Lego Logistics: Tangible Interactive Matrix Meets Last Mile Logistics Simulation

MIT Media Lab Changing Places Group and MIT Center for Transportation and Logistics are developing a decision support tool for calculating delivery service areas. Logistics experts can use the platform to present parametric models of logistics in a real-time, changeable environment. Researchers expect the tool to improve collaboration and consensus when optimizing distribution networks for last mile logistics.

Video by Nina Lutz.

The tool uses the tangible interactive matrix (TIM) developed at MIT Changing Places Group. TIM uses an array of optically tagged Lego objects, computer vision, and 3D projection mapping.

Users operate the tool by manipulating tangible objects that represent distribution centers (Fig. 1). All together, the objects represent a distribution network. Meanwhile, algorithms provide real-time performance evaluation of the users’ configuration. Key performance metrics in a demonstration include average delivery cost and customer demand saturation.

Figure 1. Two distribution centers are placed upon the tangible interactive matrix (TIM). Photo by James Li.

Figure 1. Two distribution centers are placed upon the tangible interactive matrix (TIM). Photo by James Li.

The use of both tangible bricks and geospatial models led us to adopt a voxel-based method for data abstraction.  (Note: a voxel is a multi-dimensional pixel).  The result is a mathematical model uniquely structured to be compatible with TIM (Fig. 2).

Figure 2. A typical GIS polygon construct (left) is translated into a TIM-compatible voxel and Lego construct (right).

Figure 2. A typical GIS polygon construct (left) is translated into a TIM-compatible voxel and Lego construct (right).

GIS data such as US Census parcels are processed and cleaned to be compatible with the system at three scales: 2km, 1km, and 500m per pixel.  In this scenario, we use population as a proxy for demand (Fig. 3).

Figure 3. Voxel-ized data can represent different areas at different scales.

Figure 3. Voxel-ized data can represent different areas at different scales.

Average delivery cost is a function of both distance traveled from distribution centers and the density of deliveries made at the “last mile”. Average delivery cost “C” is proportional to customer’s distance from a distribution center “D” divided by density of customers at last mile,  “ρ” (source: MIT Center for Transportation and Logistics).

C α D / ρ

The “last mile” refers to the short but most difficult last leg of a journey, such as a walk from a subway station to home. In the case of delivery logistics, the last mile can refer to the difficulty of handing off packages to customers at home or finding short-term parking. Cost is reduced when many drop-offs can occur within a small area. 

Figure 5. Service area solutions for 3 different placements of a single distribution center.

Figure 5. Service area solutions for 3 different placements of a single distribution center.

Customer demand is saturated when a distribution center has capacity to serve a given area.  Service areas are automatically allocated in a global manner such that average cost is minimized (Fig. 5). The result is often a non-intuitive pattern of service areas (Fig. 6).

Figure 6. Complex solution with five distribution centers of various capacities.  Green denotes cheaper areas to serve, while red areas are more expensive.

Figure 6. Complex solution with five distribution centers of various capacities.  Green denotes cheaper areas to serve, while red areas are more expensive.

Collaborators

MIT Media Lab
Ira Winder

MIT Center for Transportation and Logistics
Matthias Winkenbach
Daniel Merchan

Special Thanks

Edgar Blanco
Brandon Martin-Anderson
Mike Winder
Nina Lutz
James Li