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

Gasimov R. N., SİPAHİOĞLU A., Sarac T.

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, vol.179, no.1, pp.64-79, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 179 Issue: 1
  • Publication Date: 2007
  • Doi Number: 10.1016/j.ejor.2006.03.016
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.64-79
  • Keywords: cutting, 1.5-dimensional assortment problem, multi-objective programming, weighted sum scalarization, conic scalarization, mixed integer linear programming, ALGORITHM, PACKING
  • Eskisehir Osmangazi University Affiliated: Yes


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. (c) 2006 Elsevier B.V. All rights reserved.