Utilizing Idle Time for Job Clusters Reduces Inventory and Total Job Completion Time for Single Machine Scheduling

Introduction

Job that finishes ahead of schedule must be kept in inventory until its due date in a JIT scheduling system, but a job that finishes after its due date may interfere with a customer’s activities. A perfect schedule consists of one in which every task is completed precisely on the scheduled due date. Scheduling methods with both earliness and tardiness (E/T) costs tackle the important scheduling aspect of the JIT approach. Producing fact, JIT involves a far wider set of concepts than those relevant to due dates. The creation of no delay programs has been the focus of the vast bulk of scheduling research. However, the insertion idle time (IIT) schedules are a class of schedules that we are interested in since they are more broadly speaking.

The use of JIT, or just-in-time delivery, which attempts to deliver the customer’s order at the precise requested moment, has recently grown in importance. This is an earliness/ tardiness (E/T) model in the scheduling sector [1]. Since it is usually preferable to include idle time in the schedule than not, several academics. Pinedo ML [2] have pointed out that the assumption of no idle time is incompatible with the E/T model. Feng G, et al. [3] investigated at the multi-machine scheduling problem with early and late charges and schedule based setup durations, and found that the problem may be divided into two sub problems: scheduling and timetabling. By using a lexicographical mixed-integer linear programming model and an improved simulated annealing technique, Cheng L, et al. [4] studied an Assembly job-shop scheduling problem with the aim of minimizing both a regular primary objective, the total completion time, and an irregular additional intended, the overall inventory time. Review the existing literature on inserted idle time scheduling after Kanet JJ, et al. [5] developed a classification of the situations in which inserted idle time scheduling is applicable. In order to reduce the overall completion time of all jobs, He N, et al. [6] and Tsai CY, et al. [7] assumed that the degradation of processing time and setup time is of a linear increasing function with regard to the starting time. To reduce the overall completion time and total energy cost under time-of-use electricity tariffs, Rubaiee S, et al. [8] suggested a preemptive planning issue on a single machine, which is a mixed-integer multiobjective mathematical programming model. A single-machine scheduling issue with weighted earliness and tardiness penalties is investigated by Chen JY, et al. [9]. Jobs may have several due dates and may have idle time in between them Babor M, et al. [10] looked at three production lines from small- and medium-sized bakeries to determine the ideal idle time for the makespan and ovens. reduction of the highest anticipated cost for stochastic processing time whereas five factors influence processing times. Mahnam M, et al. [11] tackled the issue of minimising the sum of maximum earlyness and tardiness on a single machine with unequal release times and idle insert based on realistic assumptions and real-world production settings. The existing research on the above scheduling problem is divided into three main groups by: Senthilkumar P & Narayanan S [12] offline scheduling, online scheduling, and other scheduling. The vertex cover problem and the single-machine scheduling problem were linked [13]. Specifically, for series-parallel precedence restrictions. To reduce the weighted sum of completion times, Mastrolilli M, et al. [14] investigated the single machine scheduling problem. By substituting a set of potential vectors, referred to as scenarios, for the numerical values in the description of the instance, we model uncertainty. In the worst-case situation, the schedule with the lowest value must be found. Yazdani M, et al. [15] created a mixed integer linear programming (MIP) formulation of the job shop scheduling issue using the new goal function, and he also researched The goal function's greatest earliness and tardiness requirements for the job shop scheduling issue. Seda M [16] suggests mathematical solutions to the problems of permutation flow shop scheduling and job shop scheduling.

Inserted Idle Time

In this work, The creation of heuristics for creating inserted idle time schedules is crucial for the following reasons:

(i) Minimizing Inventory Problems

(ii) IIT scheduling issues are highly complex, making it unlikely that particular solutions will ever be used (iii) In actuality, the problem definition is constantly changing due to the unpredictable nature of real-life scheduling conditions, making quick fixes absolutely necessary.

Problem Description

Consider 10 jobs associated with probability and assigned with earliness and tardiness penalty . A block is described as a series of clusters that are continuously processed.Think about the block . One or more clusters may come before such a block, but none may come after it. Let jr represent the final early task in cluster ór, or the early job with the smallest earliness (Tables 1-3).

Results and Discussion

The algorithm must decide how much to extend each job’s completion time because the completion times in the original schedule are the earliest feasible times. In reality, since each cluster’s workloads are all shifted by the same amount, computing the best shift for each cluster is adequate. The given job sequence j= 1. . . n can be decomposed into a set of m clusters.With each cluster consisting job sequence. A block is described as a series of clusters that are continuously processed.

In Table 4, completion time remains same for first two clusters. After removing first two cluster. Apply step (v), and hence by step (x), Increase all completion time in the 3rd and 4th cluster by one time unit.

Table 5 shows the fixed current completion time for above jobs. Hence after inserting the idle time the completion time of given jobs 4,7,15,19,26,30,32,34,39,44.

Conclusion

Our clustering experiments have demonstrated the efficacy of our scheduling approach, particularly in situations with predictable conditions. The approach excels in reducing material usage and time required for single machine scheduling by accounting for idle time within work clusters. Moreover, our extension of this research to stochastic settings showcases its adaptability to more uncertain scenarios. Overall, our work highlights the potential of our approach to optimize scheduling challenges across various contexts, offering improved efficiency and resource utilization.

Acknowledgment

Data for this article was gathered from Geebon Small Scale Industry in Chennai.

Conflict of Interest

There is no conflict of interest.

Funding

This research did not receive any financial support.