The Generalized Bin Packing Problem: Models and Bounds
نویسندگان
چکیده
We present the Generalized Bin Packing Problem (GBPP), a new packing problem where, given a set of items characterized by volume and profit and a set of bins with given volumes and costs, one aims to select the subsets of profitable items and appropriate bins to optimize an objective function which combines the cost of using the bins and the profit yielded by loading the selected items. The GBPP thus aims to generalize many other packing problems such as the Bin Packing Problem (BPP), the Variable Size Bin Packing Problem (VSBPP), the Variable Cost and Size Bin Packing Problem (VCSBPP), the Knapsack Problem (KP), and the Multiple Knapsack Problem (MKP). It also provides the means to identify and analyze the trade-off between item and bin selections that are part of many transportation and logistics planning problems [1]. From a practical point of view, the GBPP models many real-life situations, including scenarios where orders may be urgent or a dispatching priority is associated to each item to be shipped. Moreover this paper contributes to enhance the transportation literature and to cope some issues in the specific literature on packing problems [2, 3]. We present two mixed integer programming formulations of the GBPP, as well as lower and upper bounds. The efficiency and accuracy of these bounds are proved by means of an extensive set of computational results.
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تاریخ انتشار 2012