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AbstractThis article considers a dynamic lot‐sizing problem with storage capacity limitation in which backlogging is allowed. For general concave procurement and inventory costs, we present an O(T2) dynamic programming algorithm where T is the length of the planning horizon. Furthermore, in case of a fixed‐charge cost structure without speculative motives, we show that the problem can be solved in O(T) time. By carefully choosing decompositions of the problems, we can use classical results like an efficient matrix searching algorithm and geometric techniques to achieve the results. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we introduce a new production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is NP-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the effectiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

International audience ; Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we study a production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is N P-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the competitiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

International audience ; Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we study a production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is N P-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the competitiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

International audience ; Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we study a production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is N P-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the competitiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

AbstractIn this article, we study a biobjective economic lot‐sizing problem with applications, among others, in green logistics. The first objective aims to minimize the total lot‐sizing costs including production and inventory holding costs, whereas the second one minimizes the maximum production and inventory block expenditure. We derive (almost) tight complexity results for the Pareto efficient outcome problem under nonspeculative lot‐sizing costs. First, we identify nontrivial problem classes for which this problem is polynomially solvable. Second, if we relax any of the parameter assumptions, we show that (except for one case) finding a single Pareto efficient outcome is an ‐hard task in general. Finally, we shed some light on the task of describing the Pareto frontier. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 386–402, 2014