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The generalized bin packing problem (GBPP) is a novel packing problem arising in many transportation and logistic settings, characterized by multiple items and bins attributes and the presence of both compulsory and non-compulsory items. In this paper, we study the computational complexity and the approximability of the GBPP. We prove that the GBPP cannot be approximated by any constant, unless [ABSTRACT FROM AUTHOR]

The problem consists in finding a transshipment facilities location that maximizes the total net utility when the handling utilities at the facilities are stochastic variables, under supply, demand, and lower and upper capacity constraints. The total net utility is given by the expected total shipping utility minus the total fixed cost of the located facilities. Shipping utilities are given by a deterministic utility for shipping freight from origins to destinations via transshipment facilities plus a stochastic handling utility at the facilities, whose probability distribution is unknown. After giving the stochastic model, by means of some results of the extreme values theory, the probability distribution of the maximum stochastic utilities is derived and the expected value of the optimum of the stochastic model is found. An efficient heuristics for solving real-life instances is also given. Computational results show a very good performance of the proposed methods both in terms of accuracy and efficiency. [ABSTRACT FROM AUTHOR]