2-approximation and hybrid genetic algorithm for long chain design problem in process flexibility

Long chain flexibility strategy is an effective way to match the supply with the uncertain demand in manufacturing system. However there are few studies on the long chain design problem with nonhomogeneous link costs. This paper first presents a mixed 0-1 LP model and proves that it belongs to NP-complete. Then an approximation algorithm is proposed which includes three steps: 1) solve a relaxed LP; 2) generate a minimum spanning tree; 3) find the optimal local match. Under the quadrangle inequality assumption, we show that it is a 2-approximation algorithm. At last, based on another equivalent reformulation, we embed the 2-approximation algorithm and a 2-opt exchange local search into a hybrid genetic algorithm. By comparison with CPLEX solver, numerical experiments validate the effectiveness of the proposed algorithms.