电器公司生产计划案例分析报告

《数据模型与决策》电器公司成产计划案例分析报告工商管理学院MBA学习中心班级：2017级MBA全日制1班姓名：苏景霞学号：2017217536

电器公司产品计划1案例描述问题背景某公司从事电脑配件的生产销售业务，主要产品的市场需求和市场价格如表1所示。表1产品市场需求及价格产品电源线硬盘线软盘线打印机线CD线最低销售数量20000070000450003000035000单价6.515.312.214.53.2单位产品生产需要的成品材料或元件如表2所示。表2单位产品生产需要的成品材料或元件成品材料或元件单位主要产品电源线硬盘线软盘线打印机线CD线塑料包皮克6012080100201#铜芯线克120180160150602#铜芯线克—30203010触头个44836488塑胶卡壳克104030405合金插头根44836488合金螺丝根———4—各种产品单位成品材料（或元件）所需要的原材料情况如表3所示。表3单位成品材料（或元件）生产需要的原材料情况成品材料或元件单位原材料（克）塑胶粒铜清洗剂焊丝金精钢塑料包皮克1.00120.051#铜芯线克1.01250.0062#铜芯线克1.00820.004触头个0.0020.0120.00050.15塑胶卡壳克1.0050.002合金插头根0.0250.0050.0052.05合金螺丝根0.2150.12525.12.3目标函数已知：利润=收入—成本收入来自电脑配件的销售业务，已知产品的需求及价格，所以收入可表示为：6.5*x1+15.3*x2+12.2*x3+14.5*x4+3.2*x5成本来自两部分：一部分是生产过程中的6道工序，单位工时的费用；一部分是：购买原材料所需费用。工序成本：冲压：3.25/60*（0.085*x1+0.365*x2+0.28*x3+0.38*x4+0.45*x5）成型：4/60*（0.05*x1+0.125*x2+0.105*x3+0.16*x4+0.02*x5）清洗：2.57/60*（0.24*x1+0.275*x2+0.25*x3+0.26*x4+0.12*x5）组装：2.85/60*（0.152*x1+0.125*x2+0.105*x3+0.185*x4+0.075*x5）喷漆：2.9/60*（0.062*x1+0.1025*x2+0.0985*x3+0.0855*x4+0.025*x5）包装：2.8/60*（0.05*x1+0.055*x2+0.055*x3+0.06*x4+0.025*x5）整理为：0.031*x1+0.054*x2+0.045*x3+0.058*x4+0.037*x5原材料成本：塑胶粒：3.78/1000*（70.122*x1+160.344*x2+110.246*x3+140.32*x4+25.049*x5）铜：18.5/1000*（121.6*x1+213.696*x2+183.064*x3+184.181*x4+71.032*x5）清洗剂：7.4/1000*（3.768*x1+7.616*x2+5.352*x3+6.936*x4+1.466*x5）焊丝：6.45/1000*（0.068*x1+0.816*x2+0.612*x3+0.816*x4+0.136*x5）金：95.2*（0.002*x1+0.024*x2+0.018*x3+0.024*x4+0.004*x5）精钢：2.18/1000*（8.8*x1+105.6*x2+79.2*x3+206*x4+17.6*x5）整理为：2.752*x1+7.136*x2+5.733*x2+6.728*x2+1.839*x2则目标函数可表示为：Z=收入-工序时间成本-原材料成本整理后可得：Z=3.715*x1+8.109*x2+6.420*x3+7.712*x4+1.323*x5约束条件需要满足产品市场的最低销售数量：电源线：x1>=200000硬盘线：x2>=70000软盘线：x3>=45000打印机线：x4>=30000CD线：x5>=35000产品生产过程中需要经过6道工序，每道工序有工时限制：冲压：0.085*x1+0.365*x2+0.28*x3+0.38*x4+0.45*x5<=1350*60成型：0.05*x1+0.125*x2+0.105*x3+0.16*x4+0.02*x5<=600*60清洗：0.24*x1+0.275*x2+0.25*x3+0.26*x4+0.12*x5<=1800*60组装：0.152*x1+0.125*x2+0.105*x3+0.185*x4+0.075*x5<=1000*60喷漆：0.062*x1+0.1025*x2+0.0985*x3+0.0855*x4+0.025*x5<=650*60包装：0.05*x1+0.055*x2+0.055*x3+0.06*x4+0.025*x5<=500*60原材料供应量限制：塑胶粒：70.122*x1+160.344*x2+110.246*x3+140.32*x4+25.049*x5<=36500*1000铜：121.6*x1+213.696*x2+183.064*x3+184.181*x4+71.032*x5<=60000*1000清洗剂：3.768*x1+7.616*x2+5.352*x3+6.936*x4+1.466*x5<=1800*1000焊丝：0.068*x1+0.816*x2+0.612*x3+0.816*x4+0.136*x5<=300*1000金：0.002*x1+0.024*x2+0.018*x3+0.024*x4+0.004*x5<=4000精钢：8.8*x1+105.6*x2+79.2*x3+206*x4+17.6*x5<=21000*1000模型建立根据上述条件，整理之后的线性规划模型如下：MaxZ=3.716*x1+8.109*x2+6.420*x3+7.712*x4+1.323*x5S.t.0.085*x1+0.365*x2+0.28*x3+0.38*x4+0.45*x5<=1350*600.05*x1+0.125*x2+0.105*x3+0.16*x4+0.02*x5<=600*600.24*x1+0.275*x2+0.25*x3+0.26*x4+0.12*x5<=1800*600.152*x1+0.125*x2+0.105*x3+0.185*x4+0.075*x5<=1000*600.062*x1+0.1025*x2+0.0985*x3+0.0855*x4+0.025*x5<=650*600.05*x1+0.055*x2+0.055*x3+0.06*x4+0.025*x5<=500*6070.122*x1+160.344*x2+110.246*x3+140.32*x4+25.049*x5<=36500*1000121.6*x1+213.696*x2+183.064*x3+184.181*x4+71.032*x5<=60000*10003.768*x1+7.616*x2+5.352*x3+6.936*x4+1.466*x5<=1800*10000.068*x1+0.816*x2+0.612*x3+0.816*x4+0.136*x5<=300*10000.002*x1+0.024*x2+0.018*x3+0.024*x4+0.004*x5<=40008.8*x1+105.6*x2+79.2*x3+206*x4+17.6*x5<=21000*1000x1>=20000x2>=70000x3>=45000x4>=30000x5>=35000模型求解录入数据：模型求解：综合分析由模型结果可知：在满足各工序及原材料的要求下，可获得的最大利润为：1,820,562元。在利润最高的情况下，电源线、硬盘线、软盘线、打印机线、CD线各生产数量：184,706、70000、450000、30000、3500