.
000011.
921059.60500basic-M M3X
35.
000013.
110065.55000basic-M M4X
43.
000013.
320039.96000basic-MM5X
515.
000013.
1920197.88000basic-MM6X
660.
000010.
9335656.01000basic-MM7X
710.
000013.
8120138.12000basic-MM8X
860.
000011.
7000702.00000basic-M MObjectiveFunctionMax.=2,
032.9000ShadowLeft HandRight HandSlack orAllowableAllowableConstraintDirection PriceSurplus—SideSideMin.RHS Max.RHSIC17,
516.40009,
000.0000L
483.600007,
516.4000M=2C
2823.90001,
378.
0000554.
10000823.9000M=3C
3794.00001,
386.
0000592.
00000794.0000M=4C41,
072.40002,
061.
0000988.60000L
072.4000M=5C
5580.
0000693.
0000113.
00000580.0000M=G C61,
057.20002,
067.00001,
009.80000L
057.2000M=7C
7951.0000K
382.
0000431.
00000951.0000M=8C
8632.30001,
362.
0000729.
70000632.3000M=9C
9706.40001,
370.
0000663.
60000706.4000M=10C
10468.
5000693.
0000224.
50000468.5000M=11C
11483.
6000693.
0000209.
40000483.6000M=12C
1215.0000—
15.
0000011.
5850047.285713C
135.
00005.
0000011.
9210038.7950=14C
145.
00005.
0000013.
1100035.5405—15C
153.0000—
3.
0000013.
3200031.250016C16_
15.
000015.
0000013.
1920044.7368—57C
1760.0000=
60.
0000010.
9335097.370318C
1810.
000010.
0000013.
8120037.5610=19C
1960.0000=
60.
0000011.
7000092.46394该车间设备的生产能力已经相当充足,但人工的严重不足限制了生产而且人工加班不是长久之计,所以解决方案是增加生产工人人数、提高设备的无人看管性或改进工艺降低人工工时消耗。