Descending rolling horizon procedure for equipment replacement problem

To handle the computational complexity of large-scale optimization problem, a special rolling horizon decomposition procedure is developed to address equipment replacement problems with long decision-horizons and multiple alternatives in this paper. The global objective is to minimize the total equipment replacement expense. The rolling horizon procedure decomposes the whole decision-horizon into serial rolling sub-decision-horizons where equipment replacement subproblems are established based on local objectives involving partial global objective. The rolling horizon procedure can easily handle the computational complexity of a large-scale equipment replacement problem. However, the rolling segmentation and merely local optimization are not able to necessarily lead to the global optimal solution because local objectives are not completely consistent with the global one. A terminal penalty is added into the local objective function of each sub-problem to lessen the disadvantageous impact of horizon decomposition. The terminal penalty is the maximum evaluation of replacement expense increment for the latter sub-decision-horizons due to merely considering local optimization in the current sub-problem without any consideration of the global objective. The theoretical analysis proves that the rolling replacement procedure with terminal penalty can make the global objective function values descending as serial sub-problems are solved and their partial solutions are merged into the global solution step by step. An extensive experiment was conducted to test the effectiveness of descending rolling replacement procedure. The computational results also demonstrate that this procedure is better than traditional rolling horizon procedure for equipment replacement problem while only moderate computational efforts are needed.