Piecewise Linear Model of MNLP. We introduce the following additional decision variables:
The MNLP model can be approximately reformulated as the following mixed 0-1 linear programming model (MLP1) based on linearization of learning curves and quality constraints:
To test the performance of the models, plenty of instances generated randomly are calculated using models of MNLP, MLP1, and MLP2.
The original MNLP model is firstly calculated using Lingo.
Column 2 shows the average gaps between objective values and lower bounds of MNLP model calculated by Lingo within the time limitation of 7200 seconds.
(1) The piecewise linearization method can effectively improve the calculation performance of MNLP model.