Fuzzy closed-loop supply chain models with quality and marketing effort-dependent demand

While previous literature studies the market demand affected by quality or marketing effort in a supply chain, this paper explores the pricing and collection strategies of different closed-loop supply chain models in regard to a quality and marketing effort-dependent demand in a fuzzy environment. Specifically, a manufacturer produces new and remanufactured products with three collection scenarios, namely, a manufacturer undertaking collection operations, a retailer undertaking collection operations, and a third party undertaking collection operations. Considering the uncertainty of many parameters in a supply chain, we apply triangular fuzzy variables to describe some parameters, such as, the changeable collection cost of used products, the manufacturing/remanufacturing cost of products, and the market demand (e.g., the market base, the elastic coefficient). By adopting a game theoretical approach, we conduct three collection modes in a deterministic environment as benchmark models and three fuzzy mathematical models, then obtain the equilibrium results and the optimal expected profit of each supply chain member. Furthermore, we conduct numerical experiments to compare the optimal outcomes of three collection modes considering a fuzzy environment and a deterministic environment, then analyze the impacts of fuzziness of parameters on the expected profits. Among three collection modes in a fuzzy environment, we observe when the manufacturer is responsible for the collection business, the whole supply chain system has the highest efficiency, and the expected profit of each chain member is the highest. Simultaneously, with the same collection mode, the performance of supply chain considering the fuzzy environment is better than that in the deterministic environment. The expected profits of the manufacturer and the retailer descend with the increase of the quality effort cost coefficient. Similarly, when the cost coefficient of the marketing effort increases, the expected profits of the manufacturer and the retailer have downward trends. When the fuzziness of the marketing/quality effort coefficient changes, the retailer's expected profit is more affected than that of the manufacturer.