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facility location problem

1. Facility Location Problem Shivam sahoo .(2102041038) Bidhan hasda .(2102041059)

2. Outline: Introduction Types Minimum facility location Maximum facility location. Application Objective analysis

3. I NTRODUCTION: The facility location problem (FLP)  seeks to locate a number of facilities to serve a number of customers. It is also known as location analysis. It is a branch of operations to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities. The techniques also apply to cluster analysis.

4. Types: Minimum facility location: It seeks a location which minimizes the maximum distance to the sites, where the distance from one point to the sites is the distance from the point to its nearest site . Maximum facility location : It seeks a location which maximizes the minimum distance to the sites.

5. Application: Facility location problems are utilized in many industries to find the optimal placement of various facilities like Warehouses power plant s   polling locations cell towers to maximize efficiency In more unique applications, extensive research has been done in applying FLPs to humanitarian efforts, such as identifying disaster management sites to maximize accessibility to healthcare and treatment

6. Objective: And its objective is: Same day-delivery via private drivers. To assure quality and maximize profits, it has to place it warehouses efficient. Three factors are driving the decision: Cost of delivery per km Fix cost per warehouse Building price for a new warehouse

7. Analysis: Warehouses are randomly placed within odisha and the total production costs are calculated Algorithm moves each warehouse into all four directions and calculates the resulting transportation costs Then, it proceeds with the direction, which lowered the total production costs This procedure is repeated until no further reduction can be reached in any direction Thus, one local minimum is obtained The computer reiterates this algorithm many times, and chooses the local minimum with lowest transportation costs

8. Expression: Let us formulate the above problem as a mathematical optimization model. Consider  n � customers  i =1,2,…, n �=1,2,…,� and  m � sites for facilities  j =1,2,…, m �=1,2,…,�. Define continuous variables  xij ≥0 ���≥0 as the amount serviced from facility  j � to demand point  i �, and binary variables  yj =1 ��=1 if a facility is established at location  j �,  yj =0 ��=0 otherwise. An integer-optimization model for the capacitated facility location problem can now be specified as follows: