Thomas Makuschewitz

A distributed routing concept for vehicle routing problems

Traditional solution concepts for the vehicle routing problem (VRP) are pushed to their limits, when applied on dynamically changing vehicle routing scenarios—which are more close to reality than the static formulation. By contrast, the introduced distributed routing concept is designed to match packages and vehicles and to continuously make route decisions especially within a dynamic environment. In this autonomous control concept, each of these objects makes its own decisions. The developed algorithm was entitled Distributed Logistics Routing Protocol (DLRP). But in spite of the restricted suitability of the traditional VRP concepts for dynamic environments, they are still the benchmark for any VRP-similar task. Therefore, we first present a description of the developed DLRP. Then an adapted vehicle routing problem is defined, which both sides, static and dynamic concepts, can cope with. Finally, both concepts are compared using a tabu search algorithm as a well working instance of traditional VRP-concepts. For a quantitative comparison, four solutions are given for the same adapted problem: the optimal solution as a lower bound, the DLRP solution, a tabu search solution and a random-like solution as an upper bound.

Measurement and optimization of robust stability of multiclass queueing networks: Applications in dynamic supply chains

Multiclass queueing networks are an essential tool for modeling and analyzing complex supply chains. Roughly speaking, stability of these networks implies that the total number of customers/jobs in the network remains bounded over time. In this context robustness characterizes the ability of a multiclass queueing network to remain stable, if the expected values of the interarrival and service times distributions are subject to uncertain shifts. A powerful starting point for the stability analysis of multiclass queueing networks is the associated fluid network. Based on the fluid network analysis we present a measure to quantify the robustness, which is indicated by a single number. This number will be called the stability radius. It represents the magnitude of the smallest shift of the expected value of the interarrival and/or service times distributions so that the associated fluid network looses the property of stability. The stability radius is a worst case measure and is a conceptual adaptation from the dynamical systems literature. Moreover, we provide a characterization of the shifts that destabilize the network. Based on these results, we formulate a mathematical program that minimizes the required network capacity, while ensuring a desired level of robustness towards shifts of the expected values of the interarrival times distributions. This approach provides a new view on long-term robust production capacity allocation in supply chains. The capabilities of our method are demonstrated using a real world supply chain.

Some Remarks on Stability and Robustness of Production Networks Based on Fluid Models

The dynamics of complex, large-scale production networks present an important issue not only for the management of such networks but also for scientific research. This problem is usually investigated either by numerical simulations or by mathematical analysis of the associated queueing model. One major property of stable production networks is the robustness of these networks with respect to perturbations of the arrival process of jobs from outside. Given a generic structure of the considered network with several production locations, different products and re-entrant material flows the determination of robustness is non trivial. In this paper we use a fluid model approach to analyse the robustness of queueing networks. First conditions for stability of a fluid network are introduced. These conditions allow to assess the dynamic behavior of the production network. Second the obtained results are investigated with the help of a simulation of the fluid and queueing network. Simulations of a test case scenario accompany the results of the theoretical analysis.

A comparison of mathematical modelling approaches for stability analysis of supply chains

Production and transportation processes along a supply chain are dynamic. In particular they are subject to perturbations (e.g., breakdown of a resource) that can destabilise the network. Stability is a major property of a supply chain that is essential for a sustainable relationship to its customers. In order to verify the stability of a given supply chain different criteria have been developed. This paper addresses the problem of choosing a proper mathematical modelling approach for a real world network in order to investigate stability. For this reason we discuss different modelling approaches. Each of these approaches can model different characteristics of a supply chain and features a specific stability criterion. By comparing these approaches the paper supports choosing a proper modelling approach for a real world supply chain.

An approach for the sustainable integration of production and transportation scheduling

Complex relationships and dynamic environments challenge the management of global supply chains. This paper first reviews conceptual frameworks for managing relationships along supply chains and concepts for the coordination of planning and scheduling processes. On the sequence, the integrated production and transportation scheduling problem for an original equipment manufacturer is formulated as a mixed integer program. The program combines an open flow shop problem and vehicle routing problem. The subsequent computational analysis shows that the formulated program supports the sustainable alignment between production and transportation systems and that heuristics are needed for suitably dealing with this kind of complex problem.

A Genetic Algorithm for the Integrated Scheduling of Production and Transport Systems

The integrated scheduling of production and transport systems is a NP-hard mixed-integer problem. This paper introduces a genetic algorithm (GA) that addresses this problem by decomposing it into combinatorial and continuous subproblems. The binary variables of the combinatorial subproblem form the chromosomes of each individual. Knowledge-based evolutionary operators are deployed for reducing the solution search space. Furthermore, dependent binary variables are identified which can be efficiently determined rather by a local search than by the evolutionary process. Then, in the continuous subproblem, for fixed binary variables, the optimization problem turns into a linear program that can be efficiently solved, so that the fitness value of an individual is determined.

A SURVEY OF AUTONOMOUS CONTROL ALGORITHMS BY MEANS OF ADAPTED VEHICLE ROUTING PROBLEMS

The German Collaborative Research Centre 637 “Autonomous Cooperating Logistic Processes – A Paradigm Shift and its Limitations”, develops, among other things, autonomous routing algorithms for transport networks. The discussed algorithm is designed to match goods and vehicles and to continuously make route decisions within a dynamic transport network. Here, each object makes its own decisions. It is called Distributed Logistics Routing Protocol – DLRP. Because of obvious similarities to the Vehicle Routing Problem (VRP), one question arises for both practitioners and researchers: How efficient is this protocol compared to traditional, established algorithms or in comparison to the optimal solution? This article tries to answer this question, which appears simple on the first and challenging on the second view.Copyright

Dynamic Scheduling of Production and Inter-Facilities Logistic Systems

This paper addresses the integrated production and transportation scheduling problem (PTSP) along global supply chains. An optimal solution for the PTSP requires solving simultaneously the production scheduling for all production facilities and the routing problems for the inter-facilities transportation of intermediate products. Moreover, in dynamic environments information concerning logistic capabilities and employment level has to be appropriately utilised to determine most effective production plans. Since the underlying mathematical programs are NP-hard, an excessive computational effort is required even for dealing with small problems. In this paper we present a decentralised approach for the PTSP, where the supply chain is featured as a sequence of planning entities. Each of these entities consists of one production facility and is responsible for its production scheduling as well as for the transport routing to the subsequent planning entities. The scheduling is performed on the basis of an optimisation model that takes current capabilities of the inter-facility transportation and the production system into account. The analysis of computational results demonstrates the need for developing heuristics for suitably dealing with this kind of complex problem.

An Approach to Model Reduction of Logistic Networks Based on Ranking

Simulations or mathematical analysis of a real-world logistic network require a model. In this context two challenges occur for modelling: First, the model should represent the real-world logistic network in an accurate way. Second, it should foster simulations or analytical analysis to be conducted in a reasonable time. A large size is often a drawback of many models. In the case of logistic networks this drawback can be overcome by reducing the number of locations and transportation links of the graph model. In this paper we present an approach to model reduction of a logistic network based on ranking. The rank of a given location states the importance of the location for the whole network. In order to calculate the importance of a location we introduce an adaptation of the PageRank algorithm for logistic networks. The information about the rank and the structural relations between the locations are used for our approach to model reduction. Depending on the structural relation between locations we suggest three different approaches to obtain a model of lower size.

Supply Network Engineering: An Approach to Robust Capacity Allocation for Stochastic Production Processes

Abstract The dynamics of supply networks can exhibit considerable complexity. Expected and unexpected events can reduce the production capacity available on average and put the timely satisfaction of customer demand at risk. In this paper we model supply networks as multiclass queueing networks and present an approach to robust capacity allocation with respect to perturbations of the production processes. To this end we consider the fluid model of a multiclass queueing network and use its stability radius to measure the robustness. The stability radius reflects the smallest decrease of production rate that destabilizes the network. Based on results concerning this measure we set up an optimization problem for the capacity allocation.