Study on Convex Resource Allocation Scheduling with a Time-Dependent Learning Effect

Abstract

In classical schedule problems, the actual processing time of a job is a fixed constant, but in the actual production process, the processing time of a job is affected by a variety of factors, two of which are the learning effect and resource allocation. In this paper, single-machine scheduling problems with resource allocation and a time-dependent learning effect are investigated. The actual processing time of a job depends on the sum of normal processing times of previous jobs and the allocation of non-renewable resources. With the convex resource consumption function, the goal is to determine the optimal schedule and optimal resource allocation. Three problems arising from two criteria (i.e., the total resource consumption cost and the scheduling cost) are studied. For some special cases of the problems, we prove that they can be solved in polynomial time. More generally, we propose some accurate and intelligent algorithms to solve these problems.

Optimal Different Due-Date Assignment Scheduling with Group Technology and Resource Allocation

“…In 2023, Shioura et al [10] delved into a parallel-machine problem with resource allocation. Wang and Wang [11] investigated single-machine resource-allocation scheduling with a time-dependent learning effect. Under the convex resource function, for three versions of the scheduling cost and total-resource-consumption cost, they demonstrated that some special cases of the problem can be solved in polynomial time.…”

Scheduling with Group Technology, Resource Allocation, and Learning Effect Simultaneously

“…For the total processing cost plus scheduling measure minimizations, they proved that the problems are polynomially solvable. Wang and Wang [16] addressed the single-machine scheduling with convex resource allocation and a time-dependent learning effect. For three versions stemming from the total resource consumption cost and the scheduling cost, they proposed some solution algorithms.…”