Single-Machine Scheduling with Fixed Periodic Preventive Maintenance to Minimise the Total Weighted Completion Times

Hongming Zhou,Shenquan Huang,Fuh-Der Chou,Yarong Chen,Ya-Chih Tsai,Bekir Sahin

doi:10.1155/2021/8891322

Abstract

The single-machine scheduling problem with fixed periodic preventive maintenance, in which preventive maintenance is implemented periodically to maintain good machine operational status and decrease the cost caused by sudden machine failure, is studied in this paper. The adopted objective function is to minimise the total weighted completion time, which is representative of the minimisation of the global holding/inventory cost in the system. This problem is proven to be NP-hard; a position-based mixed integer programming model and an efficient heuristic algorithm with local improvement strategy are developed for the total weighted completion time problem. To evaluate the performances of the proposed heuristic algorithms, two new lower bounds are further developed. Computational experiments show that the proposed heuristic can rapidly achieve optimal results for small-sized problems and obtain near-optimal solutions with tight average relative percentage deviation for large-sized problems.

Highlights

Production scheduling is concerned with the allocation of limited resources to tasks in the manufacturing systems of enterprises to optimise certain objective functions such that their competitive position is maintained or improved in fast-changing markets
For the 1, hk|nr| 􏽐 wiCi problem, we proposed a new MIP model, two new lower bounds, and a heuristic algorithm. e proposed heuristic algorithm adopted a bin-packing scheme that considers batch formation and batch sequence and applied the optimality properties in the local improvement strategy to efficiently obtain optimal or near optimal solutions
To the best of our knowledge, a recent new study on the same problem was conducted by Krim et al [29]. us, we took their proposed methods including the MIP model, lower bound methods, and better heuristic algorithms as the benchmark approaches

Summary

Introduction

Production scheduling is concerned with the allocation of limited resources (machines or operators) to tasks in the manufacturing systems of enterprises to optimise certain objective functions such that their competitive position is maintained or improved in fast-changing markets. Liao and Chen [11] extended a single PM activity to multiple and periodic maintenance activities for a singlemachine scheduling problem; they proposed a BAB algorithm and an efficient heuristic for minimising the maximum tardiness. Another deterministic case is when the maintenance period [u, v] is arranged in advance and maintenance operations should be undertaken within the period [u, v], where the maintenance time (w) is not longer than the maintenance period, i.e., w ≤ (v − u) Some contributions under this assumption for different scheduling problems can be found in Chen [25], Yang et al [4], etc. Is study focuses on scheduling jobs on a single machine with periodic unavailability periods due to implementing PM activities; the objective is to minimise the total weighted completion times.

Mixed Integer Programming Model

Lower Bounds

Heuristic Algorithms

Findings

Conclusions