Parallel-Machine Scheduling with DeJong’s Learning Effect, Delivery Times, Rate-Modifying Activity, and Resource Allocation

Li Sun,Lei Ning,Bin Wu

doi:10.1155/2021/6687525

Li Sun, Lei Ning + Show 1 more

Open Access

https://doi.org/10.1155/2021/6687525

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Abstract

We investigate parallel-machine scheduling with past-sequence-dependent (p-s-d) delivery times, DeJong’s learning effect, rate-modifying activity, and resource allocation. Each machine has a rate-modifying activity. We consider two versions of the problem to minimize the sum of the total completion times, the total absolute deviation of job completion times, and the total resource allocation and the sum of the total waiting times, the total absolute deviation of job waiting times, and the total resource allocation, respectively. The problems under our present model can be solved in polynomial time.

Highlights

A finite amount of resource usually is allocated to a job to control its actual processing, which is the so-called scheduling problem with controllable processing times
ALGORITHM 1: Algorithm to solve the problem of minimizing the sum of total completion times and total absolute deviation of job completion times with linear resource consumption
ALGORITHM 2: Algorithm to solve the problem of minimizing the sum of total waiting times and total absolute deviation of job waiting times with linear resource consumption

Summary

Introduction

A finite amount of resource usually is allocated to a job to control its actual processing, which is the so-called scheduling problem with controllable processing times. Liu and Feng [2] address two-machine flowshop scheduling problems in which the processing time of a job is a function of its position in the sequence and its resource allocation. Luo [10] addresses a single-machine scheduling problem with a deteriorating rate-modifying activity to minimize the number of tardy jobs. He proposed an optimal polynomial time algorithm. To the best of our knowledge, scheduling with p-s-d delivery times, DeJong’s learning effect, rate-modifying activity, and resource allocation has not been studied in the literature. See the work of Ma et al [31]

Cases with Linear Resource Consumption Function

Cases with Convex Resource Consumption Function

Conclusions