W3_L3.7: Generalized median problem

Welcome to Week 3 Lecture 3 Part 7 of the course "Industry 4.0" by Prof. Rahul R Marathe. Full Course: https://study.iitm.ac.in/ds/course_pa... Video Overview The lecture begins with a recap of key location models including set covering which minimizes the number of facilities needed partial set covering which maximizes the number of nodes covered with limited facilities and the p median problem which minimizes total weighted distance for a fixed number of facilities using assignment variables. The generalized median problem is then introduced shifting focus from distance minimization to cost minimization. A feasibility parameter a_ij is included again indicating whether node i can be served by node j. New cost parameters f_j for fixed facility cost and c_ij for variable serving cost are added leading to the objective of minimizing the sum of fixed and variable costs. Constraints include the p median constraints along with an assignment constraint using feasibility parameters. The lecture then explains the maximal covering problem which generalizes partial set covering. Instead of maximizing the number of nodes it maximizes the total population covered. Examples show how a location serving fewer nodes may be chosen if it serves more people. A layered version of the problem is used in emergency services involving primary coverage within a short time and mandatory coverage within a longer time using separate feasibility parameters. All these formulations including set covering p median generalized median and maximal covering are integer type problems making them computationally harder than standard linear programs. 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/stud... #facilitylocation #operationsmanagement #generalizedmedian #maximalcovering #industrialengineering #locationmodels #industry4 #iitm