Convex resource allocation scheduling in the no-wait flowshop with common flow allowance and learning effect

We study the problem of two-machine no-wait flowshop scheduling with learning effect and convex resource-dependent processing times. Under the condition of the due-date assignment with common flow allowance (i.e. slack (SLK) due-date assignment), we provide a bi-criteria analysis where the first criterion is to minimise the scheduling criteria (i.e. the weighted sum of earliness, tardiness and flow allowance costs), and the second criterion is to minimise the resource consumption cost (i.e. the weighted sum of resource consumption cost). The objective is to determine the optimal job sequence, resource allocations and common (flow allowance) slack time that minimise the three different versions of the two criteria. We prove that these problems can be solved in polynomial time.