A polyhedral approach to the single row facility layout problem

Amaral, André Renato Sales; Letchford, Adam N.

doi:10.1007/s10107-012-0533-z

Cited by 71 publications

(51 citation statements)

References 35 publications

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“…Let us give an illustrating example by looking at the concrete cost structure of a small bipartite instance with V 1 = {1, 2, 3}, V 2 = {4, 5, 6, 7} and E 1 = {(1, 4), (1,5), (1,6), (2,4), (2,5), (2,7), (3,4), (3,6)}. The matrix C 1 is indexed rowwise by the pairs (1, 2), (1, 3), (2, 3).…”

Section: Multi-level Crossing Minimizationmentioning

confidence: 99%

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Semidefinite relaxations of ordering problems

Hungerländer

Rendl

2013

Math. Program.

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Ordering problems assign weights to each ordering and ask to find an ordering of maximum weight. We consider problems where the cost function is either linear or quadratic. In the first case, there is a given profit if the element u is before v in the ordering. In the second case, the profit depends on whether u is before v and r is before s.The linear ordering problem is well studied, with exact solution methods based on polyhedral relaxations. The quadratic ordering problem does not seem to have attracted similar attention. We present a systematic investigation of semidefinite optimization based relaxations for the quadratic ordering problem, extending and improving existing approaches. We show the efficiency of our relaxations by providing computational experience on a variety of problem classes.

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Section: Multi-level Crossing Minimizationmentioning

confidence: 99%

“…[2,3] proposed a cutting plane algorithm that improved on the algorithm in [5]. Amaral also introduced new instances with 33 and 35 departments, solved them to optimality and pointed out that he could not solve larger instances with his approach as the involved linear programs became too large and too difficult.…”

Section: The Single-row Facility Layout Problemmentioning

confidence: 99%

Semidefinite relaxations of ordering problems

Hungerländer

Rendl

2013

Math. Program.

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“…These are the integer linear programming (ILP) approaches of Amaral and Letchford [4] and Amaral [3], the SDP approach of Anjos and Vanelli [8] building on relaxation (SDP 2 ) and the SDP approach from [26] building on relaxation (SDP 3 ).…”

Section: Comparison Of Globally Optimal Methods For Small and Medium mentioning

confidence: 99%

“…Recently Amaral and Letchford [4] achieved significant progress in that direction by identifying several classes of valid inequalities and using them as cutting planes. Amaral [3] improved the LP relaxation by modelling (SRFLP) via n 3 binary betweenness variables.…”

Section: The Most Successful Modelling Approaches To (Srflp)mentioning

confidence: 99%

“…However all these models suffer from weak lower bounds and hence have high computation times and memory requirements. But just recently Amaral and Letchford [4] achieved significant progress in that direction through the first polyhedral study of the distance polytope for (SRFLP) and showed that their approach is quite effective for instances with challenging size (n ≥ 30). Amaral [3] suggested an LP-based cutting plane algorithm using betweenness variables that proved to be highly competitive and solved instances with up to 35 facilities to optimality.…”

Section: Introductionmentioning

confidence: 99%

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A computational study and survey of methods for the single-row facility layout problem

Hungerländer

Rendl

2012

Comput Optim Appl

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Abstract. The single-row facility layout problem (SRFLP) is an NP-hard combinatorial optimization problem that is concerned with the arrangement of n departments of given lengths on a line so as to minimize the weighted sum of the distances between department pairs. (SRFLP) is the one-dimensional version of the facility layout problem that seeks to arrange rectangular facilities so as to minimize the overall interaction cost. This paper compares the different modelling approaches for (SRFLP) and applies a recent SDP approach for general quadratic ordering problems from Hungerländer and Rendl to (SRFLP). In particular, we report optimal solutions for several (SRFLP) instances from the literature with up to 42 departments that remained unsolved so far. Secondly we significantly reduce the best known gaps and running times for large instances with up to 100 departments.

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See the light: Optimization of put‐to‐light order picking systems

Boysen

Füßler

Stephan

2020

Naval Research Logistics

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Put‐to‐light order picking systems invert the basic logic of conventional picker‐to‐parts systems. Instead of successively visiting the storage positions of the stock keeping units (SKUs) when collecting picking orders, an order picker accompanies successive bins each containing multiple items of a specific SKU along a lane of subsequent orders. Whenever the picker passes an order requiring the current SKU, which is indicated by a light signal, she puts the requested number of items into the bin associated with the order. Such an order picking system is well‐suited if the assortment is not overly large and all orders demand similar SKUs, so that it is mainly applied in distribution centers of brick‐and‐mortar retail chains. This paper evaluates four different setups of put‐to‐light systems, which, during operations, require the solution of different storage assignment and SKU sequencing problems. We formulate these problems, prove computational complexity, and suggest suited solution algorithms. By applying these algorithms in a comprehensive computational study, we benchmark the impact of the four different setups on picking performance. In this way, warehouse managers receive decision support on how to set up their put‐to‐light systems.

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A polyhedral approach to the single row facility layout problem

Cited by 71 publications

References 35 publications

Semidefinite relaxations of ordering problems

Semidefinite relaxations of ordering problems

A computational study and survey of methods for the single-row facility layout problem

See the light: Optimization of put‐to‐light order picking systems

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