Locations of Medians on Stochastic Networks

Abstract

The definition of network medians is extended to the case where travel times on network links are random variables with known discrete probability distributions. Under a particular set of assumptions, it is shown that the well-known theorems of HAKIMI and of LEVY can be extended to such stochastic networks. The concepts are further extended to the case of stochastic oriented networks. A particular set of applications as well as formulations of the problem for solution using mathematical programming techniques are also discussed briefly.

Analysis of MCLP, Q-MALP, and MQ-MALP with Travel Time Uncertainty Using Monte Carlo Simulation

“…Mirchandani and Odoni [44] extended the -median problem to account for stochastic travel times. Their model assumes travel times to be known when a demand for service arises; however, the state of the system (as described by the link travel times) changes over time according to a Markov process.…”

Multiperiod medians on networks

“…Levy [8], A. Goldman [3], L. Hakimi and S, Maheshwari [6], and R. Wendell and A. Hurter [14]; and a concise abstract of these extensions can be consulted in the paper of B. Tansel, R. Francis and T. Lowe [12]. Furthermore, that property has been extended to stochastic networks by P. Mirchandani and A. Odoni [11] and to absolute conditional problems by E. Minieka [10]. On the other hand, P. Hansen and M. Labbé [7] consider continuous p-medians which were introduced as absolute gênerai médians by E. Minieka [9], and were defined so that they minimize the sum of the distances from each link to the closest facility.…”

Solving structured multifacility location problems efficiently

“…Hooker, Garfinkel and Chen (1991) studied a large number of continuous network location problems in an effort to identify a finite set of points on the network which would contain the new facility locations in an optimal solution. They called such a set of points for a given problem a. finite domination set Problem 1. m-Median Problem (Hakimi, 1964(Hakimi, ,1965 (Goldman, 1971) (Mirchandani and Odoni, 1979) (Dearing, Francis, and Lowe, 1976;Kolen, 1986;Fernandez-Baca, 1989;Chhajed and Lowe, 1990) Problem 6. m-C enter Problem (Hakimi, 1965) (Hooker, Garfinkel and Chen, 1991). Let C be the union of all such points for all i,j and pe AinAj.…”