On the generalized bin packing problem
نویسندگان
چکیده
The Generalized Bin Packing Problem (GBPP) is a novel packing problem arising in many transportation and logistic settings, characterized by multiple item and bin attributes and by the joint presence of both compulsory and non-compulsory items. We introduce a change in the definition of the problem that does not impact either on its feasible solution set or on its optimal solutions, but guarantees an objective function that is always non-negative, in order to satisfy the non-negativity requirement of the the worst-case ratio definition. In this way we can properly study the approximability of the GBPP. In this paper we study the computational complexity of the GBPP and we prove that the GBPP cannot be approximated by any constant ε , unless P = NP. Since the proof of non-approximability exploits the presence of two bin types, a separate study is made with a single bin type. We show that, in this particular case, the GBPP reduces to the Bin Packing with Rejections (BPR), which is approximable. In this particular setting we also study the behavior of standard and widespread heuristics like the FIRST FIT and the BEST FIT, showing that they fail in approximating the GBPP, even with just one bin type. Finally, we prove that the GBPP satisfies the Bellmans optimality principle and, exploiting this result, we develop a dynamic programming solution approach.
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عنوان ژورنال:
- ITOR
دوره 24 شماره
صفحات -
تاریخ انتشار 2017