Interactive fuzzy goal programming for a multi‐objective closed‐loop logistics network

Over the last decade, there has been increased attention to closed‐loop logistics networks. Environmental legislation requires companies to be more responsible by collecting used products from customers. Companies can also benefit from savings that are related to recovering and recycling used products. Unlike previous studies, which only consider single products or a single period of time in multi‐objective problems, this paper considers a multi‐product multi‐period closed‐loop logistics network with different types of facilities. A multi‐objective mixed‐integer nonlinear programming formulation is developed to minimize the total cost, the delivery time of new products, and the collection time of used products. Thus, this model better approximates real‐life applications of closed‐loop logistics problems. Interactive fuzzy goal programming (IFGP) is applied to solve the model for handling multiple objective problems with conflicting objectives and to address the imprecise nature of decision‐makers’ aspiration levels for goals. The results from computational experiments performed here show that by changing the upper or lower bound of each objective function, one can obtain a better final solution of the problem and also can provide more options for decision makers to choose from based on their situation. Finally, the utilization rate of facilities is shown to be an important indicator when designing a logistics network.