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1

Joint allocation and transportation problem in supply network optimisation

Filcek G.

Management and Production Engineering Review

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2012

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Vol. 3, No. 3

3-10

EN

The paper concerns joint allocation and transportation as an optimization problem in selected supply networks. The network consists of a set of suppliers of the raw material, a set of production units and a set of product receivers. The raw material is treated as fast perishing good like vegetables or fruits. The production units are described by time models. In the optimization process, the time of the production and cost of the transportation is taken into account. The objective function is in general non-convex function of raw material allocation and transportation plans of the raw material and the product. To solve the problem considered, exact and heuristic algorithms have been developed and presented. To solve convex problems, solver Lingo developed by Lindo systems is proposed. The idea of a computer decision supported system integrating all presented algorithms is presented as well as four numerical examples illustrating some properties of the assumed supply network model.

2

Managing production and transportation in balanced supply networks

Filcek G., Józefczyk J.

Systems Science

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2009

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Vol. 35, no 4

49-59

EN

The paper deals with a special case of supply networks that consist of three interconnected subsystems: raw material warehouses, production units and product warehouses. The purpose of the decision-making for such systems is to allocate a raw material among parallel production units and to determine transportation plans for the raw material and for a product in such a way as to minimize the total cost connected with the production and the transportation. The solution algorithm for a special case of supply networks, where all production units can produce the same amount of the product from a unit of the raw material, is presented. It is based on a special decomposition of the problem which allows us to determine the solution consecutively for the increasing number of production units involved in the manufacture, starting from the case with only one production unit. A sufficient condition for the optimal solution is proved, and the properties of the algorithm are presented.

3

Algorytm łącznego rozdziału surowców oraz transportu w sieci dostaw

Filcek G.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

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2008

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z. 151

103-109

PL

W pracy podano sformułowanie problemu jednoczesnego rozdziału surowców między równolegle pracujące jednostki produkcyjne oraz transportu surowców i produktów jako problemu optymalizacyjnego. Przedstawiono dokładny algorytm rozwiązania tego problemu dla przypadku dwóch jednostek produkcyjnych. Rozważania są zilustrowane przykładowymi uruchomieniami algorytmu oraz wynikającymi z nich wnioskami dotyczącymi jego własności.

EN

The paper concerns a problem of an optimal allocation of a raw material among parallel and independent production units and transportation of the raw material and a product. An exact algorithm which solves the problem for a case of two production units is proposed. A numerical example illustrating the properties of the solution algorithm is given.

4

Decision-making for supply chains with transportation and production units

Józefczyk J., Filcek G.

Systems Science

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2007

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Vol. 33, no 1

53-59

EN

The paper concerns a supply chain system, that consists of three interconnected sub-systems (stages): a set of raw material warehouses, a set of production units and a set of product warehouses. The purpose of the decision-making for such a system is the allocation of a raw material among parallel production units and the determination of the transportation plans for the raw material and the product to minimize the total cost. In the paper, two versions of the decision-making problem are formulated. In the first one, all decisions are made jointly. The second simplified version consists in a consecutive determination of optimal allocation of the raw material and both transportation plans. The problem formulation for both cases are given. The equivalence condition of both versions for the simple case is presented. The numerical example completes the paper.