A multi-objective programming approach to 1.5-dimensional assortment problem

• Published in: European journal of operational research Vol. 179; no. 1; pp. 64 - 79
• Main Authors: Gasimov, Rafail N., Sipahioglu, Aydin, Saraç, Tugba
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.05.2007; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: 1.5-dimensional assortment problem; Applied sciences; Conic scalarization; Cutting; Cutting stock problem; Exact sciences and technology; Flows in networks. Combinatorial problems; Integer programming; Inventory management; Linear programming; Mathematical programming; Mixed integer linear programming; Multi-objective programming; Operational research and scientific management; Operational research. Management science; Optimization; Studies; Weighted sum scalarization; Cutting; Weighted sum scalarization; Conic scalarization; Multi-objective programming; Mixed integer linear programming; 1.5-dimensional assortment problem; Ordered set; Cutting stock problem; Multiobjective programming; Scalarization; Minimization; Mixed integer programming; Convex programming; Linear model; Non convex analysis
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2006.03.016

In this paper we study a 1.5-dimensional cutting stock and assortment problem which includes determination of the number of different widths of roll stocks to be maintained as inventory and determination of how these roll stocks should be cut by choosing the optimal cutting pattern combinations. We propose a new multi-objective mixed integer linear programming (MILP) model in the form of simultaneously minimization two contradicting objectives related to the trim loss cost and the combined inventory cost in order to fulfill a given set of cutting orders. An equivalent nonlinear version and a particular case related to the situation when a producer is interested in choosing only a few number of types among all possible roll sizes, have also been considered. A new method called the conic scalarization is proposed for scalarizing non-convex multi-objective problems and several experimental tests are reported in order to demonstrate the validity of the developed modeling and solving approaches.