## 4 Empirical Case Study
### Optimization Modelling  
The definition of ECs is built based on Company A's capabilities. CRs and CS-F relationship functions are built based on market research and survey. They support the backend operation of the product configuration system. Once they are ready, the system is ready to take customer inputs and recommend optimal solutions.  
Company B approaches Company A to order 100 units of laptops for their customers. The expected budget is around $1000 per unit, out of which, $750 is allocated to the primary functional ECs (CPU, GPU, RAM, HDD, and SSD). The importance weight for each CR is given as shown in Table 13.  
Based on the profile of the target user, the optimization model can be formulated below.  
**Decision Variables:**  
\[X_{jk}=\left\{\begin{array}{ll}1&\quad\text{if Part $jk$ is selected}\\ 0&\quad\text{otherwise}\end{array}\right.\]  
**Objective Function:**  
\[max\quad S\]  
**Constraints:**  
**<Total price must be no more than $750.>**  
\(53\;X_{A1}+89\;X_{A2}+166\;X_{A3}+\ldots+216\;X_{E4}+603\;X_{E5}\leq 750\)  
**<Exactly one part must be chosen from each group.>**  
\(X_{A1}+X_{A2}+X_{A3}+X_{A4}+X_{A5}+X_{A6}=1\)  
\(X_{B1}+X_{B2}+X_{B3}+X_{B4}+X_{B5}=1\)  
\(X_{C1}+X_{C2}+X_{C3}+X_{C4}=1\)  
\(X_{D1}+X_{D2}+X_{D3}+X_{D4}+X_{D5}+X_{D6}=1\)  
\(X_{E1}+X_{E2}+X_{E3}+X_{E4}+X_{E5}=1\)  
**<Calculation of overall normalized score \(m\) of \(EC_{j}\)**, \(S^{\prime}_{j,m}\)>**  
\(0.521\;X_{A1,1}+0.680\;X_{A2,1}+0.781\;X_{A3,1}+0.756\;X_{A4,1}+\;X_{A5,1}+X_{ A6,1}=S^{\prime}_{A,1}\)  
\(0.243\;X_{A1,2}+0.463\;X_{A2,2}+0.521\;X_{A3,2}+0.756\;X_{A4,2}+0.89\;X_{A5,2} +X_{A6,2}=S^{\prime}_{A,2}\)  
\(0.118\;X_{A1,3}+0.225\;X_{A2,3}+0.255\;X_{A3,3}+0.368\;X_{A4,3}+0.659\;X_{A5,3} +X_{A6,3}=S^{\prime}_{A,3}\)  
\(0.126\;X_{B1}+0.286\;X_{B2}+0.563\;X_{B3}+0.784\;X_{B4}+X_{B5}=S^{\prime}_{B,1}\)  
\(0.185\;X_{C1}+0.244\;X_{C2}+0.854\;X_{C3}+X_{C4}=S^{\prime}_{C,1}\)  
\(0.063\;X_{D2}+0.125\;X_{D3}+0.25\;X_{D4}+0.5\;X_{D5}+X_{D6}=S^{\prime}_{D,1}\)  
\(0.937\;X_{D2}+0.971\;X_{D3}+X_{D4}+0.874\;X_{D5}+0.73\;X_{D6}=S^{\prime}_{D,2}\)  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Target User** & **Office Clerks, White-Collar** \\ \hline Total Budget Allocated & 750 \\ Customer Requirement & Importance Weight \\ Business Performance & 0.5 \\ Multimedia Performance & 0.15 \\ Computation Performance & 0.25 \\ Storage & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Customer profile.  
\(0.125\,X_{\rm E2}+0.25\,X_{\rm E3}+0.5\,X_{\rm E4}+X_{\rm E5}=S^{\prime}_{E,1}\)  
\(0.998\,X_{\rm E2}+0.996\,X_{\rm E3}+0.994\,X_{\rm E4}+X_{\rm E5}=S^{\prime}_{E,2}\)  
**<Calculation of fulfillment level of \(\text{CR}_{i}\)**, \(F_{i}\)>**  
\(0.379\,S^{\prime}_{A,1}+0.047\,S^{\prime}_{A,2}+0.047\,S^{\prime}_{A,3}+0.11\,S ^{\prime}_{B,1}+0.05\,[PERSON]^{\prime}_{C,1}+0.11\,[PERSON]^{\prime}_{D,2}+0.26\,[PERSON]^{\prime}_ {E,2}=F_{1}\)  
\(0.071\,[PERSON]^{\prime}_{A,1}+0.143\,[PERSON]^{\prime}_{A,2}+0.024\,[PERSON]^{\prime}_{A,3}+0.43\,[PERSON] ^{\prime}_{B,1}+0.05\,[PERSON]^{\prime}_{C,1}+0.14\,[PERSON]^{\prime}_{D,2}+0.14\,[PERSON]^{\prime}_ {E,2}=F_{2}\)  
\(0.038\,[PERSON]^{\prime}_{A,1}+0.038\,[PERSON]^{\prime}_{A,2}+0.305\,[PERSON]^{\prime}_{A,3}+0.19\, [PERSON]^{\prime}_{B,1}+0.05\,[PERSON]^{\prime}_{C,1}+0.14\,[PERSON]^{\prime}_{D,2}+0.24\,[PERSON]^{\prime}_ {E,2}=F_{3}\)  
\(0.89\,S_{D}+0.11\,S_{E}=F_{4}\)  
**<Calculation of customer satisfaction level of \(\text{CR}_{i}\)**, \(\text{CS}_{i}\)>**  
\(-1.503\,e^{-F_{1}}+0.828=\text{CS}_{1}\)  
\(1.125\,F_{2}-0.467=\text{CS}_{2}\)  
\(0.529\,e^{-F_{3}}-0.87=\text{CS}_{3}\)  
\(-1.622\,e^{-F_{4}}+1.067=\text{CS}_{4}\)  
**<Calculation of overall customer satisfaction level**, \(\text{S}\)>**  
\(0.55\,CS_{1}+0.15\,CS_{2}+0.2\,CS_{3}+0.1\,\text{CS}_{4}=S\)  
**<Incompatibility Constraint(s)>**  
\(X_{\rm D1}+X_{\rm E1}\leq 1\)