# Data-Driven Decision Making in Maintenance Service Delivery Process: A Case Study
## 5 Case Study
### The Maintenance Service Delivery Stream
#### 5.3.1 Cross Analysis
Other assumptions that characterized the model:  
* Each technician \(t\in T\) owns a set of skills that define its competencies and the intervention modes they can execute. Skillsets influence the technician's ability to deal with certain requests, resolution typologies (e.g., on-field vs. remote), and execution length. * When allocating the intervention, the technician's schedule is not blank. There are availability windows for all the technicians. * Each time an on-field intervention is performed, the technician leaves from (and returns to) the headquarter before executing the following one. This is a realistic assumption since the technicians need to take the equipment and tools for the next intervention. The following equations describe the optimization model:  
\[minZ=\sum_{r\in R,m\in M_{r}\in T,m\in W}\left(C_{t}^{INT}\cdot t_{mt}^{INT}+C _{m}^{TOP}\cdot t_{m}^{TOP}+C_{m}^{SS}\cdot t_{r}^{SS}\right)\cdot x_{mtw}+ \sum_{r\in R}(penalty_{r}\cdot U_{r}) \tag{1}\]  
s.t. \[\sum_{m\in M_{r},t\in T,w\in W:\theta_{w}\geq\underset{w}{min\{t_{mt}^{INT}\}} }x_{mttw}=1\quad\forall r\in R \tag{2}\]  
\[C_{r}\geq\sum_{m\in M_{r},t\in T,w\in W}\left(s_{w}+t_{mt}^{INT}+max\left(t_{ rm}^{TOP};t_{r}^{SS}\right)\right)\quad\forall r\in R \tag{3}\]  
\[C_{r}\leq\sum_{m\in M_{r},t\in T,w\in W}\left(e_{w}-t_{rm}^{TOP}\right)\quad \forall r\in R \tag{4}\]  
\[\sum_{r\in R,m\in M_{r},t\in T}\left(t_{mt}^{INT}+t_{rm}^{TOP}\cdot 2\right) \cdot x_{mtw}\leq\theta_{w}\quad\forall w\in W \tag{5}\]  
\[x_{mttw}\cdot M_{rm}\leq\sum_{s\in S}(\delta_{rms}\cdot\omega_{mts})\quad \forall r\in R,\forall m\in M_{r},\forall t\in T,\forall w\in W \tag{6}\]  
\[C_{r}\leq DD_{r}+bigM\cdot U_{r}\quad\forall r\in R \tag{7}\]  
\[U_{r}\in 0,1 \tag{8}\]\[x_{rmtw}\in 0,1\quad\forall r\in R,\forall m\in M_{r},\forall t\in T,\forall w\in W \tag{9}\]  
\[minZ=\sum_{r\in R,m\in M_{r}\in T,m\in W}\left(C_{t}^{INT}\cdot t_{mt}^{INT}+C _{m}^{TOP}\cdot t_{m}^{TOP}+C_{m}^{SS}\cdot t_{r}^{SS}\right)\cdot x_{mtw}+ \sum_{r\in R}(penalty_{r}\cdot U_{r}) \tag{1}\]0  
The objective function (1) minimizes the value \(Z\), which represents the total cost of the interventions considering the hourly technician cost (\(Co_{t}^{INT}\)), the time required for the intervention (\(t_{rmt}^{INT}\)), the travel cost for the technician (\(Co_{r}^{TOP}\)), its travel time (\(t_{rmt}^{TOP}\)), the travel cost for the spare parts (\(Co_{m}^{SS}\)) with their travel time (\(t_{r}^{SS}\)) (when needed) and the penalty cost (\(penalty_{r}\)) due to the tardy interventions (\(U_{r}\)). Such an objective is relevant in the considered case because it minimizes the cost to execute the maintenance service and the costs that must be paid due to the late resolution of the customer problems. In this modeling, the penalty cost is fully sustained independently from the fact that the intervention began before the due date and finishes after or that it starts already after the due date expiration. Constraint set (2) stipulates that each intervention request (\(x_{rmtw}\)) is allocated exactly once. Constraint sets (3) and (4) define the completion time (\(C_{r}\)) of the intervention executed through the mode \(m\in M_{r}\), assuring that the intervention starts after the beginning of the availability window (\(s_{w}\)) and concludes before its end (\(e_{w}\)), leaving the technician the time to execute the intervention (\(t_{rmt}^{INT}\)) and travel back to the headquarter (\(t_{rmt}^{TOP}\)). Constraint set (5) verifies that, if multiple interventions (\(x_{rmtwtw}\)) are allocated to the same window \(w\in W\), then the technician \(t\in T\) has enough time (\(\theta_{w}=e_{w}-s_{w}\)) to go back and forth from the headquarter (\(t_{rmt}^{TOP}\cdot 2\)) in all the cases and execute all the interventions (\(t_{rmt}^{INT}\)). Constraint set (6) defines the match between technician and intervention mode based on the skills required (by the mode--\(M_{rm}\)) and owned (by the technician--\(\delta_{rms}\cdot\omega_{mts}\)).