, Volume 26, Issue 1, pp 30–67 | Cite as

Optimization model for a production, inventory, distribution and routing problem in small furniture companies

  • Pedro L. Miranda
  • Reinaldo Morabito
  • Deisemara Ferreira
Original Paper


Production and distribution are two key decisions in supply chain planning. In order to achieve an effective operational performance, it is important for these two decisions to be integrated, especially in supply chains with low inventory levels. In this paper, we propose a mixed integer programming model to integrate production, inventory, distribution and routing decisions in a single framework. The model was inspired by small Brazilian furniture companies and focuses on production and distribution decisions at an operational level. In particular, we consider a scenario in which only one production line and one vehicle, which makes multiple trips over the planning horizon, are available to produce items and deliver final products, respectively. We also take into account some features rarely considered in the literature, but commonly found in real-world applications, such as producing and stocking multiple items, distribution routes extending over one or more periods, multiple time windows and customers’ due dates. Computational tests on a set of randomly generated instances were carried out using a well-known optimization software and six relax-and-fix heuristics, which explore different criteria for partitioning and fixing variables. We also implemented two hybrid heuristics in which an initial solution is first constructed and then fed into the optimization software to improve it. The results showed that one relax-and-fix and the two hybrid heuristics performed better than the solver on the largest instances.


Production, inventory, distribution routing problem Production routing problem Integrated production–distribution planning Furniture industry 

Mathematics Subject Classification

90B06 90C11 90C27 



The authors would like to thank the two anonymous reviewers for their useful comments and suggestions of revision.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2017

Authors and Affiliations

  1. 1.Department of Production EngineeringFederal University of São CarlosSão CarlosBrazil
  2. 2.Department of Physics, Chemistry and MathematicsFederal University of São CarlosSorocabaBrazil

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