A global optimization approach for solving three-dimensional open dimension rectangular packing problems

An effective placement method for the single container loading problem

“…In Experiment 1, we used the benchmark dataset in Tsai et al (2014) as small-scale instances with 10 n  (cf. Table 1, 2 and 3) to compare the computational times and solution qualities required by the reference MILP model, SL, BL and the proposed loading placement heuristic.…”

“…Table 1, 2 and 3) to compare the computational times and solution qualities required by the reference MILP model, SL, BL and the proposed loading placement heuristic. Tsai et al, 2014).…”

“…[Place Table 2 in this location] Table 3 Dataset in Instances 7-10 (cf. Problem 7-10 of Tsai et al, 2014).…”

“…Denote the length, width, and height of the space required to pack all the n boxes into a container by x, y and z, respectively. Referring to Chen et al (1995), Tsai and Li (2006), and Tsai et al (2014), the 3DCLP model studied in this paper can be stated as follows: The notation used in the 3DCLP model (cf. Chen et al, 1995;Tsai and Li, 2006;Tsai et al, 2014) is described below:…”

“…They modified the MINLP by reducing the number of binary variables and utilizing a piecewise linearization technique to find a global optimum within a tolerable error. Tsai et al (2014), subsequently, converted the original MINLP into an MILP with an improved piecewise linearization technique using fewer extra zero-one variables and constraints to enhance the computational efficiency. On the other hand, Hu et al (2012) developed a transformation method to convert the nonlinear objective function in the 3DCLP into an increasing function with single variable and two fixed parameters.…”