带有恶化效应和运送时间的凸资源分配排序

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中图分类号：0223 文献标志码：Adoi： 10.3969/j .issn.1673-5862.2025.03.003

Convex resource allocation scheduling with deterioration effects and delivery times

ZHAO Yufang，SONG Hairuo （College of Mathematics and Systems Science，Shenyang Normal University，Shenyang 11oo34，China）

Abstract： This paper studies the single-machine scheduling problems with linear deterioration effects，delivery times and convex resources. The actual processng time of the job is related to its starting time and the amount of resources allocated to it. The delivery time depends on the waiting time of the completed jobs. The aim is to determine the optimal scheduling and the optimal allocation of resources，minimize the following three types of problems：The first type of problem is to minimize the weighted sum of the scheduling cost and the total resource consumption cost；the second type of problem is to minimize the scheduling cost under the condition of limited resources; the third type of problem is to minimize the total resource consumption cost under the condition of limited scheduling cost，where the scheduling costs are the makespan，the total completion time， the total waiting time，the total absolute differences in completion times，and the total absolute differences in waiting times，respectively. The optimal properties of the problem are analyzed. By converting them into assignment problems，a polynomial-time optimal algorithm is given，and the effectiveness of the algorithm is verified by example.

Key Words： single-machine scheduling；deterioration effect；delivery time;convex resource

在实际的生产制造流程中，工件所需的加工时间往往会受到机器老化等因素的影响。（剩余5945字）