A bi-objective network design model for multi-period, multi-product closed-loop supply chain

Abstract

Concerns over environmental degradation legislative requirements and growing business needs have fueled the growth of closed-loop supply chains (CLSCs). This paper addresses a bi-objective network design problem for multi-period, multi-product CLSC to minimize the total supply chain costs and to maximize the service efficiency of the warehouses and hybrid facilities. We develop a bi-objective mixed integer linear programming model to assist decisions in (1) location/operating decisions for warehouses, hybrid facilities and manufacturing facilities and (2) production and distribution of products between stages in the supply chain. Goal programming models and compromise programming techniques are used to solve the problem. An application of the model is demonstrated using a case study from the literature.

Keywords:

• closed-loop supply chain
• mixed-integer linear programming model
• goal programming
• compromise programming

Notes

1. Products produced and recycled in time period t is transported to warehouses. Finished goods inventory is not maintained at manufacturer.

2. As it is a multi-product environment, all manufacturers may not be capable of producing all kinds of products. Return of products to appropriate manufacturers has to be considered.

3. A solution i is dominated by solution k if and only if f_kj ⩾  f_ij , for all j = 1, 2,…, p and for at least one j, f_kj  > f_ij , where j is the criteria(objectives). A solution which is not dominated by any other feasible solution is called as a non-dominated solution [24].