Parallel computation of large-scale dynamic market network equilibria via time period decomposition

In this paper we consider a dynamic market equilibrium problem over a finite time horizon in which a commodity is produced, consumed, traded, and inventoried over space and time. We first formulate the problem as a network equilibrium problem and derive the variational inequality formulation of the problem. We then propose a parallel decomposition algorithm which decomposes the large-scale problem into T + 1 subproblems, where T denotes the number of time periods. Each of these subproblems can then be solved simultaneously, that is, in parallel, on distinct processors. We provide computational results on linear separable problems and on nonlinear asymmetric problems when the algorithm is implemented in a serial and then in a parallel environment. The numerical results establish that the algorithm is linear in the number of time periods. This research demonstrates that this new formulation of dynamic market problems and decomposition procedure considerably expands the size of problems that are now feasible to solve.