Discrete Optimization
Aversion scheduling in the presence of risky jobs

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Abstract

Empirical studies have shown that human schedulers use special procedures to deal with troublesome jobs that are perceived to disrupt manufacturing or that will take substantially longer than the industrial engineering standards. These troublesome jobs present a risk to the manufacturing process and to the schedule robustness. One strategy is to delay them whenever possible and to allow other work to overtake. The Aversion Dynamics concept is used to include this type of logic in scheduling heuristics such that a trade-off analysis of penalties occurs in light of the expected performance results. This is accomplished by altering processing time estimates to achieve a form of “safety time” for risky jobs. This paper conducts a large empirical study within the single-machine static arrival environment to demonstrate that the concept of special sequencing based on job risk is significant and that robust strategies can be developed.

Introduction

Robust scheduling implies that a generated schedule has a reasonable chance of being realized—the shop floor can execute the work sequence as planned. Variability in processing times, product yield, and various other unexpected perturbations associated with manufacturing resources create challenges for schedule robustness. Truly random variability in processing has been addressed by a number of strategies as noted in the review on uncertainty in scheduling by Aytug et al. (2005). As shown in this review, a number of the strategies have been shown to be effective for dealing with what can be considered as manufacturing noise (i.e., unpredictable variability in processing times). In the majority of research, the noise is applied in a general way to all jobs and to the complete planning horizon, or processing time is varied in a learning curve fashion using time as the variable. Neither of these two approaches varies the job processing time in a job-dependent fashion nor is suitable for minor processing variations. However, there are other forms of variability and instability found in real manufacturing situations. McKay (1992) noted in a longitudinal field study that 10–15% of the decisions made by the scheduling and dispatch positions were associated with issues beyond normal manufacturing noise. These were cases in which the variability in processing time was often >100%.

The special decisions and choices documented by McKay focused on perceived variability that translated into risks. Consider three such examples. First, certain jobs may be scheduled during the weekday shift because they may need special support from the engineering staff and, if that support was not available, there would be high setup and waste costs and longer processing times. Second, a job may be advanced (left-shifted) in the schedule to provide extra slack time to absorb the risk associated with various material and process changes that have occurred since the last time the job was run. Third, another job may be delayed (right-shifted) in the schedule to allow other work to proceed since that job is considered unstable, unpredictable and likely to cause problems.

In the case of delayed work as illustrated by the third example, the scheduler may believe that it would be advantageous to get as much other work done as possible before allowing the risky job to be run. Not only might the risky job delay other work, it may actually affect the stability of the machine or the process and ultimately affect the actual processing of other jobs. In this research, we will focus on this third example of special decisions and investigate several questions. First, did the human scheduler’s scheduling procedure make sense from a quantitative viewpoint? The scheduler was not doing any mathematics; he just did what made sense to him. Was the scheduler doing a wise thing? Second, are there ways to determine or calculate how much work should be allowed to overtake the risky job and to what extent the risky job should be delayed? Third, are there general policies or guidelines that can be derived to capture the essence of the logic without all of the computational and experimental overhead?

This paper is organized as follows. First, a brief literature review highlights the general approaches used to address manufacturing variability in job scheduling. The concept of risky jobs is then developed for the single-machine static arrival problem and Aversion Dynamics is used to derive the model constructs that capture the risky job phenomena. The experimental design and analysis is then presented. A discussion of the general concept concludes the paper.

Section snippets

Literature review

The core of the problem is the uncertainty and variability associated with risky jobs in real factories and how the scheduling and planning logic could create better schedules by recognizing these phenomena. Research on uncertainty and schedule robustness or feasibility has been an active domain (see Aytug et al., 2005). Consider how uncertainty and variability have been addressed in recent production control literature:

  • using different methods for modeling uncertainty (e.g., fuzzy logic review

Model

When the scheduler is averse to processing a risky job during a period of high load and moves it out into the future, the scheduler’s behavior can be viewed as being roughly equivalent to the case where the planning processing time has been inflated for the risky job, thus lowering its dispatching priority. If the standard scheduling algorithm uses “nominal” or “perfect environment” processing times, then it might be appropriate to correct the processing times to the expected processing

Experimentation design

The experimental objective is to derive robust safety time values (i.e., policies) to use under various conditions and objective functions. Accordingly, extensive simulation experimentation will be performed. At the end of this section, we will discuss the intractability of the problem under consideration and the need for the simulation methodology.

In the designing the experimentation, we pose the following general questions:

  • 1.

    If we have some idea of the mean risk level, is it best to simply add

Main study

Table 1.1, Table 1.2, Table 1.3, Table 1.4, Table 1.5, Table 1.6, Table 1.7, Table 1.8, Table 1.9 of Appendix 1 show the results of the nine major cases involving the negative exponential risk distribution. These nine tables correspond to the 3 × 3 risk level/risk knowledge design. Each table contains the safety time value yielding the minimum (i.e., best) objective value, the corresponding objective value and the objective value at ST = −1 (i.e., prioritize using only nominal times) and ST = 0

Summary and conclusions

In summary, we have validated two hypotheses stated at the beginning of Section 4 and have established simple ST (safety time) approximation policies for use in practice. The goal of these policies is to increase performance under a variety of scheduling objectives when risky jobs are present. The ST serves to mitigate the risk due to processing time variability in such cases. We have also investigated the sensitivity of ST to the risk distribution; the results appear robust.

This study of

Acknowledgment

This research has been supported in part by NSERC Grant OGP 0121274 on ‘Adaptive Production Control’.

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