Problem description

In a location-routing problem, a supplier of a product seeks to satisfy demands raised by some retailers in different locations. To do this, the supplier has to establish a number of DCs. The problem is defined as the determination of locations for DCs. The transportation network connecting supplier to potential DCs supposed to be a multimodal network including three transportation modes (road, railways and seaways); and transportation from DCs to retailers is performed via a road network (one mode). On road network products pass through routing tours to be moved from DCs to retailers. Figure 1 demonstrates the problem schematically. The multimodal links on the figure can represent either of a road, a railway, a seaway, or a combination of these transportation modes with multimodal terminals to change modes.

Fig. 1 Schematic of the proposed problem




This problem is based on the following assumptions:

  • Each transportation mode has a specific and determined cost.
  • During the transportation operation, transportation mode may be changed at some nodes along the multimodal network.
  • Transportation mode can be changed at multimodal terminals where at least two different transportation modes start/end. Providing mode change facilities imposes a fixed cost to the system.
  • Product unit does not change when transportation mode changes.
  • DCs need a fixed cost to establish.
  • Capacities of DCs are constrained by the capacities of the allocated vehicles.
  • Retailers' demands are determined and satisfied through routing tours starting from established DCs. The tours return back to the DC after meeting a number of retailers.
  • For each DC, one vehicle is allocated with one tour determined for each vehicle.
  • Each retailer is assigned to a pair of vehicle and DC.
  • Total allocated retailers' demand cannot exceed the vehicle capacity.