We develop an exact integer programming formulation to design a loop materi
al flow system for unit-load automated guided vehicles. The model simultane
ously determines both the design of the unidirectional loop flow pattern an
d the location of the pickup and delivery stations. The objective is to min
imize the total loaded-vehicle trip distances. To solve the problem, we con
centrate on developing a better formulation for the LP subproblem, preproce
ssing the problem, identifying the appropriate set of LP/IP routines, analy
zing the mathematical properties of the problem, and developing an intellig
ent branch and bound solution procedure.