Solving network design problems via iterative aggregation

Bärmann, Andreas; Liers, Frauke; Martín, Alexander; Merkert, Maximilian; Thurner, Christoph; Weninger, Dieter

doi:10.1007/s12532-015-0079-1

Cited by 13 publications

(14 citation statements)

References 23 publications

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“…Instead of only one level of aggregation (from items to clusters), allow multiple levels, and iteratively refine the placement plan at each level. This technique has been applied successfully to other aggregationbased optimization frameworks, e.g., Bärmann et al (2015) and Shetty and Taylor (1987), and has the potential of further enhancing scalability without severely impacting the optimality gap.…”

Section: Discussionmentioning

confidence: 99%

Item Aggregation and Column Generation for Online-Retail Inventory Placement

Chen

Graves

2021

M&SOM

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Problem definition: This paper studies an online retailer’s problem of choosing fulfillment centers in which to place items. We formulate the problem as a mixed-integer program that models thousands or millions of items to be placed in dozens of fulfillment centers and shipped to dozens of customer regions. The objective is to minimize the sum of shipping and fixed costs over one planning period. Academic/practical relevance: A good placement plan can significantly reduce the operational cost, which is crucial for online-retail businesses because they often have a low profit margin. The placement problem can be difficult to solve with existing techniques or off-the-shelf software because of the large number of items and the fulfillment center fixed costs and capacity constraints. Methodology: We propose a large-scale optimization framework that aggregates items into clusters, solves the cluster-level problem with column generation, and disaggregates the solution into item-level placement plans. We develop an a priori bound on the optimality gap, and we also apply the framework to a numerical example that consists of 1,000,000 items. Results: The a priori bound provides insights on how to select the appropriate aggregation criteria. For the numerical example, our framework produces a near-optimal solution in a few hours, significantly outperforming a sequential placement heuristic that approximates the status quo. Managerial implications: Our study provides a computationally efficient approach for solving online-retail inventory placement as well as similar large-scale optimization problems in practice.

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Section: Discussionmentioning

confidence: 99%

Item Aggregation and Column Generation for Online-Retail Inventory Placement

Chen

Graves

2021

M&SOM

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“…Aggregation (coarsening) is a powerful approach that is used to compute approximate solutions for optimization problems. At a fundamental level, coarsening omits local details of the problem while preserving the global structure [17]. For instance, one can partition the elements of an optimization model (e.g., nodes in an underlying graph or network) according to attributes.…”

Section: Introductionmentioning

confidence: 99%

“…The aggregation process then aims to aggregate/cluster elements with similar attributes by minimizing a distance measure [18]. This distance can be defined, for instance, as the geographical distance between nodes in a graph [17] or demands of products [19]. Product aggregation has been used in inventory management problems [18] and production planning problems [20].…”

Section: Introductionmentioning

confidence: 99%

Solution of Large-Scale Supply Chain Models using Graph Sampling & Coarsening

Ma¹,

Zavala

2021

Preprint

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We present a graph sampling and coarsening scheme (gSC) for computing lower and upper bounds for large-scale supply chain models. An edge sampling scheme is used to build a lowcomplexity problem that is used to finding an approximate (but feasible) solution for the original model and to compute a lower bound (for a maximization problem). This scheme is similar in spirit to the so-called sample average approximation scheme, which is widely used for the solution of stochastic programs. A graph coarsening (aggregation) scheme is used to compute an upper bound and to estimate the optimality gap of the approximate solution. The coarsening scheme uses node sampling to select a small set of support nodes that are used to guide node/edge aggregation and we show that the coarsened model provides a relaxation of the original model and a valid upper bound. We provide numerical evidence that gSC can yield significant improvements in solution time and memory usage over state-of-the-art solvers. Specifically, we study a supply chain design model (a mixed-integer linear program) that contains over 38 million variables and show that gSC finds a solution with an optimality gap of < 0.5% in less than 22 minutes.

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“…The aggregation is then dynamically updated to obtain the optimum of the column generation. In [2], aggregation is applied to a network design model: nodes are aggregated, and an ad-hoc scheme is proposed to disaggregate the current partition, based on min-cut algorithms.…”

Section: Introductionmentioning

confidence: 99%

Iterative aggregation and disaggregation algorithm for pseudo-polynomial network flow models with side constraints

Clautiaux

Hanafi

Macedo

et al. 2017

European Journal of Operational Research

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International audienceThis paper develops a general solution framework based on aggregation techniques to solve NP-Hard problems that can be formulated as a circulation model with specific side constraints. The size of the extended Mixed Integer Linear Programming formulation is generally pseudo-polynomial. To efficiently solve exactly these large scale models, we propose a new iterative aggregation and disaggregation algorithm. At each iteration, it projects the original model onto an aggregated one, producing an approximate model. The process iterates to refine the current aggregated model until the opti-mality is proved. The computational experiments on two hard optimization problems (a variant of the vehicle routing problem and the cutting-stock problem) show that a generic implementation of the proposed framework allows us to out-perform previous known methods

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Solving network design problems via iterative aggregation

Cited by 13 publications

References 23 publications

Item Aggregation and Column Generation for Online-Retail Inventory Placement

Item Aggregation and Column Generation for Online-Retail Inventory Placement

Solution of Large-Scale Supply Chain Models using Graph Sampling & Coarsening

Iterative aggregation and disaggregation algorithm for pseudo-polynomial network flow models with side constraints

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