Bi-objective uniform parallel machine scheduling considering outsourced manufacturing and order financing

With the specializing and clustering development of the manufacturing, outsourced manufacturing plays a significant role in enhancing production efficiency. Meanwhile, small and medium-sized enterprises (SMEs) usually suffer capital shortage, as an important supply chain financing tool, order financing is receiving increasing attention. This paper investigates a brand new bi-objective uniform parallel machine scheduling issue considering outsourced manufacturing and order financing, with the objectives to minimize makespan and maximize profit simultaneously. To solve the problem, a bi-objective mixed-integer linear programming model is constructed, and is transformed into a set of single objective problems with $\varepsilon$-constraint method. The effectiveness of the proposed model is verified by CPLEX with a practice-based case and a series of randomly generated instances.