### Jesse O'Hanley (University of Kent)

#### Reliable hub network design

*Wednesday 11 May 2016 at 16.00, JCMB 4325A*

##### Abstract

Hub network design involves the location of hub sites in a network through
which flows from origins to destinations must be routed at least cost. Many
practical applications of hub location exist for transportation,
telecommunications, and other logistics systems. In this talk, I will focus
on a critical issue in hub location planning that has, thus far, received
little attention in the literature: hub reliability. The few existing studies
dealing with hub reliability unrealistically assume that either dedicated
backups can be located which never fail or that at most one unreliable hub
will fail at any given time.

A more general approach for designing reliable hub networks would be to
account for multiple, random hub failures. To this end, formulation and
solution techniques are proposed for the uncapacitated, single allocation
p-hub median location problem with independent hub failure probabilities. A
mixed integer nonlinear programming model is formulated for locating
unreliable hubs and assigning demand nodes to hubs in order to minimize the
expected demand weighted cost of customer flows plus a penalty in the event
all hubs fail. One of the key accomplishments is the development of a linear
model which embeds a specialized flow network structure referred to as a
probability lattice. A probability lattice extends the concept of probability
chains recently introduced in the OR literature for evaluating high-order
probability terms. A probability lattice involves interlinking multiple
probability chains together to form a backbone probability chain and series
of spur probability chains.

A Tabu search algorithm which makes use of a parallel computing strategy is
also proposed to find optimal to near optimal solutions for large problem
instances. Experimental results carried out on several benchmark instances
show the efficiency of the linearized model and heuristic algorithm. Compared
to a standard hub median model that disregards the potential for hub
failures, the proposed model produces solutions that serve larger numbers of
customers and at lower cost per customer.

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