#### Date of Submission

6-28-2007

#### Date of Award

6-28-2008

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Mathematics

#### Department

Advance Computing and Microelectronics Unit (ACMU-Kolkata)

#### Supervisor

Das, Sandip (ACMU-Kolkata; ISI)

#### Abstract (Summary of the Work)

The facility location problem is a resource allocation problem that mainly deals with adequate placement of various types of facilities to serve a distributed set of demands satisfying the nature of interactions between the demands and facilities and optimizing the cost of placing/maintaining the facilities and the quality of services.The facility location problem is well-studied in the Operations Research literature and recently has received a lot of attention in the Computer Science community. For a company, the facility location problem provides more strategic decisions than just giving importance to locate the lowest cost space for storing its products. While identifying the location of the companyâ€™s distribution centers (facilities) for maintaining the necessary service levels to the customers, it must consider several things, for example, the freight costs, the cost of a new/leased structures, several other logistics costs, and also the inherent risk and viability involved in the choice of those locations. Several variations of facility location problem can be formulated depending on the nature of the objective function and the constraints on the facilities. As examples, we may cite the problems on cost reduction, demand capture, equitable service supply, fast response time etc. For locating emergency facilities, such as hospitals, fire-fighting stations etc., covering a region using minimum radius circles is a natural mapping of the corresponding facility location problem where the objective is to minimize the radius of the circles indicating the worst-case response time.In the classical facility location problem, it is generally assumed that the communication path between a facility and a customer should not be obstructed by any obstacle. But, this is not always a realistic assumption with respect to the practical instances. So, depending upon the application, we model the problem assuming both the customers and the facilities as points in a polygonal region P and we measure the distance between a customer ci and a point-facility xj by their geodesic distance, i.e., the shortest path between ci and xj in P avoiding the obstacles. Finding the geodesic shortest path is an essential tool for solving several variations of the facility location problem. The complication of identifying the geodesic shortest paths increases when we consider different constraints that should be obeyed by the resulting path, or the region under study goes in higher dimension.This thesis is a study on designing efficient algorithms for some application specific geometric facility location and constrained path planning problems. In the next two sections, we briefly overview the existing literature on the facility location problem and the geodesic path planning problem in two and higher dimensions. The scope of the thesis appears in the next section.Facility Location A typical facility location problem deals with locating facilities as a subset of a given set of objects on a given environment to cover the clients located on the same environment, say a bounded/unbounded plane, a terrain or some network, with an aim to optimize certain objective function. Formally, the problem is defined as follows: given a weighted set D of demand locations with weight distribution w, a set F of feasible facility locations with nonnegative cost distribution f, and a distance function d that measures cost between a pair of locations; the objective is to find a set F 0 âŠ† F, so as to optimize

#### Control Number

ISILib-TH335

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Roy, Sasanka Dr., "Algorithms for Some Geometric Facility Location and Path Planning Problems." (2008). *Doctoral Theses*. 47.

https://digitalcommons.isical.ac.in/doctoral-theses/47

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28842823