Strategic container flow planning: a concept for simultaneously optimizing flows
of full and empty containers.
Report 93.3.LT.4029, Transport Technology, Logistic Engineering.
The objective of this rapport is to provide a concept for the strategie
optimization of flows of full and empty containers, in order to
contribute maximally to corporate profit.
As a consequence of the global imbalance of trade empty containers need to be
repositioned, such that structural stability in the network is achieved. The
invoked repositioning cost must be diminished, while simultaneously taking in
account the cost and profits of flows of full containers. This rapport focuses
primarily on these trade-offs between full and empty flows. Chapter 1 describes
the actual problem and assesses the available information.
In chapter 2 a strategic fundamental approach is proposed. The basic idea
behind this approach is that for every connection (arc) of the network an
epitome of flow can be determined, according to the maximum contribution
to profit of that connection. These super-optimal flow volumes are
unrestricted. Subsequently applying nodal conservation gives insight in
the true demand for capacity, and allows effective analysis of capacity
bottlenecks. Adding capacity and weight restrictions to the model yields
the optimal flow volumes for the current network. These flows can be
further optimized by gradually imposing optimized capacity deployment
upon the network.
The key insight of the proposed approach is that for
every connection a cost function can be constructed that depicts the cost
in relation to the incorporated full and empty flows as total flow
volume on a connection. The cost functions are piece-wise linear,
separable, and convex (eq. concave profit functions). These mathematical
aspects are addressed in chapter 3.
Chapter 4 deals with the characterization of the problem, and eventually
classifies it as a piece-wise linear convex minimum cost network flow
problem with side constraints. Furthermore, it gives the final
mathematical formulation as a network flow problem. The side constraints
comprise the capacity and weight restrictions, and withhold the problem
from being modelled as a pure network flow problem. This also affects the
solution strategy and possible applicable algorithms, as discussed in
The solution strategy considered to be most promising regarding
computation time, concerns an implementation of a combination of an
interior point solver and consecutively a simplex solver. This extensive
customizing of optimization strategies places high requirements on the
software, and with respect to the considerable problem size also on
the hardware. Chapter 6 provides a survey regarding software.
The right software choice is especially important when keeping in mind the
further developments and possible extensions, as presented in chapter 7. At
this time one of the most important potential extensions is to adequately
aggregate from strategie level down to tactic level.
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