# Optimizing Design of Smart Workplace through Multi-Objective Programming
## Appendix G Link SETs and OOs:
### Develop SETs deployment scenario:
* Fall detectors sense patient fall situations and are attached to every patient. * The bed pressure sensors are attached to every bed in the hospital to detect when patients wake up. * The WiFi routers enable internet service inside the hospital's locations. The Bluetooth scanners can be used to securely transfer patients' data inside the hospital building. * The control system includes two microcontrollers gateways installed on the two floors of the hospital. Figure 5: (**a**) One typical SETs deployment scenario on the first floor of the hospital. (**b**) One typical SETs deployment scenario on the second floor of the hospital. Now, the next step involves conducting the optimization step using the computed data from the previous steps, including the weights of OOs, the positive impacts of SETs on OOs of the clinic workplace, and the total cost of each individual SETs obtained from a typically proposed scenario. **I. Formulate fuzzy goal programming (FGP)**  
Goal programming begins with defining the basic model decision variables [36], then the formulation of fuzzy goals, followed by formulating the fuzzy goal programming model as follows:  
(a)   Defining decision variables:  
\[X_{i}\ =\ \left\{ \begin{array}{ll}1\ if\ i^{\text{th}}\ \ \text{If smart technology, $T_{i}$ is adopted}\\ 0\ \text{Otherwise}\end{array} \right.\]  
where: \(i=1,2,\ldots,19\). Index 1 refers to the motion sensor, \(T_{1}\), and so on. (b)   The initial formulation of goal inequalities:  
The goals of maximizing positive impacts of SETs on the OOs extracted from the resultant matrix in Table 8 are expressed in form of inequalities. The target levels represent fuzzy inspiration quantities, expressed by the symbols \(\gtrsim\) or \(\lesssim\), depending on either maximization or minimization. Here, we have to maximize total positive impact, so they are set to equal 90% of total maximum possible impact ever when all the SETs are adopted, 19 (i.e., 19 SETs, each of which has a maximum impact equal to 1) which is equal 17.1. Of course, an achievement which is restricted by the budget limit for the project (i.e., $50,000). Hence our target is 17.1 as shown below. **Goal 1:** Attain the maximum target positive impact level on \"Speed-up patient check-in\" objective:  
\[ \begin{array}{ll}0.8\ X_{1}+0.8\ X_{2}+0.8\ X_{3}+X_{4}+0.8\ X_{5}+0.8\ X_{6}+0.6\ X_{7}+0.8\ X_{8}+0.8\ X_{9}+0.8\\ X_{10}+0.8\ X_{11}+0.8\ X_{12}+0.8\ X_{13}+0.8\ X_{14}+0.8\ X_{15}+0.8\ X_{16}+1 _{17}+0.8\ X_{18}+\\ 0.8\ X_{19}\gtrsim 17.1\end{array} \]  
**Goal 2:** Attain the maximum target positive impact level on \"Optimize patient flow\" objective:  
\[ \begin{array}{ll}0.8\ X_{1}+0.8\ X_{2}+X_{3}+X_{4}+0.8\ X_{5}+0.8\ X_{6}+0.8 \ X_{7}+X_{8}+0.6\ X_{9}+0.8\ X_{10}+0.8\\ X_{11}+0.8\ X_{12}+0.8\ X_{13}+0.8\ X_{14}+X_{15}+X_{16}+X_{17}+X_{18}+X_{19} \gtrsim 17.1\end{array} \]  
**Goal 3:** Attain the maximum target positive impact on the \"Enhancing information support\" objectives:  
\[ \begin{array}{ll}X_{1}+X_{2}+X_{3}+X_{4}+0.8\ X_{5}+0.8\ X_{6}+0.8\ X_{7}+X_{8 }+X_{9}+X_{10}+X_{11}+X_{12}+X_{13}+X_{14}\\ +X_{15}+X_{16}+X_{17}+X_{18}+X_{19}\gtrsim 17.1\end{array} \]  
**Goal 4:** Attain the maximum target positive impact on the \"Speed up diagnosis\" objectives:  
\[ \begin{array}{ll}0.8\ X_{1}+0.8\ X_{2}+0.8\ X_{3}+0.8\ X_{4}+0.8\ X_{5}+0.6\ X_{6}+0.6\ X_{7}+0.8\ X_{8}+X_{9}+X_{10}+\\ X_{11}+X_{12}+0.8\ X_{13}+0.6\ X_{14}+0.8\ X_{15}+0.8\ X_{16}+X_{17}+X_{18}+X_{19 }\gtrsim 17.1\end{array} \]  
**Goal 5:** Attain the maximum target positive impact on the \"Improve safety and security\" objectives:  
\[ \begin{array}{ll}X_{1}+X_{2}+X_{3}+X_{4}+X_{5}+X_{6}+0.8\ X_{7}+X_{8}+X_{9}+X _{10}+X_{11}+X_{12}+X_{13}+X_{14}+X_{15}+\\ X_{16}+X_{17}+X_{18}+X_{19}\gtrsim 17.1\end{array}