A bi-objective integrated procurement, production, and distribution problem of a multi-echelon supply chain network design: A new tuned MOEA

Efficient management of supply chain (SC) requires systematic considerations of miscellaneous issues in its comprehensive version. In this paper, a multi-periodic structure is developed for a supply chain network design (SCND) involving suppliers, factories, distribution centers (DCs), and retailers. The nature of the logistic decisions is tactical that encompasses procurement of raw materials from suppliers, production of finished product at factories, distribution of finished product to retailers via DCs, and the storage of raw materials and end product at factories and DCs. Besides, to make the structure more comprehensive, a flow-shop scheduling model in manufacturing part of the SC is integrated in order to obtain optimal delivery time of the product that consists of the makespan and the ship time of the product to DCs via factories. Moreover, to make the model more realistic, shortage in the form of backorder can occur in each period. The two objectives are minimizing the total SC costs as well as minimizing the average tardiness of product to DCs. The obtained model is a bi-objective mixed-integer non-linear programming (MINLP) model that is shown to belong to NP-Hard class of the optimization problems. Thus, a novel algorithm, called multi-objective biogeography based optimization (MOBBO) with tuned parameters is presented to find a near-optimum solution. As there is no benchmark available in the literature, the parameter-tuned multi-objective simulated annealing algorithm (MOSA) and the popular non-dominated sorting genetic algorithm (NSGA-II) are developed to validate the results obtained and to evaluate the performance of MOBBO using randomly generated test instances.

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