How to graph efficient frontier in excel

With the conflicting objectives, selecting one of them will always mean attributing a higher weight to one of the objectives over the others. However, none of the solutions is better than the other. Solution H already requires a decline of 62% and 74%, respectively, for the same objectives, which is nonimplementable at the company level. Solution F is obtained with a deterioration of the economic and environmental performances of 20% and 25%, respectively. Solutions F, G, and H are the closest to a so-called solution of compromise.

Even though the fixed costs with warehouses and entities decrease, the transportation costs increase significantly.

This is due to the reduction in the number of distribution centers that occurs from solution I (with three distribution centers) through Q (with only one distribution center), so as to locate the maximum number of workers in the less populated regions. In the third group (solutions I through Q), a significant deterioration of the economic and environmental performances is necessary for small improvements in the social performance of the supply chain. The increase in the transportation is balanced with the increase in the number of warehouses, to achieve the lowest possible cost and environmental impact. In the second group (solutions F, G, and H) the model locates two to three of the four distribution centers in the less populated regions to achieve a higher social benefit. This is possible without a meaningful increase in the transportation activities, which is the highest contributor to the increase in environmental impact and cost, as shown in Section 13.4.1. By simply replacing one distribution center located in a densely populated region with one that is located in a less populated region the social benefit increases significantly. This is achieved with different combinations of the four distribution centers. In fact, a significant increase in the social benefit (decrease in the social assessment objective function) can be obtained with a relatively small compromise of the economic and environmental performances. The first group comprehends solutions A through E, which appear to tend to the ideal solution. Regarding the social performance, an improvement is only attained with a deterioration of the economic and environmental performances.ДЄnalyzing the three-dimensional representation, it is possible to identify three distinctive groups of solutions. Hence, these results might in reality be different and more linear than presented. However, as mentioned before, the environmental impact methodology used does not take into account the difference between building several smaller warehouses and building only a large one.

This linearity results from the fact that both costs and environmental impact vary linearly with the area of the installed entities and with the distance traveled. One of the first conclusions that can be taken from the two dimensional representations is the fact that the economic and environmental objectives vary linearly, with the exception of solution A where a lower environmental impact is obtained at a higher cost than solution B. The ideal solution that would combine the lowest cost (from solution B) with the lowest environmental impact (from solution A) with the highest social benefit (from solution Q) is also represented for comparison (see FigureВ 13.5 on the left). Solution Q represents the one with the higher social benefit (lower value obtained with the minimization of the social assessment objective function, equivalent to scenario S3). Solutions A and B represent the solutions with less environmental impact (scenario S2) and lower cost (scenario S1), respectively. (b3) Environmental impact versus social assessment. (b2) Total cost versus social assessment. (b1)В Total cost versus environmental impact. (a) Multiobjective approach for the minimization of cost with social benefit and environmental impact limitation measured through ReCiPe.

How to graph efficient frontier in excel