Solution Approaches for the Bi-Objective Skiving Stock Problem

The Skiving Stock Problem (SSP) aims to determine an optimal plan for producing as many large objects as possible by combining small items. The skiving process may needs different considerations depending on the production area and the product characteristics. In this study, we address the bi-objective SSP with two conflicting objectives. One common objective is to minimize the trim loss remaining after skiving. In the casewhere welding is an element of the skiving process, increasing the number of items for each product indicates compromised quality. Therefore, minimization of the number of small items for each product becomes a primary objective in such cases. To solve this bi-objective version of the NP-hard problem, we implement a Lexicographic Method (LM) in which the importance of the objectives impose their preference orders. We first implement a Column Generation (CG) approach to obtain the optimal pattern set that minimizesobjective function values and provides non-dominated LP relaxation solution in a Lexicographic procedure. Then we apply Integer programming (IP) to the problem to obtain the non-dominated integer solution. In the lexicographic procedure, the solution of a higher priority objective function becomes a constraint for the lesser important objective function. Application results demonstrate the efficiency of the solution methodology for a preemptive multi-objective SSP. Furthermore, for the tight or large problems whereInteger Programming is not efficient in terms of CPU time to obtain the integer non-dominated solution, a heuristic approach is proposed to where Dragonfly Algorithm is modified for the SSP and integrated with the Constructive Heuristic, in order to obtain a feasible integer solution for the bi-objective SSP directly. Performances of heuristic approach and CG-IP combination are compared in terms of the quality of solutionsand CPU times. Furthermore, experiments are carried out for the instances which are selected from real world cases