In this lesson the problem of city transport is solved. The problem is described in the Chapter 4.3, Lesson 5: 4.3.4. The decision making problem deals with city logistic in Pardubice and focuses on the problem sustainable last-mile delivery. It is a typical kind of a multi criteria decision making problem since multiple conflicting criteria affect the micro-hub location selection such as area, cargo bike availability, costs, etc. It is a typical kind of a multi criteria decision making problem since multiple conflicting criteria affect the micro-hub location selection such as area, cargo bike availability, costs, etc.
The real decision making problem is described three alternatives and five criteria, see the Table 1.
We start by definition of a 3-level hierarchy structure of AHP. The first level is represented by ‘goal of decision’, the second represents the set of criteria and the third consists the set of alternatives. The hierarchy structure is in the Fig. 1.
In the following part the choice of the micro-hub location selection is explained and shown in the MS Excel. The goal of this decision is to select the most suitable micro-hub location in Pardubice from three candidates. There are three alternatives that are considered as possible locations for a micro-hub location for the last-mile delivery purpose. Those three possible were selected from the urbanization plan of the city. It is ‘Labsky Palouk’ (A1), ‘Hurka‘ (A2) and ‘Nemosicka’ (A3).
The choice of the best locality is realized on the basis of the set of criteria: C1 is Cycle distance (in metres), C2 is Area (in square metres), C3 is Cargo bike availability (in points), C4 is Costs (in Czech crown) and C5 is Sum of distances from sorting centre (in kilometres).
The Saaty matrix for criteria pairwise comparisons and calculation of the vector of non-normalized criteria weights and the criteria normalized priority Vector is in the Table 2. The function GEOMEAN is applied for the calculation of the vector of non-normalized criteria weights. The function is used for the row of Saaty matrix.
The very important parameter ‘Consistency Ratio’ (CR) which tells about a correctly constructed Saaty matrix is calculated in MATLAB by the function ‘eigen’. The term ‘Consistency of Saaty Matrix’ is used. The CR must be less than 0.1. The script (M-file) of CR for MATLAB is in the Fig. 2.
The next step is to calculate priorities for the candidates A1 (Labsky Palouk), A2 (Hurka) and A3 (Nemosicka) with respect to C1 (Cycle distance), C2 (Area), C3 (Cargo bike availability), C4 (Costs) and C5 (Sum of distances) like in the calculation of criteria priority. See the Table 3. We assume that the matrixes are consistent, it means C.R. is less 0.1.
The final step is to calculate priorities (total evaluations) for the candidates. See Table 4.
The alternative A3 was chosen (the total evaluation is 0.510). Looking only at A1 (Labsky Palouk) we can see that its total evaluation with respect to the Goal is 0.235, calculated as follows:
- Labsky Palouk priority with respect to C1 (Cycle distance) is 0.5695 x 0.2045 is E1
- Labsky Palouk priority with respect to C2 (Area) is 0.0719 x 0.5959 is E2
- Labsky Palouk priority with respect to C3 (Cargo bike availability) is 0.5000 x 0.0968 is E3
- Labsky Palouk priority with respect to C4 (Costs) is 0.0810 x 0.0622 is E4
- Labsky Palouk priority with respect to C5 (Sum of distances) is 0.5396 x 0.0406 is E5
- for a total evaluation of Labsky Palouk is E1 + E2 + E3 + E4 + E5 = 0.235.
If we compare the results of choosing the best micro-hub location A3 > A2 > A1 (see Table 4) with results from the Lesson 4.4.3. in this module (A2> A3 >A1) we see the difference between the order of the first places. In this case, we are inclined to use the AHP method because it suppresses subjective evaluation.