Bi-objective optimization model with economic and environmental consideration for an integrated supply chain with random demand and flexible production rate

An integrated production–inventory model that simultaneously considers economic and environmental dimensions is developed in this paper. In the area of supply chain management, researchers and practioners often minimize the cost or profit, keeping the environmental aspect as a constraint. Only a few papers have taken up multi-objective optimization to offer better decision-making. The order quantity, re-order level, production rate, shipment number and vehicle velocity are optimized to minimize the total expected cost and the emissions simultaneously under random demand and in the presence of backorder and loss of sales. A Pareto front is developed to present the trade-off between expected cost and emission. The solution of the multi-objective model is obtained through a benchmark and widely used multi-objective algorithm NSGA-II. The key insights and outcomes are presented through numerical illustration and sensitivity analysis of important parameters. It has been observed that with increasing velocity total expected cost decreases. The total expected emission also decreases initially and increases after a threshold limit. Production rate takes few distinct values while offering the trade-off between expected cost and emission.