Value Path Approach

The presentation of results presents a critical link, in any multi-objective problem. Any sophisticated analysis, just becomes numbers, if they are not presented to the DM in an effective way. In case of multi-objective problems, a lot of information needs to be conveyed which not only includes performance of 

Fuzzy GP Ideal Values Weights Scaling Constant Target for Fuzzy GP Actual Achieved Whether Goal Achieved Suppliers Chosen 

The value path approach (Schilling et al., 1983) is one of the most efficient ways to demonstrate the trade-offs among the criteria obtained by the different solutions. The display consists of a set of parallel scales one for each criterion, on which is drawn the value path for each of the solution alternative. Value paths have proven to be an effective way to present the trade-offs in problems wifh more fhan two objectives. The value assigned to each solution on a particular axis is that solution s value for the appropriate objective divided by the best solution for that objective. The minimum value will be one if all fhe objectives were to minimize. Following are some properties of the value path approach (Schilling et al., 1983)  

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Value Path Approach for the Supplier Selection Case Study... 

To present these results to the DM, value path approach is used as follows ... 

Criteria Values for Value Path Approach (Case Study 2)... 

Based upon the preference of the DM, the preferred suppliers and the quantity ordered from each can change. The value path approach is a useful tool to compare the trade-offs among the suppliers. In some cases, the price of the product may dictate the suppliers who are chosen and in some other cases, the suppliers chosen may be dictated by lead-time or quality. Hence, value path approach can be used to study the trade-offs between different solutions. For example, from Figure 6.7 it can be seen that preemptive GP does... 

Graphical representation of value path approach (Case study 2). 

Comparison of phase 2 results by value path approach. 

In this section, we compare the supply chain design alternatives and their trade-offs using the value path approach (VPA) proposed by Schilling et al. (1983) in order to display the trade-offs among objective function values of different solutions and levels of goal achievement. 

Value Path Approach for Comparison of Multi-Objective Problems... 

The value assigned to each solution on a particular axis is that solution s value for the appropriate objective divided by the best solution for that objective. Therefore, the minimum value for each axis is 1. Following are some properties of the value path approach ... 

For a molecule at RTP this is of the order of a few hundred molecular diameters. In our ideal gas there is a distribution of velocities of the molecules about a mean value c. The mean free path defines a length scale in gases. As the density of the gas is increased and the mean free path approaches the molecular dimensions, a short-range molecular order develops and the material condenses to a liquid. The diffusional length scale is now much shorter range as a molecule encounters its... 

One approach to measuring the residence time of aerosols is to calculate the time required for presumed initial values in an air mass of two or more nuclides in a decay chain to evolve to the observed values. This approach yields a measure of the effect of removal processes along the path of transport of the air mass being sampled. 

The / -value of a wall or roof structure that involves layers of uniform thickness is determined easily by simply adding up the unit thermal resistances of the layers that are in series. But when a structure involves components such as wood studs and metal connectors, then the thermal resistance network involves parallel connections and possible two-dimensional etfects. The overall / -value in this case can be dctcimined by assuming (1) parallel heal flow paths through areas of different construction or (2) isothermal planes normal to the direction of heal transfer. The first approach usually overpredicts the overall thermal resistance, whereas the second approach usually underpredicts it. The parallel heat flow path approach is more suitable for wood frame walls and roofs, whereas the isothermal planes approach is more suitable for inasoiuy or metal frame walls. 

That is, instead of determining the transport properties from the rather theoretical Enskog solution of the Boltzmann equation, for practical applications we may often resort to the much simpler but still fairly accurate mean free path approach (e.g., [12], section 5.1 [87], chap. 20 [34], section 9.6). Actually, the form of the relations resulting from the mean free path concept are about the same as those obtained from the much more complex theories, and even the values of the prefactors are considered sufficiently accurate for many reactor modeling applications. 

The equation of the path differs from that of an ellipse with the parameter l and eccentricity e by the factor y. While r goes through one libration, the true anomaly 0 increases by 2ir/y. The path approaches more nearly to an ellipse the smaller the coefficient cl of the additional term in the potential energy, and for c1=0 it becomes an ellipse. For small values of c1 we can regard the path as an ellipse, whose perihelion slowly rotates with the angular velocity... 

In (a), a pulse of ions is formed but, for illustration purposes, all with the same m/z value. In (b), the ions have been accelerated but, because they were not all formed in the same space, they are separated in time and velocity, with some ions having more kinetic energy than others. In (c), the ions approach the ion mirror or reflectron, which they then penetrate to different depths, depending on their kinetic energies (d). The ones with greater kinetic energy penetrate furthest. In (e), the ions leave the reflectron and travel on to the detector (f), which they all reach at the same time. The path taken by the ions is indicated by the dotted line in (f). 

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