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

This books 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 which is not easy to solve optimally in offline situations. The author considered a polynomial case and developed 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. Reasonable solutions for the offline case covering a whole day with a few hundred orders are 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. The branch-and-bound method developed 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 the author has 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.