In this paper we suggest a new variant of Variable neighborhood search designed for solving Mixed integer programming problems. We call it Variable neighborhood formulation search (VNFS), since both neighborhoods and formulations are changed during the search. | Yugoslav Journal of Operations Research 27 (2017), Number 3, 301–322 DOI: VARIABLE NEIGHBORHOOD FORMULATION SEARCH APPROACH FOR THE MULTI-ITEM CAPACITATED LOT-SIZING PROBLEM WITH TIME WINDOWS AND SETUP TIMES Ridha ERROMDHANI Université de Sfax, FSEGS, Tunisie erromdhaniridha@ Bassem JARBOUI Emirates College of Technology, Abu Dhabi, United Arab Emirates bassem_jarboui@ Mansour EDDALY Université de Sfax, FSEGS, Tunisie Abdelwaheb REBAI Université de Sfax, FSEGS, Tunisie ´ Nenad MLADENOVIC University of Belgrade, FOS, Belgrade, Serbia Received: April 2016 / Accepted: September 2016 Abstract: In this paper we suggest a new variant of Variable neighborhood search designed for solving Mixed integer programming problems. We call it Variable neighborhood formulation search (VNFS), since both neighborhoods and formulations are changed during the search. VNS deals with integer variables, while an available (commercial) solver is responsible for continues variables and the objective function value. We address the multi-item capacitated lotsizing problem with production time windows and setup times, under the non-customer specific case. This problem is known to be NP-hard and can be formulated as a mixed 0-1 program. Neighborhoods are induced from the Hamming distance in 0-1 variables, while the objective function values in the corresponding neighborhoods are evaluated using different mathematical programming formulations of the problem. The computational experiments show that our approach is more effective and efficient when compared with the existing methods from the literature. Keywords: Production Planning, Multi-item lot-sizing, Variable Neighborhood Search, Formulation Space Search, Matheuristic. MSC: 90B06, 90C05, 90C08. 1. INTRODUCTION Lot sizing problem. The production planning process aims to establish an overall level of manufacturing .
