Temporal Decomposition Scheme for Nonlinear Multisite Production Planning and Distribution Models

Abstract

In this paper we propose a multiperiod nonlinear programming model for the production planning and product distribution of several continuous multiproduct plants that are located in different sites and supply different markets. The unique feature of the proposed model is that each plant is represented through nonlinear process models. To solve the resulting large-scale model, we present two solution techniques based on Lagrangean decomposition. Spatial decomposition is based on the idea of dualizing interconnection constraints between the plants and markets in order to be able to optimize each site and market individually. For the temporal decomposition, the interconnection constraints are defined between each time period through the inventory variables so that the entire production and distribution plan can be optimized independently in each time period. It is shown that the proposed decomposition methods yield significant computational savings, and temporal decomposition is shown to be the superior decomposition approach in terms of faster computational times and tighter bounds to the optimal solutions.