能源化工循环经济中类Cobb-Douglas生产函数简化及资源优化分配

为了使能源化工循环经济工业园区在一定资源使用量下的产出最大，需要对园区内企业间进行原料资源的优化配置. 分析了能源化工企业产出和各个生产要素的关系，以Cobb-Douglas生产函数为基础，构建描述循环经济中的能源化工企业生产特点的类Cobb-Douglas生产函数；为方便求解，通过进一步假设和简化得到能源化工企业产出与原料使用量的线性关系，从而将原料优化配置问题简化成可计算的线性规划问题. 为不使优化后利润率低的企业分配不到资源，人为设置优化后的利润不低于原规划固定成本一定比例，称为利润下限，并以陕北锦界工业园区为例求解，在无利润下限的约束下，优化后的园区利润提高了76.0%；有利润下限的约束，优化后的园区利润提高了26.8%. 将该资源优化方法应用于正在规划的循环经济园区，可得到园区产出（或利润）最大，且每个企业的利润率最高；对于已建设好的园区，由于企业生产规模不能改变，求解只可以得到园区产出（或利润）最大的结果，该方法可为正在建设或已建成的循环经济工业园区中企业间资源分配优化或企业规模优化提供借鉴.

Simplification of quasi-Cobb-Douglas production function and the optimization of resources distribution for circular economy

To maximize the output of an energy and chemical industry zone under certain resources consumption, the distribution of resources between enterprises should be optimized. The relationship between the output and the various production factors was analyzed. And on the basis of Cobb-Douglas production function, a generic production function that could describe the production trait of a energy and chemical enterprise was generated. Through further assumption and simplification, the relationship between output and resources comsumption was derived, which simplifies the calculation of optimization of resources distribution as computable linear programming. To avoid that certain enterprise had no resources via optimization, the linear programming should be subject to artificial lower limit constraint of gain. Jinjie industry zone in Shaanxi province was taken as an example to explain the optimization method resulting in that the gain of this industry zone increased 76.0% without lower limit constraint of gain and 26.8% with lower limit constraint of gain after optimization. As for industry zone under planning, maximum output of overall industry zone as well as profit margins of each enterprise could be obtained by this method, while those constructed could only obtain a maximum output because scale of each enterprise can't be changed. This method could be a reference for the optimization of resources distribution or the enterprise scale in an energy and chemical industry zone.