Bi-objective coordinated production and transportation scheduling problem with sustainability: formulation and solution approaches

This paper studies a new variant of integrated production scheduling and vehicle routing problem where production of customer orders are performed under job-shop environment and order deliveries are made by a heterogeneous fleet of vehicles, each of which is allowed to take multiple trips. Two conflicting objectives are considered, namely minimisation of the total amount of CO2 emitted by the vehicles and minimisation of maximum tardiness resulting from late deliveries. To this end, we present a bi-objective mixed-integer programming formulation. Augmented ε-Constraint (Augmecon) method is implemented to find Pareto optimal solutions. Due to problem complexity, Augmecon cannot provide solutions even with small-sized problems. Thus, we adopt Pareto Local Search (PLS) and non-dominated sorting genetic algorithm-II (NSGA-II) for practical sized instances. For small-sized instances involving 5, 6, and 7 customers, experimental results indicate that CPU time of Augmecon are 11, 84, and 524 sec, respectively with an average number of Pareto efficient solution of 3.5. In terms of hypervolume index, Augmecon shows the best performance, followed by NSGA-II with 11.32% and PLS with 20.75% degradation for small-sized instances. For medium and large-sized instances, PLS shows worse performance than NSGA-II by 16.87% and 40.48%.