grab · paradite · Oct 25, 2017 · Oct 25, 2017
diff --git a/_posts/2017-10-20-the-data-and-science-behind-grabshare-part-i.md b/_posts/2017-10-20-the-data-and-science-behind-grabshare-part-i.md
@@ -66,7 +66,7 @@ The assignment flow of typical GC bookings is stated in Algorithm I. For every n
   <small class="post-image-caption">Algorithm I. GrabCar booking assignment flow</small>
 </div>
 
-Specifically, Algorithm II gives the assignment flow of Grab- Share bookings. We can see that its overall structure is the same with GrabCar except for two differences. Firstly, the candidate driver set is different. For every new GrabShare booking, we search for in-transit GrabShare drivers who are currently serving at least one GrabShare booking. Therefore, we need to check seat availability condition to ensure that the vehicle has enough remaining seats to serve the new GrabShare booking. Mathematically, the following seat reservation constraint needs to be satisfied for a successful assignment between booking bki and driver drj: 
+Specifically, Algorithm II gives the assignment flow of Grab- Share bookings. We can see that its overall structure is the same with GrabCar except for two differences. Firstly, the candidate driver set is different. For every new GrabShare booking, we search for in-transit GrabShare drivers who are currently serving at least one GrabShare booking. Therefore, we need to check seat availability condition to ensure that the vehicle has enough remaining seats to serve the new GrabShare booking. Mathematically, the following seat reservation constraint needs to be satisfied for a successful assignment between booking bki and driver drj:
 
 ![constraint](/img/the-data-and-science-behind-grabshare-part-i/constraint.png)
 
@@ -86,24 +86,24 @@ Secondly, GrabShare’s user experience is different from GrabCar due to the sha
 
 This is ultimately deemed a good match, but the details on how we quantify this and its corresponding optimisation model are explained in **Part II**. 
 
-### References 
+### References
 
 <a name="1" href="#1">[1]</a>  Grab, "Grab extends grabshare regionally with malaysias first on-demand carpooling service," 2017. [Online]. Available: <https://www.grab.com/my/press/business/grabsharemalaysia/>
 
-<a name="2" href="#2">[2]</a>  J. Alonso-Mora, S. Samaranayake, A. Wallar, E. Frazzoli, and D. Rus, "On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment," *Proceedings of the National Academy of Sciences*, vol. 114, no. 3, pp. 462–467, Mar 2017.  
+<a name="2" href="#2">[2]</a>  J. Alonso-Mora, S. Samaranayake, A. Wallar, E. Frazzoli, and D. Rus, "On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment," *Proceedings of the National Academy of Sciences*, vol. 114, no. 3, pp. 462–467, Mar 2017. 
 
 <a name="3" href="#3">[3]</a>  A. Conner-Simons, "Study: carpooling apps could reduce taxi traffic 75 percent," 2016. [Online]. Available: <http://www.csail.mit.edu/ridesharing_reduces_traffic_300_percent>
 
-<a name="4" href="#4">[4]</a>  D. Dimitrijevic, N. Nedic, and V. Dimitrieski, "Real-time carpooling and ride-sharing: Position paper on design concepts, distribution and cloud computing strategies," in *Computer Science and Information Systems (FedCSIS), 2013 Federated Conference on*. IEEE, 2013, pp. 781–786.  
+<a name="4" href="#4">[4]</a>  D. Dimitrijevic, N. Nedic, and V. Dimitrieski, "Real-time carpooling and ride-sharing: Position paper on design concepts, distribution and cloud computing strategies," in *Computer Science and Information Systems (FedCSIS), 2013 Federated Conference on*. IEEE, 2013, pp. 781–786. 
 
-<a name="5" href="#5">[5]</a>  N. Agatz, A. Erera, M. Savelsbergh, and X. Wang, "Optimization for dynamic ride-sharing: A review," *European Journal of Operational Research*, vol. 223, no. 2, pp. 295–303, 2012.  
+<a name="5" href="#5">[5]</a>  N. Agatz, A. Erera, M. Savelsbergh, and X. Wang, "Optimization for dynamic ride-sharing: A review," *European Journal of Operational Research*, vol. 223, no. 2, pp. 295–303, 2012. 
 
-<a name="6" href="#6">[6]</a>  A. Amey, J. Attanucci, and R. Mishalani, "Real-time ridesharing: opportunities and challenges in using mobile phone technology to improve rideshare services," *Transportation Research Record: Journal of the Transportation Research Board*, no. 2217, pp. 103–110, 2011.  
+<a name="6" href="#6">[6]</a>  A. Amey, J. Attanucci, and R. Mishalani, "Real-time ridesharing: opportunities and challenges in using mobile phone technology to improve rideshare services," *Transportation Research Record: Journal of the Transportation Research Board*, no. 2217, pp. 103–110, 2011. 
 
-<a name="7" href="#7">[7]</a>  N. D. Chan and S. A. Shaheen, "Ridesharing in north america: Past, present, and future," *Transport Reviews*, vol. 32, no. 1, pp. 93–112, 2012.  
+<a name="7" href="#7">[7]</a>  N. D. Chan and S. A. Shaheen, "Ridesharing in north america: Past, present, and future," *Transport Reviews*, vol. 32, no. 1, pp. 93–112, 2012. 
 
-<a name="8" href="#8">[8]</a>  M. Furuhata, M. Dessouky, F. Ordonez, M.-E. Brunet, X. Wang, and S. Koenig, "Ridesharing: The state-of-the-art and future directions," *Transportation Research Part B: Methodological*, vol. 57, pp. 28–46, 2013.  
+<a name="8" href="#8">[8]</a>  M. Furuhata, M. Dessouky, F. Ordonez, M.-E. Brunet, X. Wang, and S. Koenig, "Ridesharing: The state-of-the-art and future directions," *Transportation Research Part B: Methodological*, vol. 57, pp. 28–46, 2013. 
 
 <a name="9" href="#9">[9]</a>  Lyft, "Matchmaking in lyft line—part 1," 2016. [Online]. Available: <https://eng.lyft.com/matchmaking-in-lyft-line-9c2635fe62c4>
 
-<a name="10" href="#10">[10]</a>  M. Ester, H.-P. Kriegel, J. Sander, X. Xu *et al.*, "A density-based algorithm for discovering clusters in large spatial databases with noise." in *Kdd*, vol. 96, no. 34, 1996, pp. 226–231.  
+<a name="10" href="#10">[10]</a>  M. Ester, H.-P. Kriegel, J. Sander, X. Xu *et al.*, "A density-based algorithm for discovering clusters in large spatial databases with noise." in *Kdd*, vol. 96, no. 34, 1996, pp. 226–231.