Achim Koberstein

Modeling and optimizing of strategic and tactical production planning in the automotive industry under uncertainty

This work considers the strategic flexibility and capacity planning under uncertain demands in production networks of automobile manufacturers. We present a deterministic and a stochastic model, which extend existing approaches, especially by an anticipation scheme for tactical workforce planning. This scheme is compared to an extended formulation of the deterministic model, which incorporates workforce planning via detailed shift models. The stochastic model is efficiently solved by an accelerated decomposition approach. The solution approach is integrated into a decision support system, which calculates minimum-cost product allocations and capacity plans. Our numerical results show that, in spite of the considerably increased complexity, our approach can efficiently handle hundreds of scenarios. Finally, we present an industrial case study.

Strategic Network Design

This chapter deals with the long-term strategic planning and design of the supply chain. Section 6.1 explains the planning situation and the problem setting. Section 6.2 outlines the formulation of the problem as an optimization model and Sect. 6.3 the use of such models within the strategic planning process. Section 6.4 reviews case reports in the literature and Sect. 6.5 the software modules available in APS.

Progress in the dual simplex algorithm for solving large scale LP problems: techniques for a fast and stable implementation

During the last fifteen years the dual simplex method has become a strong contender in solving large scale LP problems. However, the lack of descriptions of important implementation details in the research literature has led to a great performance gap between open-source research codes and commercial LP-systems. In this paper we present the mathematical algorithms, computational techniques and implementation details, which are the key factors for our dual simplex code to close this gap. We describe how to exploit hyper-sparsity in the dual simplex algorithm. Furthermore, we give a conceptual integration of Harris’ ratio test, bound flipping and cost shifting techniques and describe a sophisticated and efficient implementation. We also address important issues of the implementation of dual steepest edge pricing. Finally we show on a large set of practical large scale LP problems, that our dual simplex code outperforms the best existing open-source and research codes and is competitive to the leading commercial LP-systems on our most difficult test problems.

Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms

Abstract The dual simplex algorithm has become a strong contender in solving large scale LP problems. One key problem of any dual simplex algorithm is to obtain a dual feasible basis as a starting point. We give an overview of methods which have been proposed in the literature and present new stable and efficient ways to combine them within a state-of-the-art optimization system for solving real world linear and mixed integer programs. Furthermore, we address implementation aspects and the connection between dual feasibility and LP-preprocessing. Computational results are given for a large set of large scale LP problems, which show our dual simplex implementation to be superior to the best existing research and open-source codes and competitive to the leading commercial code on many of our most difficult problem instances.

Reconfiguration of assembly lines under the influence of high product variety in the automotive industry–a decision support system

In this paper we consider the mixed model assembly line reconfiguration problem in the context of auto production which is characterised by a make-to-order production process and a huge product variety. Starting from a given line balancing solution the goal is to minimise production costs in the short term for a largely known production program by reassigning and shifting tasks between workstations. We present a mathematical optimisation model that aims at minimising the costs incurred by overload situations, regular workers and reconfiguration measures. Due to the models complexity, lack of data and acceptance issues it is hardly possible to fully automate the solution process in an industrial environment. Therefore, we present a decision support approach that consists of visualisation components, new numerical indicators and an integrated heuristic optimisation procedure to semi-automate the reconfiguration process. In particular, reconfiguration costs can be taken into account and no complete precedence graph is required. Finally, we show on the basis of two industrial case studies that our approach can be successfully applied in a practical environment where it was capable of drastically reducing the occurrence of overload situations.

Aggregate production planning in the automotive industry with special consideration of workforce flexibility

We present a new mixed integer linear programming approach for the problem of aggregate production planning of flowshop production lines in the automotive industry. Our model integrates production capacity planning and workforce flexibility planning. In contrast to traditional approaches, it considers discrete capacity adaptations which originate from technical characteristics of assembly lines as well as from work regulations and shift planning. In particular, our approach takes change costs into account and explicitly represents a working time account via a linear approximation. A solution framework containing different primal heuristics and preprocessing techniques is embedded into a decision support system. Finally, we present an illustrative case study and computational results on problem instances of practically relevant complexity.

Lagrangian Cardinality Cuts and Variable Fixing for Capacitated Network Design

We present a branch-and-bound approach for the Capacitated Network Design Problem. We focus on tightening strategies such as variable fixing and local cuts that can be applied in every search node. Different variable fixing algorithms based on Lagrangian relaxations are evaluated solitarily and in combined versions. Moreover, we develop cardinality cuts for the problem and evaluate their usefulness empirically by numerous tests.

Dynamic sequencing and cut consolidation for the parallel hybrid-cut nested L-shaped method

The nested L-shaped method is used to solve two- and multi-stage linear stochastic programs with recourse, which can have integer variables on the first stage. In this paper we present and evaluate a cut consolidation technique and a dynamic sequencing protocol to accelerate the solution process. Furthermore, we present a parallelized implementation of the algorithm, which is developed within the COIN-OR framework. We show on a test set of 51 two-stage and 42 multi-stage problems, that both of the developed techniques lead to significant speed ups in computation time.

Integrated Strategic Planning of Global Production Networks and Financial Hedging Under Uncertain Demands and Exchange Rates

In this paper, we present a multi-stage stochastic programming model that integrates financial hedging decisions into the planning of strategic production networks under uncertain exchange rates and product demands. This model considers the expenses of production plants and the revenues of markets in different currency areas. Financial portfolio planning decisions for two types of financial instruments, forward contracts and options, are represented explicitly by multi-period decision variables and a multi-stage scenario tree. Using an illustrative example, we analyze the impact of exchange-rate and demand volatility, the level of investment expenses and interest rate spreads on capacity location and dimensioning decisions. In particular, we show that, in the illustrative example, the exchange-rate uncertainty cannot be completely eliminated by financial hedging in the presence of demand uncertainty. In this situation, we find that the integrated model can result in better strategic planning decisions for a risk-averse decision maker compared to traditional modeling approaches.

A stochastic model for the implementation of postponement strategies in global distribution networks

When designing global production and distribution systems an important aspect becoming more and more relevant is the question of how to deal with demand uncertainties. Due to the proliferation of product variants that have to be handled in production and distribution, long lead times due to overseas transportation and increasingly volatile, uncertain and market specific demands, an appropriate concept to deal with these problems has to be established. One concept that has been proposed but not yet been fully explored in this context is postponement. In this concept the customization and finalization of a product is procrastinated, i.e., the final products are not completed in factories but in facilities of a distribution network that are located on the network from factories to customers. This may also entail a resequencing of manufacturing steps. Until now, research has mainly focused on general statements regarding advantages and disadvantages of postponement strategies. In contrast, quantitative models that allow for decision making for specific postponement implementations are rare, particularly models that explicitly take into account stochastic demands and long lead times. In order to allow for decision making for specific postponement implementations in uncertain environments, we present a two-stage stochastic mixed integer linear programming model in this paper. We design a case study inspired by decision support issues in the apparel industry. By means of this case study we show that the presented model formulation can support managers to determine an appropriate production and distribution network in uncertain environments. Benefits from the concept of postponement are exemplified using (commercially) available mathematical programming software.