W3_L3.3: Two dimensions - single facility problem

Welcome to Week 3 Lecture 3 Part 3 of the course "Industry 4.0" by Prof. Rahul R Marathe. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMS4001.html Video Overview The lecture explains the cross median approach where the optimal location in a single dimension is chosen at the median of demand ensuring equal weight on both sides. The problem is extended to two dimensions using the metropolitan distance measure where the objective is to minimize weighted travel in both x and y directions. Because the x and y components are independent the 2d problem is separated into two single dimension problems finding the optimal x coordinate using the cross median on the x axis and the optimal y coordinate using the cross median on the y axis. An example with four zones shows the optimal x coordinate as a range from 2 to 3 and the optimal y coordinate as 2 resulting in a line segment of possible facility locations. The euclidean distance version is then discussed where x and y cannot be separated making the problem nonlinear and requiring simultaneous optimization leading to a single unique solution. The center of gravity method is introduced as a heuristic using weighted average formulas to estimate the facility location which is easy to compute but not truly optimal and mainly serves as a starting point for more complex numerical methods. About IIT Madras' online Bachelor of Science programme IIT Madras offers four year BS programmes that aim to provide quality education to all irrespective of age educational background or location. The BS programme has multiple levels which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education) Diploma(s) from IIT Madras or BSc BS Degrees from IIT Madras. For more details Visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #facilitylocation #operationsmanagement #manhattandistance #euclideandistance #industrialengineering #centerofgravity #industry4 #iitm