The location-production-routing problem
We consider the case of a two-level distribution system between a limited set of producers and a potentially very large set of customers. In order to reduce distribution costs, a network design option consists of installing intermediate Distribution Centers (DC) between the producers and the customers. Thus, the distribution network is organized in two stages: a rst stage delivers to DCs from the producers through a set of routes visiting one or more DCs. The second stage consists in delivering each customer directly from the DC to which it is assigned.
The associated decisions consist of
- locating distribution centers,
- planning production at the producers sites,
- planning distribution from production sites to distribution centers and customers,
- routing vehicles delivering the products from producers to DCs.
- Customer demands are assumed to be time varying (dynamic demands) and deterministic. The objective is to
- minimize total cost composed of:
- xed setup costs,
- unit production costs
- inventory holding costs at the production site and distribution centers
- transportation costs
This problem is an extension of the production routing problem (PRP) with location decisions. The PRP is an integration of production planning (lot sizing) and vehicle routing decisions. Though the earliest work on the PRP dates to the 1990s (e.g.  and ), it has attracted the attention of researchers during the last decade. In addition to the consideration the PRP with a single product and basic routing constraints , many extensions were studied including the multi-product case with dierent types of constraints . A survey on the PRP can be found in .
Reviews on facility location problems  and  show their relationship with other supply chain decision problems including production, inventory and routing. While  focus on mathematical formulations of the xed charge facility location problem and how they can be extended to incorporate routing decisions and inventory control decisions,  cover a wider range of papers (with 139 references) and classify them based on
dierent criteria such as the number of layers in the supply chain, the number of planning periods, and the different extensions.
The surveys show that integration of production-routing with location decisions did not receive much attention. This might be due to the fact that, historically, most location-allocation studies are concerned with strategic decisions while routing decisions are of operational nature. Some recent studies  showed evidence from practice that the integration of location-allocation, production and distribution decisions can be very important especially when warehousing is provided by 3PL companies in which case contracts can be revised annually.
The aim of this PhD subject is to model one or several innovative cases of integrated location, production and routing problems and develop optimization models and/or algorithms to solve them. In a rst phase, a literature review should be carried out to identify either new interesting extensions of the problem or problems which cannot be solved eciently with the existing methods. The next phase will focus on the implementation of chosen ecient combinatorial optimization methods. Finally, we seek to apply this work to real problems in various elds especially in biomass production and energy supply chains, health logistics, and urban logistics.
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The candidate must hold a master's degree in industrial engineering or any related eld with strong background in operations research and computer science.
The candidate must have strong programming skills in C++ or java and a professional level in English. A good knowledge of French is a plus.