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

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.

Automated summary

This paper investigates single-machine scheduling problems with resource allocation and time-dependent learning effect. 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. The goal is to determine the optimal schedule and resource allocation using convex resource consumption function. Three problems with two criteria are studied, and some special cases can be solved in polynomial time. Furthermore, accurate and intelligent algorithms are proposed to solve these problems.