A Green Mathematical Model for a Single-Machine Scheduling Problem with Batch Delivery System

This paper aims to minimize the total tardiness and the sum of delivery costs of a single machine problem when jobs are delivered to customers in various size batches. In the real world, this issue may happen within a supply chain in which submitting jobs to customers entails costs. On the one hand, to avoid delay costs manufacturers should deliver jobs to customers immediately after their completion, which leads to more number of transportation. Consequently, delivery costs related to the cost of vehicles traffic and their CO2 gas emissions increase. On the other hand, manufacturers should submit jobs in batches to reduce delivery costs and make the green supply chain. However, dispatching several jobs in the form of batches can have a negative effect on other scheduling-related objective functions such as minimizing the total tardiness. We present a mixed-integer linear programming (MILP) model to provide a trade-off between the total tardiness and the total delivery cost. As this is an MILP model, the commercial solver (CPLEX) is not guaranteed to find the optimal solution for large-size problems in a reasonable amount of time. Therefore, we present a genetic algorithm to solve the problem.