Uncapacitated two-level lot-sizing

Melo, Rafael A.; Wolsey, Laurence A.

doi:10.1016/j.orl.2010.04.001

Cited by 40 publications

(32 citation statements)

References 14 publications

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“…Then the resulting recursions for G(j 2 ) and H(j 1 , j 2 ) are identical to the dynamic programming recursions in Melo and Wolsey (2010).…”

Section: Dynamic Programming Recursion and Reformulationmentioning

confidence: 99%

“…Lee et al (2003) give an O(n 6 ) algorithm for 2-ULS-F when backlogging is allowed and there is a stepwise shipment cost between the two echelons. Melo and Wolsey (2010) propose a dynamic programming algorithm with an improved running time, O(n 2 log n), and a compact tight extended reformulation for 2-ULS-F. For a review of valid inequalities and extended formulations for m-ULS-F, we refer the reader to Pochet and Wolsey (2006). An effective heuristic for capacitated m-ULS-F using strong formulations for each echelon is proposed in Akartunalı and Miller (2009).…”

Section: Introductionmentioning

confidence: 99%

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A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands

Zhang

Küçükyavuz

Yaman

2012

Operations Research

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Abstract. In this paper, we study a multi-echelon uncapacitated lot-sizing problem in series (m-ULS), where the output of the intermediate echelons has its own external demand, and is also an input to the next echelon. We propose a polynomial-time dynamic programming algorithm, which gives a tight, compact extended formulation for the two echelon case (2-ULS). Next, we present a family of valid inequalities for m-ULS, show its strength and give a polynomial-time separation algorithm. We establish a hierarchy between the alternative formulations for 2-ULS. In particular, we show that our valid inequalities can be obtained from the projection of the multi-commodity formulation. Our computational results show that this extended formulation is very effective in solving our uncapacitated multi-item 2-echelon test problems. In addition, for capacitated multiitem multi-echelon problems, we demonstrate the effectiveness of a branch-and-cut algorithm using the proposed inequalities.

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“…Then the resulting recursions for G(j 2 ) and H(j 1 , j 2 ) are identical to the dynamic programming recursions in Melo and Wolsey (2010).…”

Section: Dynamic Programming Recursion and Reformulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands

Zhang

Küçükyavuz

Yaman

2012

Operations Research

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“…Wolsey (2010, 2012) formulate a production-transportation problem as a two-level lot-sizing problem. In Melo and Wolsey (2010), the singleitem (finished product) uncapacitated two-level lot-sizing problem in series with one intermediate product is addressed. One unit of the finished product needs one unit of the intermediate product.…”

Section: Introductionmentioning

confidence: 99%

Models and Lagrangian heuristics for a two-level lot-sizing problem with bounded inventory

et al. 2015

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International audienceWe consider a two-level dynamic lot-sizing problem where the first level consists of N finished products competing for a single type of purchased raw material in the second level. While the procurement and production capacities are unlimited, the storage capacity of the raw material is limited and must be carefully managed. The goal is to simultaneously determine a replenishment plan for the raw material and optimal production plans for the finished products on a horizon of T periods while minimizing production, purchasing, setup and inventory holding costs. The problem is modeled using mixed-integer linear programs and solved using both a Lagrangian relaxation-based heuristic and a commercial mixed-integer linear programming solver. 123 N. Brahimi et al. Learning capabilities are integrated in the Lagrangian relaxation to update step size in the subgradient algorithm. The computational results show that the Lagrangian heuris-tic outperforms the solver on different formulations, in particular for large problems with long time horizons

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“…To the best of our knowledge, there is not much research work on the lot-sizing problem with multiple setup variables, except for multiechelon [23,12,15,24] or multi-item [22] cases. For single-echelon single-item lot-sizing problems, there are notable exceptions due to Sanjeevi and Kianfar [18] and Atamtürk and Hochbaum [4].…”

Section: Introductionmentioning

confidence: 99%

Capacitated lot-sizing problem with outsourcing

Zhang

2015

Operations Research Letters

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Uncapacitated two-level lot-sizing

Cited by 40 publications

References 14 publications

A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands

A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands

Models and Lagrangian heuristics for a two-level lot-sizing problem with bounded inventory

Capacitated lot-sizing problem with outsourcing

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