PME I J https://ojs.upv.es/index.php/IJPME International Journal of Production Management and Engineering http://dx.doi.org/10.4995/ijpme.2014.1838 Received 2013-11-07 - Accepted 2013-12-16 MILP for the inventory and routing problem for replenishment the car assembly line. Pulido, R. a,b,i,iv *, García-Sánchez, A. a,ii , Ortega-Mier, M. a,iii and Brun, A. b,v a Escuela Técnica Superior de Ingenieros Industriales. UPM. José Gutierrez Abascal 2. 28006, Madrid, Spain. i raul.pulido@upm.es ii alvaro.garcia@upm.es iii miguel.ortega.mier@upm.es b Politecnico di Milano, Dipartimento di Ingegneria Gestionale, via Lambruschini 4/b, Milan, Italy. iv raul.pulido@polimi.it v alessandro.brun@polimi.it Abstract: The inbound logistics for feeding the workstation inside the factory represents a critical issue in the car manufacturing industry. Nowadays, this issue is even more critical than in the past since more types of cars are being produced in the assembly lines. Consequently, as workstations have to install many types of components, they also need to have an inventory of different types of components in a usually compact space. The replenishment of inventory is a critical issue since a lack of it could cause line stoppage or reprocessing. On the other hand, an excess of inventory could increase the holding cost or even block the replenishment paths. The decision of the replenishment routes cannot be made without taking into consideration the inventory needed in each station during the production time, which will depend on the production, sequence plan sent by the central office. This problem deals with medium-sized instances and it is solved using online solvers. The contribution of this paper is a MILP model for the replenishment and inventory of the components in a car assembly line. Key words: Integer Programming, Routing, Inventory, Assembly line. 1. Introduction Today’s customer looks for a specifc confguration of cars; this has encouraged car manufacturers to offer plenty of options for each item of the cars. Car manufacturers have changed from offering a single model to offering a huge number of model confgurations. These car manufacturers have evolved from selling one model of one car as Ford did, with his Model-T, to offering many options (Ghosh and Gagnon, 1989). For instance single visit to a car manufacturer’s web page, such as Mercedes Benz, allows us to customized car, choosing each component such as rims, engine, tires, the design of the interior and exterior, steering, radio, safety, color, the size of engine, seats, and so on. This creates more theoretical confgurations than actual ones that could be produced in one year. Today’s factories use car assembly lines in which the setup times between models can be ignored, and then the mixed model line approach is used. This fexibility is provided by the development in the interactions between humans, machines, equipment, robots, transportation system, etc. In this paper, we are focusing on the interaction of routing and the replenishment of the components. This fexibility increases the complexity of the replenishment of the component. Assembly lines are fow-oriented production systems, which are still typical for the production of high quantity standardized commodities and they are even gaining importance in the low volume production of a customized product (Becker and Scholl, 2006). One of the most complex products that is built in the assembly lines is cars and trucks. The assembly lines are a way to mass-produce cars quickly and effciently. They rely on the ability to assign easy tasks to humans and robots and move parts from one worker to another until the car is fnished. Different tasks require certain equipment of machines, skills of workers, and components to be utilized. For the single model line (see fg.1), this was easy to solve because the requirements were periodic and homogeneous. 37 Int. J. Prod. Manag. Eng. (2014) 2(1), 37-45 Creative Commons Attribution-NonCommercial 3.0 Spain