Invited Review Mathematical programming models for supply chain production and transport planning Josefa Mula * , David Peidro, Manuel Díaz-Madroñero, Eduardo Vicens Research Centre on Production Management and Engineering (CIGIP), Universidad Politécnica de Valencia, Spain article info Article history: Received 11 March 2009 Accepted 9 September 2009 Available online 13 September 2009 Keywords: Mathematical programming Supply chain Production planning Transport planning abstract This paper presents a review of mathematical programming models for supply chain production and transport planning. The purpose of this review is to identify current and future research in this field and to propose a taxonomy framework based on the following elements: supply chain structure, decision level, modeling approach, purpose, shared information, limitations, novelty and application. The research objective is to provide readers with a starting point for mathematical modeling problems in supply chain production and transport planning aimed at production management researchers. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction A supply chain may be considered an integrated process in which a group of several organizations, such as suppliers, produc- ers, distributors and retailers, work together to acquire raw mate- rials with a view to converting them into end products which they distribute to retailers (Beamon, 1998). Simultaneously considering supply chain production and transport planning problems greatly advances the efficiency of both processes. The literature in the field is vast, so an extensive review of existing research on the topic is presented in an attempt to gain a better understanding of the mathematical modeling methods used in supply chain production and transport planning, and to provide a basis for future research. Given the globalization of operations, new models and tools for improving the forecasting, replenishment and production plans along supply chains are required. Furthermore in the context of supply chains, manufacturing companies increasingly need to inte- grate production and transport planning in order to optimize both these processes simultaneously. In general, we have selected papers based on the following main criteria to be included in this survey: (i) mathematical program- ming models, and (ii) centralized planning models. This review does not include those works which focus on the operational deci- sion levels and cover themes like lot sizing or production sequenc- ing. However, those works presenting production planning models which consider transport a resource to distribute products, and fo- cus on the tactical and/or operational levels and their possible combinations with aspects of a strategical nature, are considered in this review. We briefly describe each paper, but we do not describe or for- mulate the models that have been considered in detail. This work neither intends to identify every bibliographic work nor to extend a review of them, but to provide the reader with a starting point to investigate the literature about the best management methods for different supply chain production and transport planning prob- lems. The objective of this paper is to (i) review the literature, (ii) classify the literature based on the supply chain structure, deci- sion level, modeling approach, purpose, shared information, limita- tions, novelty and application; and, (iii) identify future research directions. This work can act as an overview of the state of the art of mathematical programming models for supply chain produc- tion and transport planning for new supply chain planning researchers. Besides, it can help practitioners to address this type of real-world problems in supply chains. The remainder of the paper consists of three other sections. The next section introduces the review methodology. Then Section 3 presents the taxonomy of the reviewed papers. Finally, the last sec- tion provides the conclusions and directions for future research. 2. Review methodology The search process was carried out with scientific-technical bib- liographic databases which include publishing portals like Elsevier, Taylor & Francis, Wiley or Emerald. The following search criteria were applied: supply chain linear programming models, supply 0377-2217/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2009.09.008 * Corresponding author. Address: Escuela Politécnica Superior de Alcoy, Plaza Ferrándiz y Carbonell, 2, 03801 Alcoy, Alicante, Spain. Tel.: +34 96 652 84 23; fax: +34 96 652 85 85. E-mail addresses: fmula@cigip.upv.es (J. Mula), dpeidro@cigip.upv.es (D. Peidro), fcodiama@cigip.upv.es (M. Díaz-Madroñero), evicens@cigip.upv.es (E. Vicens). European Journal of Operational Research 204 (2010) 377–390 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor