Server location assignment problem on a probabilistic network
Abstract
Assignment Problem is a cornerstone in operations research. In the assignment problem, a set of supply units are assigned to a set of demand units in order to minimize the sum of the cost associated with each supply-to-demand pair. Defined on a network the supplies and demands are located at vertices and the cost of a supply-to-demand pair is the distance between them. This thesis considers a location problem that precedes an Assignment problem. We are to locate the supply units on the network that will be used in an assignment problem prior to knowing the locations of demands. The demand locations are known only probabilistically at the time of choosing supply locations. The objective is to optimize locations of supply units such that the expected cost of the assignment problem is minimized. This problem is termed as Server Location Assignment Problem (SLAP). Three different models of SLAP are considered in this dissertation. The first model, which is discussed in Chapter 3, is a SLAP on a tree and the number of demand units are constant and equal to the number of supply units in all assignment problems. This problem is shown to have a simple solution procedure on a line and avails itself to a polynomial time greedy algorithm on a tree. Chapter 4 presents the second model, which extends the first model to include general networks. Principle results include showing SLAP on a general network is NP-hard, developing two heuristics, and conducting numerical tests to study their performance. In addition to uncertainty of the demand locations, the third model allows the number of demand units in the assignment problem to be a stochastic variable, taking a value up to the number of servers. This model on a tree is discussed in Chapter 5. The same heuristic approach that is used in the second model is slightly modified and applied to this problem. Finally, other applications for SLAP are discussed in Chapter 6. Future research extensions are suggested in Chapter 7.
Degree
Ph.D.
Advisors
Ward, Purdue University.
Subject Area
Management|Transportation|Operations research
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.