生产计划与控制实验报告 1.docx
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生产计划与控制实验报告1
OperationsManagement
ExperimentationReport
Name:
陈凡
Class:
工业gc1102
Studentnumber:
0121104930822
SchoolofMechanicalandElectricalEngineering
TheWuhanUniversityofTechnology
12.11.2013
Experimentation1:
QuantitativeDemandingForecasting
QuarterlySales(thousandsofgallons)
Year
Q1
Q2
Q3
Q4
1
594
570
560
565
2
540
531
515
498
3
485
479
463
456
4
319
324
336
340
5
348
355
354
367
6
375
379
385
396
7
404
416
422
430
8
436
439
450
459
9
470
475
485
489
10
505
513
516
518
画出十年中每季度的销售量散点图,可以发现第四年开始每季度呈现上升的趋势,而前4年则大体呈下降趋势。
原因可能是国家政策改变或是销售地点改变引起的改变,所以做预测时舍弃前3年的数据。
再观察数据发现离散程度很小,俩变量相关性很强,所以使用线性规划的话能较准确合适地预测下一年四季度的销量。
如果是用移动平均或指数平滑的话,预测4季度则预测范围显得过大,如3,4季度可能需用到1,2季度销量的预测值所以可能预测误差偏大。
本次预测提供了40个数据,而且数据相关性较强,使用线性规划,借用专业软件工作量也不大。
所以综合考虑选用线性规划的方法进行预测,且不需要考虑季节因素。
***TIMESERIESREGRESSIONFORECASTING***
-----------------------------------------------------
PROBLEMNAME:
Untitled
-----------------------------------------------------
SalesSalesABSOLUTE
PERIODACTUALFORECASTERROR
1319.000314.6724.328
2324.000322.3291.671
3336.000329.9856.015
4340.000337.6422.358
5348.000345.2992.701
6355.000352.9552.045
7354.000360.6126.612
8367.000368.2681.268
9375.000375.9250.925
10379.000383.5814.581
11385.000391.2386.238
12396.000398.8942.894
13404.000406.5512.551
14416.000414.2071.793
15422.000421.8640.136
16430.000429.5210.479
17436.000437.1771.177
18439.000444.8345.834
19450.000452.4902.490
20459.000460.1471.147
21470.000467.8032.197
22475.000475.4600.460
23485.000483.1161.884
24489.000490.7731.773
25505.000498.4296.571
26513.000506.0866.914
27516.000513.7422.258
28518.000521.3993.399
-----------------------------------------------------
SalesCONFIDENCEINTERVAL(90%)
PERIODFORECASTLOWERBOUNDUPPERBOUND
29529.056522.695535.416
30536.712530.351543.073
31544.369538.008550.729
32552.025545.664558.386
REGRESSIONEQUATION:
Y=a+bX
WHERE:
Y=SalesX=TIMEPERIOD
a=307.0159b=7.6565
R=0.998R-SQUARE=0.9966
MEANABSOLUTEDEVIATION(MAD)FORTHELAST28PERIODS=2.953
MEANSQUAREDERROR(MSE)FORALLPASTPERIODS=12.909
MEANERROR(bias)FORALLPASTPERIODS=0.0
STANDARDERROR(sigmasubyx)IS=3.7285
相关系数R=0.998绝对系数R2=0.996
可以看出,自变量和应变量的相关性很强,故此预测使用的方法线性回归准确度较高。
绝对误差MAD反应预测精度,本实验预测精度为2.953,说明预测精度很高。
标准差反应数据的离散程度,本实验标准差为3.7285,较小,数据离散程度低。
此次预测绝对绝对系数很高,自变量和应变量的相关性很强,因此本人对线性回归的预测值很有信心。
用另一种长期预测模型季节性线性回归再一次进行预测,得出结果:
R=0.989,R-SQUARE=0.9771,
MEAN ABSOLUTEDEVIATION(MAD)FORTHELAST28PERIODS=7.927,
MEANSQUAREDERROR(MSE)RORALLPASTPERIODS=86.5,
MEANERROR(bias)FORALLPASTPERIODS=-0.152,
STANDARDERROR(sigmasubyx)IS=9.6552
对比可以看出本次结果中相关系数与绝对系数小于上组,所以,无需考虑季节性因素影响的预测模型。
Experimentation2:
LinearProgramming(LP)
Case1:
QualityPixelsInc.
**LINEARPROGRAMMING***
==========================================================================
PROBLEMNAME:
Untitled
==========================================================================
MinZ=180X1+160X2+60X3+40X4+120X5+150X6+90X7+30X8
+150X9+130X10+190X11+140X12+40X13+35X14+160X15
+150X16+110X17+125X18+80X19+105X20+95X21+125X22
+60X23+50X24
ST
(1)1X1+1X2+1X3+1X4+1X5+1X6<=30000
(2)1X7+1X8+1X9+1X10+1X11+1X12<=20000
(3)1X13+1X14+1X15+1X16+1X17+1X18<=40000
(4)1X19+1X20+1X21+1X22+1X23+1X24<=50000
(5)1X1+1X7+1X13+1X19>=15000
(6)1X2+1X8+1X14+1X20>=15000
(7)1X3+1X9+1X15+1X21>=15000
(8)1X4+1X10+1X16+1X22>=20000
(9)1X5+1X11+1X17+1X23>=20000
(10)1X6+1X12+1X18+1X24>=15000
(11)1X1+1X7+1X13+1X19<=30000
(12)1X2+1X8+1X14+1X20<=25000
(13)1X3+1X9+1X15+1X21<=25000
(14)1X4+1X10+1X16+1X22<=40000
(15)1X5+1X11+1X17+1X23<=35000
(16)1X6+1X12+1X18+1X24<=25000
==========================================================================
SOLUTION:
==========================================================================
ITERATIONNUMBER12
VARIABLEMIXSOLUTION
--------------------
X815000.000
Slack25000.000
Slack325000.000
Slack410000.000
X1315000.000
X2320000.000
X215000.000
X420000.000
X310000.000
X2415000.000
Slack1115000.000
Slack1210000.000
Slack1310000.000
Slack1420000.000
Slack1515000.000
Slack1610000.000
Z4875000.000
==========================================================================
SENSITIVITYANALYSIS:
==========================================================================
CONSTRAINTS:
--------------------------------------------------------------------------
RANGEOFRHS
CONSTRAINTTYPEOFSHADOWFORWHICHSHADOW
NUMBERCONSTRAINTPRICEPRICEISVALID
------------------------------------------
1<=35.00020000.--35000.
2<=0.00015000.--+INF
3<=0.00015000.--+INF
4<=0.00040000.--+INF
5>=40.0000.--30000.
6>=30.0000.--20000.
7>=95.00010000.--25000.
8>=75.00015000.--30000.
9>=60.0000.--30000.
10>=50.0000.--25000.
11<=0.00015000.--+INF
12<=0.00015000.--+INF
13<=0.00015000.--+INF
14<=0.00020000.--+INF
15<=0.00020000.--+INF
16<=0.00015000.--+INF
NOTE:
THESHADOWPRICEREPRESENTSTHEAMOUNTZWOULD
CHANGEIFACONSTRAINT'SRHSCHANGEDONEUNIT.
--------------------------------------------------------------------------
DECISIONVARIABLES:
--------------------------------------------------------------------------
NONBASICAMOUNTZISREDUCED(MAX)ORINCREASED(MIN)
VARIABLEFORONEUNITOFXINTHESOLUTION
----------------------------------------------------
X1175.
X2165.
X595.
X6135.
X750.
X955.
X1055.
X11130.
X1290.
X145.
X1565.
X1675.
X1750.
X1875.
X1940.
X2075.
X2250.
--------------------------------------------------------------------------
4.1如下图给出最佳的运输方案:
Plant
Bangkok
Shanghai
SaoPaulo
Dallas
Madrid
Cairo
Mexicocity
0
0
10000
20000
0
0
Seoul
0
15000
0
0
0
0
HongKong
15000
0
0
0
0
0
Warsaw
0
0
5000
0
20000
15000
4.2HowcouldcostschangeifthecapacityoftheMexicoCityplantdecreasedto26,000pallets?
Increasedto36,000pallets?
答:
墨西哥的生产能力减少到26000,成本会增加;增加到36000,成本减少。
4.3HowcouldcostschangeiftheminimumannualrequirementsattheDallaswarehousedecreasedto14,000pallets?
Increasedto24,000pallets?
答:
当Dallas的最小需求减少到14000,成本减少;增大到24000,成本会增加。
4.4您好!
由上面的计算可知:
slack2slack3slack4均大于0,这表示Seoul、HongKong、Warsaw所对应的资源有剩余,若要减小生产成本,可以提高墨西哥工厂的生产能力。
由影子价格可知,当其产量在20000-35000时,生产每增加一个单位成本会增加35,当产量超过35000时,成本会下降。
注:
1、影子价格:
在其它条件不变的情况下,单位资源变化所引起的目标函数的最优值的变化。
这个定义是基于线性规划中的合理利用有限资源以求得最好的经济效果的规划问题。
影子价格正是这种假设条件中单位资源对目标极值的贡献,是资源的单位价格,反映资源在企业内部运用的贡献情况,称之为资源的影子价格。
通过对偶规划方程求得。
2、松弛变量(slackvariablevalues):
若所研究的线性规划模型的约束条件全是小于类型,那么可以通过标准化过程引入M个非负的松弛变量。
当约束条件为“≤”(“≥”)类型的线性规划问题,可在不等式左边加上(或者减去)一个非负的新变量,即可化为等式。
这个新增的非负变量称为松弛变量(或剩余变量),也可统称为松弛变量。
在目标函数中一般认为新增的松弛变量的系数为零。
case2:
IntegratedProductsCorporation
***LINEARPROGRAMMING***
==========================================================================
PROBLEMNAME:
Untitled
==========================================================================
MinZ=152X1+120X2+165X3+139X4+169X5+49X6+65X7
+55X8+50X9+60X10+65X11+55X12+60X13+45X14
+65X15+75X16+85X17+69X18+81X19+79X20+120X21
+122X22+125X23+136X24+119X25
ST
(1)1X1+1X2+1X3+1X4+1X5=1
(2)1X6+1X7+1X8+1X9+1X10=1
(3)1X11+1X12+1X13+1X14+1X15=1
(4)1X16+1X17+1X18+1X19+1X20=1
(5)1X21+1X22+1X23+1X24+1X25=1
(6)1X1+1X6+1X11+1X16+1X21=1
(7)1X2+1X7+1X12+1X17+1X22=1
(8)1X3+1X8+1X13+1X18+1X23=1
(9)1X4+1X9+1X14+1X19+1X24=1
(10)1X5+1X10+1X15+1X20+1X25=1
==========================================================================
SOLUTION:
==========================================================================
ITERATIONNUMBER16
VARIABLEMIXSOLUTION
--------------------
X21.000
X120.000
X181.000
X141.000
X251.000
X61.000
X110.000
X160.000
X210.000
Artificial100.000
Z402.000
AssignmentProblemSolution
Dest1Dest2Dest3Dest4Dest5
Object101000
Object210000
Object300010
Object400100
Object500001
Totalcostorprofitis$402
==========================================================================
SENSITIVITYANALYSIS:
==========================================================================
CONSTRAINTS:
--------------------------------------------------------------------------
RANGEOFRHS
CONSTRAINTTYPEOFSHADOWFORWHICHSHADOW
NUMBERCONSTRAINTPRICEPRICEISVALID
------------------------------------------
NOTE:
RHSshadowpricesarenotmeaningful
foranassignmentproblem.
--------------------------------------------------------------------------
DECISIONVARIABLES:
--------------------------------------------------------------------------
NONBASICAMOUNTZISREDUCED(MAX)ORINCREASED(MIN)
VARIABLEFORONEUNITOFXINTHESOLUTION
----------------------------------------------------
NOTE:
Herearenonbasicvariableswithzeroshadow
prices.Othershadowpricevaluesareof
questionablevalueinassignmentproblems.
--------------------------------------------------------------------------
7.1Fullyinterpretthemeaningofthesolutionthatyouobtai