Sytech国际公司的生产优化问题

Sytech国际公司的生产优化问题2013PB第9组谢质洁、祝俊元、李甲祥、叶佐旭、陈聪任务分配背景介绍数据分析Q&APPT制作李甲祥叶佐旭PPT演讲谢质洁陈聪祝俊元目录背景介绍数据分析Q&A公司简介公司名称:Sytech国际公司公司背景：同行业出于领先地位的计算机和外围设备的制造商成立时间：1951年公司总部：马萨诸塞州伯灵顿地区产品：大型计算机、小型计算机、个人计算机和打印机工厂所在地：伯灵顿、爱尔兰、中国台湾产品主要市场：北美和欧洲市场需求预测产品北美欧洲大型计算机962321小型计算机4,4171,580个人计算机48,21015,400打印机15,5406,850*对一个季度时间段里四个产品的总量预测一直是相当精确的。工厂生产能力工厂空间供应能力(1000平方英尺)劳动供应能力(1000小时)伯灵顿540.71277.71中国台湾201.00499.24爱尔兰146.9080.17资源利用率产品空间/单位劳动小时/单位大型计算机17.4879.00小型计算机17.4831.50个人计算机3.006.90打印机5.305.60单位利润贡献工厂伯灵顿中国台湾爱尔兰大型计算机北美$16,136.46$17,358.14$15,652.68欧洲$13,694.03$14,709.96$13,216.34小型计算机北美$9,092.13$10,025.32$9,429.94欧洲$7,133.90$7,926.63$7,554.28个人计算机北美$1,457.18$1,395.35$1,197.52欧洲$1,037.57$1,082.49$1,092.61打印机北美$1,663.51$1,554.55$1,478.90欧洲$1,345.43$1,270.16$1,312.44假设Xijk表示在工厂j制造用于在市场k销售的产品i的数量，其中：i:1-大型计算机；2-小型计算机；3-个人计算机；4-打印机j:1-伯灵顿；2-中国台湾；3-爱尔兰k:1-北美；2-欧洲根据“单位贡献利润”表列出利润最大化的目标函数为MAX:16136.46X111+13694.03X112+17358.14X121+14709.96X122+15652.68X131+13216.34X132+8914.47X211+6956.23X212+9951.04X221+7852.36X222+9148.55X231+7272.89X232+1457.18X311+1037.57X312+1395.35X321+1082.49X322+1197.52X331+1092.61X332+1663.51X411+1345.43X412+1554.55X421+1270.16X422+1478.90X431+1312.44X432根据“资源利用率表”和“工厂的生产能力表”可列出空间约束和劳动力约束空间约束：17.48X111+17.48X112+17.48X211+17.48X212+3X311+3X312+5.3X411+5.3X412≤54071017.48X121+17.48X122+17.48X221+17.48X222+3X321+3X322+5.3X421+5.3X422≤2010017.48X131+17.48X132+17.48X231+17.48X232+3X331+3X332+5.3X431+5.3X432≤146900劳动力约束：79X111+79X112+31.5X211+31.5X212+6.9X311+6.9X312+5.6X411+5.6X412≤27771079X121+79X122+31.5X221+31.5X222+6.9X321+6.9X322+5.6X421+5.6X422≤49924079X131+79X132+31.5X231+31.5X232+6.9X331+6.9X332+5.6X431+5.6X432≤80170同理可由“市场需求预测表”列出需求约束：X111+X121+X131≤962X112+X122+X132≤321X211+X221+X231≤4417X212+X222+X232≤1580X311+X321+X331≤48210X312+X322+X332≤15400X411+X421+X431≤15540X412+X422+X432≤6850大型计算机小型计算机个人计算机打印机不足或过剩北美欧洲北美欧洲北美欧洲北美欧洲空间劳动力伯灵顿001,683014,395015,5406,850349,4470中国台湾9623211,769033,81515,4000002,564爱尔兰009651,5800000102,4120总计9623214,4171,58048,21015,40015,5406,850不足或过剩00000000需求9623214,4171,58048,21015,40015,5406,850总利润贡献$194,244,024.67将目标函数和约束条件录入计算机运算求得以下模型(a)假设爱尔兰的劳动管理制度发生变化，在爱尔兰工厂工作的劳动供应能力减少到78,000工时大型计算机小型计算机个人计算机打印机不足或过剩北美欧洲北美欧洲北美欧洲北美欧洲空间劳动力伯灵顿002,001012,942015,5406,850348,2420中国台湾9623211,520035,26815,400000394爱尔兰008961,5800000103,6160总计9623214,4171,58048,21015,40015,5406,850不足或过剩00000000需求9623214,4171,58048,21015,40015,5406,850总利润贡献$193,879,659.74ResourceUtilizationbyPlantActualLimitBurlington-Space191,263.41540,710.00Taiwan-Space201,000.00201,000.00Ireland-Space44,487.99146,900.00Burlington-Labor277,710.00277,710.00Taiwan-Labor496,675.50499,240.00Ireland-Labor80,170.0080,170.00ResourceUtilizationbyPlantActualLimitBurlington-Space192,467.59540,710.00Taiwan-Space201,000.00201,000.00Ireland-Space43,283.81146,900.00Burlington-Labor277,710.00277,710.00Taiwan-Labor498,845.50499,240.00Ireland-Labor78,000.0078,000.00↑318↓1457↓249↑1457↓69↓364364.93由于爱尔兰工厂工作的劳动供应能力从80,170减少到78,000，减少了2,170工时，从敏感性报告中可以看到该数值属于影子价格允许的减量范围。194,244,024.67-167.91*2,170=193,879,659.97从另一个角度也印证了结论。单元格名字终阴影约束允许的允许的值价格限制值增量减量$C$78Burlington-SpaceActual191,263.410.005407101E+30349446.5873$C$79Taiwan-SpaceActual201,000.00348.492010006367.7170466695.551304$C$80Ireland-SpaceActual44,487.990.001469001E+30102412.0127$C$81Burlington-LaborActual277,710.00160.4827771014645.749212564.5$C$82Taiwan-LaborActual496,675.500.004992401E+302564.5$C$83Ireland-LaborActual80,170.00167.918017011475.004972564.5$C$87NorthAmericanMainFrameActual9621126696232.46202532364.2858722$C$88NorthAmericanMiniActual44173859441781.41269841364.2858722$C$89NorthAmericanPCActual4821035048210371.66666672122.572349$C$90NorthAmericanPrinterActual1554076515540457.94642862615.312358$C$91EuropeanMainFrameActual321861832132.46202532321$C$92EuropeanMiniActual15801984158081.41269841364.2858722$C$93EuropeanPCActual154003715400371.66666672122.572349$C$94EuropeanPrinterActual68504476850457.94642862615.312358结论：由于爱尔兰工厂的劳力属于紧约束，变动范围在影子价格的有效区间内，且影子价格在有效区间为正数，故随着劳动供应能力的减少，总利润贡献也会随着减少。(b)假设爱尔兰的劳动管理制度发生变化，在爱尔兰工厂工作的劳动供应能力增加到95,000工时大型计算机小型计算机个人计算机打印机不足或过剩北美欧洲北美欧洲北美欧洲北美欧洲空间劳动力伯灵顿000024,322015,5404,083363,7430中国台湾9623213,473023,88815,40000017,395爱尔兰009441,5800002,76788,1150总计9623214,4171,58048,21015,40015,5406,850不足或过剩00000000需求9623214,4171,58048,21015,40015,5406,850总利润贡献$196,527,672.65ResourceUtilizationbyPlantActualLimitBurlington-Space191,263.41540,710.00Taiwan-Space201,000.00201,000.00Ireland-Space44,487.99146,900.00Burlington-Labor277,710.00277,710.00Taiwan-Labor496,675.50499,240.00Ireland-Labor80,170.0080,170.00ResourceUtilizationbyPlantActualLimitBurlington-Space176,966.82540,710.00Taiwan-Space201,000.00201,000.00Ireland-Space58,784.58146,900.00Burlington-Labor277,710.00277,710.00Taiwan-Labor481,845.50499,240.00Ireland-Labor95,000.0095,000.00↑2283647.98终阴影约束允许的允许的单元格名字值价格限制值增量减量$C$78Burlington-SpaceActual191,263.410.005407101E+30349446.5873$C$79Taiwan-SpaceActual201,000.00348.492010006367.7170466695.551304$C$80Ireland-SpaceActual44,487.990.001469001E+30102412.0127$C$81Burlington-LaborAct