Brahimi, N., Dauzère-Pérès, S., Najid, N. and Nordli, A. (2003) Alagrangian Relaxation Heuristic for the Capacitated Single Item Lot Sizing Problem with Time Windows. 6th Workshop on Models and Algorithms for Planning and Scheduling Problems, Aussois, 30 March-4 April 2003, 105-106.

has been cited by the following article:

• TITLE: MIP Formulations and Metaheuristics for Multi-Item Capacitated Lot-Sizing Problem with Non-Customer Specific Production Time Windows and Setup Times

  AUTHORS: Ridha Erromdhani, Abdelwaheb Rebaï

  KEYWORDS: Variable Neighborhood Decomposition Search, Formatting, Metaheuristics, Production Planning, Capacitated Lot Sizing, Mixed Integer Programming, Matheuristics, Production Time Windows

  JOURNAL NAME: American Journal of Operations Research, Vol.7 No.2, March 14, 2017

  ABSTRACT: Our research focuses on the development of two cooperative approaches for resolution of the multi-item capacitated lot-sizing problems with time windows and setup times (MICLSP-TW-ST). In this paper we combine variable neighborhood search and accurate mixed integer programming (VNS-MIP) to solve MICLSP-TW-ST. It concerns so a particularly important and difficult problem in production planning. This problem is NP-hard in the strong sense. Moreover, it is very difficult to solve with an exact method; it is for that reason we have made use of the approximate methods. We improved the variable neighborhood search (VNS) algorithm, which is efficient for solving hard combinatorial optimization problems. This problem can be viewed as an optimization problem with mixed variables (binary variables and real variables). The new VNS algorithm was tested against 540 benchmark problems. The performance of most of our approaches was satisfactory and performed better than the algorithms already proposed in the literature.