A heuristic approach for big bucket multi-level production planning problems

Akartunalı, Kerem; Miller, Andrew J.

doi:10.1016/j.ejor.2007.11.033

Cited by 102 publications

(78 citation statements)

References 36 publications

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“…Akartunalı and Miller [2009] proved that the LP relaxations of S-ILS, FL, and SR yield the same lower bound for the CLST-ML problem. To the best of our knowledge, no other theoretical results have been demonstrated on their relationships.…”

Section: Equivalence Of Strong Formulationsmentioning

confidence: 99%

“…Denizel et al [2008] subsequently showed the equivalence of the LP relaxations of the FL and SR formulations for the CLST-ML. Akartunalı and Miller [2009] added (l, S) separation cuts to the ILS formulation, and then showed that this strengthened version of the formulation provides the same LP lower bounds as the FL and SR formulations for the CLST-ML. Furthermore, Akartunalı and Miller [2007] compare a wide variety of different lower bounds for the CLST-ML.…”

Section: Introductionmentioning

confidence: 99%

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On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Shi

Geunes

et al. 2011

J Glob Optim

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Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the socalled Facility Location formulation, the Shortest Route formulation, and the Inventory and Lot Sizing formulation with (ℓ, S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decompositionbased methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the Relax-and-Fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures.

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Section: Equivalence Of Strong Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Shi

Geunes

et al. 2011

J Glob Optim

Self Cite

View full text Add to dashboard Cite

show abstract

“…For these and other reasons, the polyhedral structure of this model is, in general, rich and complicated. However, solving such small problems to optimality (i.e., solving the pricing problem in our framework) is computationally tractable, as attested by authors who have used such submodels in primal heuristics (e.g., Stadtler 2003, Federgruen et al 2007, Akartunalı and Miller 2009. In this paper, although we do not characterize new families of inequalities, the methodology we develop is capable of providing information concerning how effective such results could be.…”

Section: Introductionmentioning

confidence: 96%

“…Solution approaches for lot-sizing problems have varied from heuristic methods to exact approaches based on mathematical programming. A variety of heuristics can be found in Stadtler (2003), Pochet and Van Vyve (2004), Federgruen et al (2007), and Akartunalı and Miller (2009). Mathematical programming approaches have mainly involved adding valid inequalities (e.g., Barany et al 1984;Constantino 1996;Wolsey 1988, 1994) and extended reformulations of the problem (e.g., Krarup and Bilde 1977, Eppen and Martin 1987, Rardin and Wolsey 1993, although few studies facilitate other techniques, such as Lagrangian relaxation (e.g., Billington et al 1986) and Dantzig-Wolfe decomposition (e.g., Bitran andMatsuo 1986, Degraeve andJans 2007).…”

Section: Introductionmentioning

confidence: 99%

Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems

Akartunalı

Fragkos

Miller³

et al. 2016

INFORMS Journal on Computing

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D espite the significant attention they have drawn, big-bucket lot-sizing problems remain notoriously difficult to solve. Previous literature contained results (computational and theoretical) indicating that what makes these problems difficult are the embedded single-machine, single-level, multiperiod submodels. We therefore consider the simplest such submodel, a multi-item, two-period capacitated relaxation. We propose a methodology that can approximate the convex hulls of all such possible relaxations by generating violated valid inequalities. To generate such inequalities, we separate two-period projections of fractional linear programming solutions from the convex hulls of the two-period closure we study. The convex hull representation of the twoperiod closure is generated dynamically using column generation. Contrary to regular column generation, our method is an outer approximation and can therefore be used efficiently in a regular branch-and-bound procedure. We present computational results that illustrate how these two-period models could be effective in solving complicated problems.

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“…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%

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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A heuristic approach for big bucket multi-level production planning problems

Cited by 102 publications

References 36 publications

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems

A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands

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