Problem Title: The Railroad Flatcar Problem

Two railroad flatcars are to be loaded with seven types of packing crates. The crates have the same width and height but varying thickness (t, in cm) and weight (w, in kg). Table 1 gives, for each crate, the thickness, weight, and number available. Each car has 10.2 meters of length available for packing the crates (like slices of toast) and can carry up to 40 metric tons. There is a special constraint on the total number of C₅, C,₆, and C₇ crates because of a subsequent local trucking restriction: The total space (thickness) occupied by these crates must not exceed 302.7 cm. Load the two flatcars (see Figure 1) so as to minimize the wasted floor space.

Table 1.
The thickness, weight, and number of each kind of crate.

Figure 1. Diagram of loading of a flatcar.

Practitioner's Commentary: The Outstanding Railroad Flatcar Problem

John J. Bartholdi, III
Georgia Industrial and Systems Engineering

Loading Two Railroad Cars

U.S. Military Academy, West Point, NY, USA

Packing a Train

University of Toronto, Toronto, Canada

Optimal Loading of Flatcars

Harvard University, Cambridge, MA, USA

Engineers Don't Drive Trains - They Pack Them

University of California, Berkeley, Berkeley, CA, USA