Sustainable recycle network of heterogeneous pharmaceuticals with governmental subsidies and service-levels of third-party logistics by bi-level programming approach

Abstract

Reverse logistics can facilitate sustainable production, and plays an important role in protecting environment and saving resources. In this paper, the management problem of pharmaceutical reverse supply chain (PRSC) is studied, where the producer, the third party logistics company (3 PL) and the government are jointly involved in recycling the leftover pharmaceutical to make a trade-off among economic, environmental and social benefits. Different from the existing models, this paper formulates such a management problem as an integrated nonlinear bi-level programming (NBLP) model, where the producer is the leader, the 3 PL company is the follower, and the government encourages donation of pharmaceuticals and more pharmaceuticals to be recycled by subsidy and tax deduction. In our model, the recovered quantity depends on incentives and service-level of the 3 PL, and the producer as the leader pays the recovery fee to the 3 PL by taking into account heterogeneity of pharmaceuticals. To solve this complicated model, we first convert the lower-level optimization model into parametric complementarity constraints, the original model then is further transformed into a series of standard smooth problems by a partially smoothing method. An efficient algorithm is developed to find an equilibrium solution of the NBLP model. Case study and sensitivity analysis demonstrate that the proposed method in this paper can efficiently provide optimal policies for the complicated pharmaceutical recovery system, and a number of important managerial implications are revealed: (1) The unit sale price of pharmaceuticals, the 3 PL’s capacity and the tax deduction of the government can generate different impacts on the profits and the optimal collected quantities of the leftover pharmaceuticals. (2) Classification recycle of the pharmaceuticals is important to the scientific management of reverse supply chain. (3) The developed model and algorithm can efficiently improve sustainability of the recycle system of pharmaceuticals.