Multi-objective optimization of production system with staggered production

In the manufacturing industry, timely order fulfilment from diverse customers is important for operational profitability, given the constraints of limited production capacity. This paper proposes a novel queueing system for a production system, in which order processing times are categorised as regular or rush based on customer preference. The proposed queueing system employs variable service rates and service strategies in conjunction with staggered production to deal with heterogeneous arrivals. We compute the steady-state probability distribution and develop system performance indicators. The lower and upper bounds of the expected sojourn time for rush and regular orders are derived. Numerical results show that an appropriate switching policy can reduce rush orders by approximately 35% while regular orders increase by less than 10%, demonstrating significant improvement in order fulfilment management. We formulate a multi-objective optimisation problem and implement the NSGA-II algorithm to obtain Pareto optimal solutions. Finally, three regression models are proposed to determine the minimum cost and the associated optimal service rates, given the maximum acceptable value of the expected number of rush orders. The established models can explain at least 80% of the dataset of the optimal solutions and thus our numerical findings provide useful guidance for decision-makers and production managers.