.... Findings Experimental results show that the proposed valid inequalities can help obtain optimal solutions for more instances and improve the lower bounds by 28.7% on average. Our ALNS algorithm can obtain optimal solutions or near-optimal solutions for small-sized instances with far less computational...

...) model is built and five types of valid inequalities for tightening the solution space are derived. An improved variable neighborhood search (IVNS) algorithm is presented combining the developed multistart initial solution strategy and modified neighborhood local search procedure. Findings...