数学建模实验六.doc

数学建模实验六上机用Lindo软件解决货机装运问题。某架货机有三个货仓:前仓、中仓、后仓。三个货舱所能装载的货物的最大重量和体积都有限,如表所示,并且,为了保持飞机的平衡,货舱中实际装载货物的重量必须与其最大容许重量成正比例前仓中仓后仓重量限制(吨)10168体积限制(米3)680087005300三个货舱装载货物的最大容许重量和体积现有四类货物供该货机本次飞行装运,其有关信息如表,最后一列指装运后所得的利润重量(吨)空间(米3/吨)利润(元/吨)货物1184803100货物2156503800货物3235803500货物4123902850四类装运货物的信息应如何安排装运,使该货机本次飞行获利最大?解答过程:模型建立:决策变量:用xij表示第i种货物装入第j个货舱的重量(吨),货舱j=1、2、3分别表示前仓、中仓、后仓。决策目标是最大化总利润,即MaxZ=3100(x11+x12+x13)+3800(x21+x22+x23)+3500(x31+x32+x33)+2850(x41+x42+x43)约束条件为:共装载的四种货物的总重量约束,即x11+x12+x13<=18x21+x22+x23<=15x31+x32+x33<=23x41+x42+x43<=122)三个货舱的重量限制,即x11+x21+x31+x41<=10x12+x22+x32+x42<=16x13+x23+x33+x43<=83)三个货舱的空间限制,即480x11+650x21+580x31+390x41<=6800480x12+650x22+580x32+390x42<=8700480x13+650x23+580x33+390x43<=53004)三个货舱装入重量的平衡约束,即模型求解将以上模型输入LINDO求解程序如下:max3100x11+3100x12+3100x13+3800x21+3800x22+3800x23+3500x31+3500x32+3500x33+2850x41+2850x42+2850x43stx11+x12+x13<=18x21+x22+x23<=15x31+x32+x33<=23x41+x42+x43<=12x11+x21+x31+x41<=10x12+x22+x32+x42<=16x13+x23+x33+x43<=8480x11+650x21+580x31+390x41<=6800480x12+650x22+580x32+390x42<=8700480x13+650x23+580x33+390x43<=53008x11+8x21+8x31+8x41-5x12-5x22-5x32-5x42=0x12+x22+x32+x42-2x13-2x23-2x33-2x43=0end得到结果如下:LPOPTIMUMFOUNDATSTEP7OBJECTIVEFUNCTIONVALUE1)