Faculty Mechanical, Maritime and Materials Engineering

Transport Technology / Logistic Engineering

Literature survey, 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 chapter 5.

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.

Reports on Logistic Engineering (in Dutch)

Modified: 2000.06.04; logistics@3mE.tudelft.nl , TU Delft / 3mE / TT / LT.