# Dynamic Planning of Mobile Service Teams' Mission Subject to Orders Uncertainty Constraints
## 6 Computational Experiments  
Considering the graph model of the transportation network from Figure 2, in which three MSTs \(\mathcal{U}=\{U_{1},U_{2},U_{3}\}\) periodically (with the period \(T=2000\) [u.t].) review the serviced stands owned, by using the customers located at nodes \(N_{2}\)-\(N_{11}\), MSTs offer the following sets of qualifications: \(\Phi_{1}=\{A,B\};\Phi_{2}=\{C,A\};\Phi_{3}=\{B,C\}\). The assumed service deadlines \(\Delta\), required qualifications \(\Psi\) and fuzzy traveling times between the nodes \(\widehat{d_{\lambda,\beta}}\) are collected in Tables 1 and 2, Figure 3, respectively. Routes \(\pi_{1}=(N_{1},N_{9},N_{10},N_{4},N_{1})\), \(\pi_{2}=(N_{1},N_{3},N_{11},N_{1})\), \(\pi_{3}=(N_{1},N_{5},N_{6},N_{7},N_{8},N_{2},N_{1})\) determine the fuzzy schedule \(\widehat{\mathbb{Y}}\) of the service mission being carried out as shown in Figure 4. It is easy to see (Figure 4) that in the second cycle of the fuzzy schedule (in the state \(M=((N_{9},N_{3},N_{5}),2500)\)), an information about suddenly reported changes in the service deadline \(\Lambda_{6}^{*}=[450;750]\) (instead \(\Delta_{6}=[650;950]\)) on node \(N_{6}\) is announced. Given this, an answer to the following question is sought:  
_Does there exist a set of routes \({}^{*}\Pi\) operated by MSTs \(U_{1},\ U_{2}\) and \(U_{3}\) for which the fuzzy cyclic schedule \({}^{*}\overline{\mathbb{Y}}\) will guarantee that all customers are serviced on time when disturbance \(IS=(S,\Delta^{*})\) occurs?_  
Figure 6: A dynamic rerouting and rescheduling algorithm. In order to find the answer to this question, the algorithm shown in Figure 6 has been employed. The problem \(\widetilde{FCS}\) (23) was then implemented in IBM ILOG CPLEX (Windows 10, Intel Core Duo2 3.00 GHz, 4 GB RAM). The solution time for the problems of this size does not exceed 60 s--see Figure 7c. The following routes were obtained: \({}^{*}\pi_{1}=(N_{1},N_{9},N_{6},N_{10},N_{4},N_{1})\), \({}^{*}\pi_{2}=(N_{1},N_{3},N_{6},N_{7},N_{1})\), \({}^{*}\pi_{3}=(N_{1},N_{5}\), \(N_{11},N_{6},N_{8},N_{2},N_{1})\). It should be noted that the new routes provide simultaneous customer service \(N_{6}\) by two MSTs: \(U_{1},U_{2}\) (whose qualifications meet the required service needs: \(\psi_{6}\subset\Phi_{1}\cup\ \Phi_{2}\)). Figure 7: Cyclic fuzzy schedule (**a**); no disturbances (**b**); occurrence of the disturbance (**c**); and no disturbances (**d**). In fuzzy schedule '\(\widehat{\triangledown}\) (Figure 7a), the operations are represented as ribbon-like \"arterial roads\", whose increasing width shows the time of vehicle movement resulting from the growing uncertainty. It is worth noting that the uncertainty is reduced at the end of each time window as a result of the operation of vehicles waiting at node \(N_{1}\).The increasing uncertainty is not transferred to the subsequent cycles of the system. Uncertainty is reduced as a result of the implementation of OFN formalism. The MST waiting time at node \(N_{1}\) has a negative orientation (laytimes \(\widehat{w_{1}^{1}}\), \(\widehat{w_{2}^{1}}\) and \(\widehat{w_{1}^{3}}\)). An example illustrating the use of standard fuzzy numbers for modeling the behavior of cyclic systems belonging to milk-run systems can be found in [44]. Taking the above into account, the proposed method of the dynamic planning of MSTs in cyclic maintenance delivery systems is unique, due to the possibility of taking into account the reduction in uncertainty in subsequent work cycles of the considered system. Moreover, the routes '\(\pi_{1}\), '\(\pi_{2}\), '\(\pi_{3}\) remain unchanged (see routes '\(\pi_{1}\), '\(\pi_{2}\), '\(\pi_{3}\) in Figure 7a) until a disturbance occurs, and then they are rerouted, rescheduled and finally synchronized again so that all customers are serviced on time. This means that the model developed in this study allows to adjust the adopted delivery plans to disturbances changing the pre-established services timetable.