Bin Packing, Variants

Years and Authors of Summarized Original Work

• 1994; Anily, Bramel, and Simchi-Levi

• 2012; Epstein, Levin

Problem Definition

The well-known bin packing problem [3, 8] has numerous variants [4]. Here, we consider one natural variant, called the bin packing problem with general cost structures (GCBP) [1, 2, 6]. In this problem, the action of an algorithm remains as in standard bin packing. We are given n items of rational sizes in (0, 1]. These items are to be assigned into unit size bins. Each bin may contain items of total size at most 1. While in the standard problem the goal is to minimize the number of used bins, the goal in GCBP is different; the cost of a bin is not 1, but it depends on the number of items actually packed into this bin. This last function is a concave function of the number of packed items, where the cost of an empty bin is zero. More precisely, the input consists of n items I = { 1, 2, …, n} with sizes $1 \geq s_{1} \geq s_{2} \geq \cdots \geq s_{n} \geq 0$and...