scholarly journals Column generation for the variable cost and size bin packing problem with fragmentation

2016 ◽  
Vol 55 ◽  
pp. 61-64 ◽  
Author(s):  
Marco Casazza ◽  
Alberto Ceselli
Keyword(s):  
Column Generation ◽  
Bin Packing ◽  
Packing Problem ◽  
Variable Cost ◽  
Bin Packing Problem

scholarly journals A hybrid VNS matheuristic for a bin packing problem with a color constraint

2021 ◽  
pp. 9-9
Author(s):  
Yury Kochetov ◽  
Arteam Kondakov
Keyword(s):  
Column Generation ◽  
Bin Packing ◽  
Packing Problem ◽  
Upper Bounds ◽  
Hard Problem ◽  
Generation Technique ◽  
Bin Packing Problem ◽  
New Variant ◽  
Finite Set ◽  
Np Hard Problem

We study a new variant of the bin packing problem with a color constraint. Given a finite set of items, each item has a set of colors. Each bin has a color capacity, the total number of colors for a bin is the unification of colors for its items and cannot exceed the bin capacity. We need to pack all items into the minimal number of bins. For this NP-hard problem we present approximability results and design a hybrid matheuristic based on the column generation technique. A hybrid VNS heuristic is applied to the pricing problem. The column generation method provides a lower bound and a core subset of the most promising bin patterns. Fast heuristics and exact solution for this core produce upper bounds. Computational experiments for test instances with number of items up to 500 illustrate the efficiency of the approach.

Efficient lower bounds and heuristics for the variable cost and size bin packing problem

2011 ◽  
Vol 38 (11) ◽  
pp. 1474-1482 ◽  
Author(s):  
Teodor Gabriel Crainic ◽  
Guido Perboli ◽  
Walter Rei ◽  
Roberto Tadei
Keyword(s):  
Lower Bounds ◽  
Bin Packing ◽  
Packing Problem ◽  
Variable Cost ◽  
Bin Packing Problem

Branch-and-price and beam search algorithms for the Variable Cost and Size Bin Packing Problem with optional items

2012 ◽  
Vol 222 (1) ◽  
pp. 125-141 ◽  
Author(s):  
Mauro Maria Baldi ◽  
Teodor Gabriel Crainic ◽  
Guido Perboli ◽  
Roberto Tadei
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
Search Algorithms ◽  
Variable Cost ◽  
Beam Search ◽  
Branch And Price ◽  
Bin Packing Problem

scholarly journals fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing

2021 ◽  
Vol 24 (67) ◽  
pp. 71-89
Author(s):  
Jorge Herrera-Franklin ◽  
Alejandro Rosete ◽  
Milton García-Borroto
Keyword(s):  
Bin Packing ◽  
Solution Method ◽  
Optimization Problems ◽  
Real Life ◽  
Packing Problem ◽  
Variable Cost ◽  
Bin Packing Problem ◽  
Trade Offs ◽  
Np Hard Problem ◽  
The Cost

The Variable Cost and Size Bin Packing Problem (VCSBPP) is a known NP-Hard problem that consists in minimizing the cost of all bins used to pack a set of items. There are many real-life applications of the VCSBPP where the focus is to improve the efficiency of the solution method. In spite of the existence of fuzzy approaches to adapt other optimization problems to real life conditions, VCSBPP has not been extensively studied in terms of relaxations of the crisp conditions. In this sense, the fuzzy approaches for the VCSBPP varies from relaxing the capacity of the bins to the items weights. In this paper we address a non-explored side consisting in relaxing the set of items to be packed. Therefore, our main contribution is a fuzzy version of VCSBPP that allows incomplete packing. The proposed fuzzy VCSBPP is solved by a parametric approach. Particularly, a fast heuristic algorithm is introduced that allows to obtain a set of solutions with interesting trade-offs between cost and relaxation of the original crisp conditions. An experimental study is presented to explore the proposed fuzzy VCSBPP and its solution.

Variable Neighborhood Search Algorithm for the Variable Cost and Size Bin Packing Problem

2019 ◽  
pp. 1-17
Author(s):  
Héctor J. Fraire-Huacuja ◽  
Alejandro Estrada Padilla ◽  
Laura Cruz-Reyes ◽  
Claudia Gómez-Santillán ◽  
Nelson Rangel-Valdez ◽  
...  
Keyword(s):  
Variable Neighborhood Search ◽  
Bin Packing ◽  
Search Algorithm ◽  
Hypothesis Test ◽  
Value Added ◽  
Packing Problem ◽  
Neighborhood Search ◽  
Variable Cost ◽  
Order Batching ◽  
Bin Packing Problem

A company that transports goods to supply customers usually needs to plan the routes that the fleet must follow, since transportation means a high percentage of the value added to goods. The vehicles must be loaded with the products located in the warehouse to fulfill the orders requested by customers. Many enterprises use order batching and picking systems to improve the warehouse management. This chapter describes a novel algorithm based on the methodology of variable neighborhood search for the variable cost and size bin packing problem. This problem considers that the sizes and costs of the bins can be different and there is no correlation between them, which is a sensible assumption for the order batching process in many applications. A series of computational experiments were conducted with a set of hard instances to validate this approach. The results show that the proposed algorithm outperforms the state-of-the-art algorithm, and a statistical hypothesis test is used to support the obtained conclusions.

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