MRP Lot Sizing with Variable Production/Purchasing Costs: Formulation and Solution
In: International Journal of Production Research 1989
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In: International Journal of Production Research 1989
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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.
BASE
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.
BASE
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.
BASE
In: Suzanne , E , Absi , N , Borodin , V & van den Heuvel , W 2021 , ' Lot-sizing for industrial symbiosis ' , Computers and Industrial Engineering , vol. 160 , 107464 . https://doi.org/10.1016/j.cie.2021.107464
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.
BASE
In: Decision sciences, Volume 22, Issue 4, p. 940-952
ISSN: 1540-5915
ABSTRACTA review of the literature indicates that the traditional approach for evaluating quantity discount offerings for purchased items has not adequately considered the effect that transportation costs may have on the optimal order quantity; despite the general fact that purchased materials must bear transportation charges.The transportation cost structure for less‐than‐truckload (LTL) shipments reflects sizable reductions in freight rates when the shipment size exceeds one of the nominal rate breakpoints. However, the shipper must also be aware of the opportunity to reduce total freight costs by artificially inflating the actual shipping weight to the next rate breakpoint, in order that a lower marginal tariff is achieved for the entire shipment. Such over‐declared shipments result in an effective freight rate schedule that is characterized by constant fixed charge segments in addition to the nominal marginal rates. Over‐declared shipments are economical when the shipment volume is less than the rate breakpoint, but greater than a cost indifference point between the two adjacent marginal rates.This paper presents a simple analytical procedure for finding the order quantity that minimizes total purchase costs which reflect both transportation economies and quantity discounts. After first solving for the series of indifference points that apply to a particular freight rate schedule, a total purchase cost expression is presented that properly accounts for the actual transportation cost structure. The optimal purchase order quantity will be one of the four following possibilities: (1) the valid economic order quantity (EOQ), QC; (2) a purchase price breakpoint in excess of QC; (3) a transportation rate breakpoint in excess of QC; and (4) a modified EOQ which provides an over‐declared shipment in excess of QC. Finally, an algorithm which systematically explores these four possibilities is presented and illustrated with a numerical example.
In: Decision sciences, Volume 32, Issue 1, p. 125-144
ISSN: 1540-5915
AbstractWe consider the optimal lot‐sizing policy for an inventoried item when the vendor offers a limited‐time price reduction. We use the discounted cash flow (DCF) approach in our analysis, thereby eliminating the sources of approximation found in most of the earlier studies that use an average annual cost approach. We first characterize the optimal lot‐sizing policies and their properties, then develop an algorithm for determining the optimal lot sizes. We analytically demonstrate that the lot sizes derived using an average annual cost approach for the different variants of the problem are, in general, larger than the DCF optimum. While DCF analysis is more rigorous and yields precise lot sizes, we recognize that the associated mathematical models and the solution procedure are rather complex. Since simple and easy‐to‐understand policies have a strong practical appeal to decision makers, we propose a DCF version of a simple and easy‐to‐implement heuristic called the "Early Purchase" (EP) strategy and discuss its performance. We supplement our analytical developments with a detailed computational analysis and discuss the implications of our findings for decision making.
In: Decision sciences, Volume 13, Issue 1, p. 101-112
ISSN: 1540-5915
ABSTRACTOften, order quantity decisions are made by purchasers facing a price schedule of quantity discounts. Traditional solution procedures have consisted of the evaluation of total cost at numerous price‐break points in search of the lowest total cost. This approach is tedious and not particularly informative, especially when one is faced with lengthy schedules.This paper presents a total setup lot‐sizing model that reduces the computations required to find the least‐total‐cost quantity, given parameters from a supplier's price schedule.The parameters are first obtained by simple regression (graphical or computer) and in themselves can provide valuable insight for the purchaser's decision making. A total setup lot‐sizing model is next developed to define a "critical interval" that contains the solution. The model and algorithm are tested under a variety of conditions. Their application offers the decision maker a convenient alternative to determine the best quantity to order from a tendered price schedule.
In: International journal of physical distribution and logistics management, Volume 23, Issue 1, p. 30-44
ISSN: 0020-7527
A comprehensive review of the literature for the problem of
lot‐size scheduling (serial and assembly) considering the uncapacitated
problem and complicated capacitated assembly manufacturing structure.
Analyses the different solution techniques and findings for each product
set.
SSRN
In: Lecture notes in economics and mathematical systems, 644
The presented work combines two areas of research: cooperative game theory and lot size optimization. One of the most essential problems in cooperations is to allocate cooperative profits or costs among the partners. The core is a well known method from cooperative game theory that describes efficient and stable profit/cost allocations. A general algorithm based on the idea of constraint generation to compute core elements for cooperative optimization problems is provided. Beside its application for the classical core, an extensive discussion of core variants is presented and how they can be handled with the proposed algorithm. The second part of the thesis contains several cooperative lot sizing problems of different complexity that are analyzed regarding theoretical properties like monotonicity or concavity and solved with the proposed row generation algorithm to compute core elements; i.e. determining stable and fair cost allocations.