Modeling and design of global logistics systems: a review of integrated strategic and tactical models and design algorithms.

*(English)*Zbl 1073.90501Summary: The overall focus of this research is to demonstrate the savings potential generated by the integration of the design of strategic global supply chain networks with the determination of tactical production-distribution allocations and transfer prices. The logistics systems design problem is defined as follows: given a set of potential suppliers, potential manufacturing facilities, and distribution centers with multiple possible configurations, and customers with deterministic demands, determine the configuration of the production-distribution system and the transfer prices between various subsidiaries of the corporation such that seasonal customer demands and service requirements are met and the after tax profit of the corporation is maximized. The after tax profit is the difference between the sales revenue minus the total system cost and taxes. The total cost is defined as the sum of supply, production, transportation, inventory, and facility costs. Two models and their associated solution algorithms will be introduced. The savings opportunities created by designing the system with a methodology that integrates strategic and tactical decisions rather than in a hierarchical fashion are demonstrated with two case studies.

The first model focuses on the setting of transfer prices in a global supply chain with the objective of maximizing the after tax profit of an international corporation. The constraints mandated by the national taxing authorities create a bilinear programming formulation. We will describe a very efficient heuristic iterative solution algorithm, which alternates between the optimization of the transfer prices and the material flows. Performance and bounds for the heuristic algorithms will be discussed.

The second model focuses on the production and distribution allocation in a single country system, when the customers have seasonal demands. This model also needs to be solved as a subproblem in the heuristic solution of the global transfer price model. The research develops an integrated design methodology based on primal decomposition methods for the mixed integer programming formulation. The primal decomposition allows a natural split of the production and transportation decisions and the research identifies the necessary information flows between the subsystems. The primal decomposition method also allows a very efficient solution algorithm for this general class of large mixed integer programming models. Data requirements and solution times will be discussed for a real life case study in the packaging industry.

The first model focuses on the setting of transfer prices in a global supply chain with the objective of maximizing the after tax profit of an international corporation. The constraints mandated by the national taxing authorities create a bilinear programming formulation. We will describe a very efficient heuristic iterative solution algorithm, which alternates between the optimization of the transfer prices and the material flows. Performance and bounds for the heuristic algorithms will be discussed.

The second model focuses on the production and distribution allocation in a single country system, when the customers have seasonal demands. This model also needs to be solved as a subproblem in the heuristic solution of the global transfer price model. The research develops an integrated design methodology based on primal decomposition methods for the mixed integer programming formulation. The primal decomposition allows a natural split of the production and transportation decisions and the research identifies the necessary information flows between the subsystems. The primal decomposition method also allows a very efficient solution algorithm for this general class of large mixed integer programming models. Data requirements and solution times will be discussed for a real life case study in the packaging industry.

##### MSC:

90B05 | Inventory, storage, reservoirs |

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\textit{M. Goetschalckx} et al., Eur. J. Oper. Res. 143, No. 1, 1--18 (2002; Zbl 1073.90501)

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