Group-scheduling with simultaneous learning effects and convex resource allocations

In this article, we investigate the resource allocations group-scheduling with position-based learning effects. Under a single-machine, the purpose is to determine an optimal group sequence, job sequence within each group, and convex resource allocations (i.e., second partial derivatives of resources are not negative) assigned to the jobs. For the total resource consumption minimization with limited makespan constraint, we certify that the problem is polynomially solvable for some special situations. For the general situation, we establish a heuristic and a branch-and-bound algorithm. Computation experiments are given to test the effectiveness of solution algorithms. The proposed model can be probably applied to green manufacturing scenarios, supporting sustainable production by considering controllable processing time.