A Multiplier Adjustment Method for Dynamic Resource Allocation Problems

Dynamic fleet management problems (with a homogeneous fleet) are classically formulated as dynamic networks, or linear programs with side constraints. Recently, a new dynamic control approach was introduced, called a logistics queueing network. Instead of a large linear program, the problem is decomposed into small subproblems that are guided by two control variables that push these local problems to produce a solution that is close to a global optimum. In prior work, these control variables were updated using a subgradient approximation. In this paper, we propose a multiplier adjustment method for solving the same problem. Numerical experiments show that this method produces better solutions with greater stability. The new method is somewhat slower, and is more difficult to implement. We believe that both methods will represent reasonable choices for solving the problem.