Optimization Based Production Planning With Hybrid Dynamics and Constraints

Optimizing production planning has tremendous economic impact for many industrial production systems. In this paper, the planning problem of a class of production systems with hybrid dynamics and constraints is considered with practical background of power generation planning and other applications. The problem is solved within the Lagrangian relaxation framework, with the system wide demand and resource limit constraints relaxed by Lagrange multipliers. A new method is developed in this paper to obtain the exact optimal solutions to the subproblems with hybrid dynamics and constraints efficiently without discretizing the continuous production levels or introducing intermediate levels of relaxation. A novel definition of the discrete state associated with a consecutive time span is introduced so that solving each subproblem is converted into solving a number of continuous optimization problems and a discrete optimization problem separately. An efficient double dynamic programming (DP) method is developed to solve these subproblems and the principle of optimality is guaranteed for both the continuous and discrete problem. The production levels in a consecutive running span with non-convex piecewise linear cost functions are determined in a DP forward sweep without discretization. The DP method is then applied to determine the optimal discrete operating states across time efficiently. Numerical testing results demonstrate that the new method is efficient and effective for optimization based production planning with the complex hybrid dynamics and constraints.