SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the capacitated concentrator location problem: a reformulation by discretization
Computers and Operations Research
A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem
Computers and Operations Research
The two-dimensional bin packing problem with variable bin sizes and costs
Discrete Optimization
A tabu search algorithm for the heterogeneous fixed fleet vehicle routing problem
Computers and Operations Research
Efficient lower bounds and heuristics for the variable cost and size bin packing problem
Computers and Operations Research
Relaxations and exact solution of the variable sized bin packing problem
Computational Optimization and Applications
Variable neighbourhood search for the variable sized bin packing problem
Computers and Operations Research
Efficient algorithms for real-life instances of the variable size bin packing problem
Computers and Operations Research
Computers and Operations Research
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In this paper we study the use of a discretized formulation for solving the variable size bin packing problem (VSBPP). The VSBPP is a generalization of the bin packing problem where bins of different capacities (and different costs) are available for packing a set of items. The objective is to pack all the items minimizing the total cost associated with the bins. We start by presenting a straightforward integer programming formulation to the problem and later on, propose a less straightforward formulation obtained by using a so-called discretized model reformulation technique proposed for other problems (see [Gouveia L. A 2n constraint formulation for the capacitated minimal spanning tree problem. Operations Research 1995; 43:130-141; Gouveia L, Saldanha-da-Gama F. On the capacitated concentrator location problem: a reformulation by discretization. Computers and Operations Research 2006; 33:1242-1258]). New valid inequalities suggested by the variables of the discretized model are also proposed to strengthen the original linear relaxation bounds. Computational results (see Section 4) with up to 1000 items show that these valid inequalities not only enhance the linear programming relaxation bound but may also be extremely helpful when using a commercial package for solving optimally VSBPP.