Performance of a Heuristic Total Weight in Combinatorial Mixture Packaging of Two Types of Items

Abstract

In this paper, a combinatorial optimization model of mixture packaging of two types of items is treated, which arises in actual packing systems, so-called multi-head weighers. The primary objective is to minimize the total weight of chosen items for a package under the condition that the total weight must be no less than a specified target weight. For a package to be produced, the weight sum of chosen items of each type must also be no less than a prescribed necessity minimum. In this paper, a heuristic algorithm is designed for the problem of minimizing the total weight, and for a given positive real ε, the performance factor is shown to be (1 + ε).

An improved performance of greedy heuristic solutions for a bi-criteria mixture packaging problem of two types of items with bounded weights

“…In this paper, we are interested in the mathematical aspect of the lexicographic bi-criteria mixture packaging problem of two types of items, and please see the literature for the detail of the repetitive motion of multi-head weighers, e.g., Morinaka (2000). We have also explained the repetitive motion of multi-head weighers in some our previous papers, e.g., see Imahori et al (2014), Imahori et al (2016), Karuno and Nakahama (2018).…”

“…The lexicographic bi-criteria mixture packaging problem of two types of items is NP-hard, while it can be solved in pseudo-polynomial time (see Imahori et al, 2014, Imahori et al, 2016. The pseudo-polynomial time algorithm based on dynamic programming is also applied to a heuristic algorithm design for the problem of minimizing the total weight of chosen items in a feasible solution (see Karuno and Nakahama, 2018). That is, for a given real ε > 0 (with an upper limit), the performance factor of the heuristic algorithm on the minimum total weight is at most (1 + ε), and the time complexity is polynomial in n = |I| and 1/ε.…”