A new coordinating model for green supply chain and batch delivery scheduling with satisfaction customers

Scheduling an integrated, detailed SC (supply chain) at the operational level is a crucial aspect of SCM (supply chain management). Simultaneous consideration of scheduling the production and distribution and assigning delivery times could lead to reduced costs and, thus, more profit. Fuel costs constitute a significant portion of total transportation costs; therefore, reducing fuel consumption could improve transportation efficiency at the operational level. Sustained reduction of fuel consumption, in turn, mitigates greenhouse gas emissions. Consequently, reduction of fuel consumption is an important element of green vehicle routing problems. The authors consider the following as the main contributions of this paper: the main problem discussed through this study is the integrated scheduling of the SC, assignment of delivery times, scheduling of orders using a manufacturing system comprising one machine, delivery in batches, heterogeneous multi-vehicle job assignment based on loading capacity, all aiming at the minimization of distribution costs, fixed fuel costs, variable fuel costs, carbon emissions, and the time it takes to deliver the shipments. We present a mathematical model based on MINLP (mixed-integer nonlinear programming) for the problem. To validate this model, an ε-constraint technique is utilized and then compared with the MOACO (multi-objective ant colony optimization) algorithm at small scale. Finally, the algorithm is evaluated by comparing it with numerical examples generated by NSGA-II and several performance metrics are employed to assess the solutions of this MOP (multi-objective problem).