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Online Storage Systems and Transportation Problems with Applications: Optimization Models and Mathematical Solutions

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This book covers the analysis and development of online algorithms
involving exact optimization and heuristic techniques, and their application
to solve two real life problems.

The first problem is concerned with a complex technical system: a
special carousel based high-speed storage system - Rotastore. It is shown
that this logistic problem leads to an NP-hard Batch PreSorting Problem
(BPSP) which is not easy to solve optimally in offline situations. We
consider a polynomial case and develope an exact algorithm for offline
situations. Competitive analysis showed that the proposed online algorithm
is 3/2-competitive. Online algorithms with lookahead improve
the online solutions in particular cases. If the capacity constraint on
additional storage is neglected the problem has a totally unimodular
polyhedron.

The second problem originates in the health sector and leads to a
vehicle routing problem. We demonstrate that reasonable solutions for
the offline case covering a whole day with a few hundred orders can be
constructed with a heuristic approach, as well as by simulated annealing.
Optimal solutions for typical online instances are computed by an efficient
column enumeration approach leading to a set partitioning problem
and a set of routing-scheduling subproblems. The latter are solved exactly
with a branch-and-bound method which prunes nodes if they are
value-dominated by previous found solutions or if they are infeasible with
respect to the capacity or temporal constraints. Our branch-and-bound
method is suitable to solve any kind of sequencing-scheduling problem
involving accumulative objective functions and constraints, which can
be evaluated sequentially. The column enumeration approach developed
to solve this hospital problem is of general nature and thus can be embedded
into any decision-support system involving assigning, sequencing
and scheduling.
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