On deterministic online scheduling: Major considerations, paradoxes and remedies

doi:10.1016/j.compchemeng.2016.08.006

Computers & Chemical Engineering

Volume 94, 2 November 2016, Pages 312-330

https://doi.org/10.1016/j.compchemeng.2016.08.006 Get rights and content

Highlights

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Rescheduling is needed even in the deterministic case, with no “trigger” events.
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We study how attributes of the online algorithm impact closed-loop solution quality.
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We explore how features of the open-loop formulation translate to closed-loop solutions.
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We propose a framework to analyze the performance of online scheduling algorithm.

Abstract

Despite research in the area, the relationship between the (open-loop) optimization problem and the quality of the (closed-loop) implemented schedule is poorly understood. Accordingly, we first show that open-loop and closed-loop scheduling are two different problems, even in the deterministic case. Thereafter, we investigate attributes of the open-loop problem and the rescheduling algorithm that affect closed-loop schedule quality. We find that it is important to reschedule periodically even when there are no “trigger” events. We show that solving the open-loop problem suboptimally does not lead to poor closed-loop solutions; instead, suboptimal solutions are corrected through feedback. We also observe that there exist thresholds for rescheduling frequency and moving horizon length, operating outside of which leads to substantial performance deterioration. Fourth, we show that the design attributes work in conjunction, hence, studying them simultaneously is important. Finally, we explore objective function modifications and constraint addition as methods to improve performance.

Introduction

Process industries employ a complex chain of operations (processes) which compete for limited resources. Hence, a resource allocation problem arises wherein decisions with regards to the start time of operations, how much to process, the equipment to utilize and several associated decisions need to be taken on a repetitive basis.

Traditionally, schedules have been constructed by experienced scheduling personnel (schedulers) using spreadsheets or heuristics-based software. In the last two decades, however, there has been an increasing thrust towards using advanced computational tools to achieve more profitable schedules. Hence, working with scheduling models to optimally plan operations has become an important problem in process systems engineering (Shobrys and White, 2002, Kelly and Mann, 2003a, Kelly and Mann, 2003b, Harjunkoski et al., 2014). Although the process systems engineering (PSE) community has worked on building accurate models and better solution methods, the aspect of rescheduling has received limited attention. Rescheduling has been emphasized in some works (Cott and Macchietto, 1989, Kanakamedala et al., 1994, Huercio et al., 1995, Rodrigues et al., 1996, Vin and Ierapetritou, 2000), but in most cases scheduling is still thought to be a static open loop problem wherein if rescheduling is carried out, the emphasis is only on restoring feasibility or optimality to the current static schedule. Quantifying the quality of the implemented schedule obtained by rescheduling has not been addressed. Accordingly, the goal of this paper is to study how the open-loop optimization problem impacts the quality of the implemented (closed-loop) schedule.

In a dynamic environment multiple disturbances such as task delays, yield losses, unit breakdowns or rush order arrivals can render a previously computed schedule suboptimal or even infeasible. In addition, Subramanian et al. (2012) emphasized that rescheduling also needs to be performed due to advancement of the scheduling horizon over which the schedule is computed even when there are no disturbances. Rescheduling has been demonstrated to lead to lower inventory accumulation in supply chains (Subramanian et al., 2014).

In this work, we first and foremost show that open-loop and closed-loop scheduling are two different problems, even in the deterministic case, when no uncertainty is present. Thereafter, we investigate how the design of the open-loop optimization problem affects the quality of the resulting implemented closed-loop schedule. The design attributes we study are scheduling horizon length, rescheduling frequency and optimality gap of each open-loop optimization. We choose illustrative process networks and extensively study combinations of the aforementioned attributes over a reasonably exhaustive set of short term demand patterns, production load, and scheduling objectives. From these test cases, we identify trends, and problem instance characteristics which can facilitate in carefully choosing the three attributes.

The paper is structured as follows: In Section 2, we present background on chemical production scheduling and discuss past work on rescheduling. In Section 3, we discuss various design considerations in closed-loop scheduling through motivating examples. In Section 4, we describe the problem library we use. We then present results in Section 5, followed by, a discussion in Section 6. Thereafter, we present several case studies in Section 7, and then provide conclusions in Section 8. We use lower case Latin characters for indices, uppercase bold Latin characters for sets, lowercase Greek characters for parameters, and uppercase Latin characters for variables.

Section snippets

Previous research

A schedule can become suboptimal or even infeasible due to, for example, a disruptive event or a change in resource availability. The revision of an existing schedule in response to disruptions or changes is termed as reactive scheduling or rescheduling. When the focus of rescheduling is only on a schedule for a fixed horizon, it results in a shrinking-horizon problem. On the other hand, when the current schedule is possibly revised, and also additional decisions are made for the time ahead, it

Considerations in online scheduling

In a dynamic environment with new incoming information, disruptive events or changes in availability of resources, new schedules are computed and implemented. Although this practice of rescheduling is adopted routinely in production facilities, it is not known how it affects the overall performance of the production systems (Vieira et al., 2003). While formulating a lot-sizing formulation for reduced nervousness in production schedules Kazan et al. (2000) noted two factors that motivate

Problems, instance types, instances and runs

Once problem features are fixed (variable batch-sizes, utilities, setups), a problem is defined by the objective function (OBJ). An instance type, is a problem expressed for a process network (PN) and a demand pattern (D). A demand pattern, which is further discussed in Section 4.1.2, is a distribution of order due-times and sizes of each order. For each instance type (OBJ.PN.D), we define an instance designated by a sample (S) from the demand pattern under consideration. Finding the

Results

In Fig. 11, Fig. 12, Fig. 13, Fig. 14, Fig. 15, Fig. 16, each subplot corresponds to a single instance type, and carries a tag of the form FpLm which denotes that orders are due, on an average every p hours, and each order has an average size of m tons for each product. For example, F6L8 means orders are due, on an average, every 6 h with mean order size of 8 tons of each product. Table 1 shows the values of FpLm used and the corresponding approximate production capacity utilization for PN-3 (

Rescheduling frequency

In general, higher rescheduling frequency leads to better closed-loop quality, however, there exists an upper threshold, beyond which closed-loop performance does not improve. Importantly, lower than a certain frequency leads to very bad closed-loop schedules. One of the factors on which this lower threshold depends, is the frequency of orders. If orders are due frequently, then rescheduling infrequently leads to poor closed-loop schedules. Even when orders are due infrequently, it is still

Case study-I: Design attributes

We compute a closed-loop schedule for PN-1 (Fig. 1) for 1-week (cost minimization) to meet a demand pattern created from tuple (p = 6, Δp = 1, m = 6, Δm = 0). First, we consider MH = 24, RF = 3, and OPTCR = 0%, and obtain a closed-loop cost of $190,744. Next, we consider MH = 36, RF = 6, and OPTCR = 5%. We use a larger OPTCR and RF = 6 to emulate the practical situation where solving a larger problem to optimality will require more time than the time available between iterations. Surprisingly, in the second

Conclusions

We presented a framework for the analysis of closed-loop schedules. First, we showed that open-loop and closed-loop scheduling are two different problems, even in the deterministic case when no uncertainty is present. Applying methods to improve solution to the open-loop problem, does not necessarily translate to good solutions for the closed-loop problem. Second, we found that it is important to reschedule periodically, even when there are no “trigger” events, something that is in contrast

Acknowledgements

The authors would like to acknowledge support from the National Science Foundation under grants CMMI-1334933 and CBET-1264096, as well as the Petroleum Research Fund under grant 53313-ND9. CTM would like to thank Dr. James Rawlings for fruitful discussions on model predictive control and, specifically, on the role of feedback.

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On deterministic online scheduling: Major considerations, paradoxes and remedies

Highlights

Abstract

Introduction

Section snippets

Previous research

Considerations in online scheduling

Problems, instance types, instances and runs

Results

Rescheduling frequency

Case study-I: Design attributes

Conclusions

Acknowledgements

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Oper. Res.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Fuzzy Sets Syst.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Eur. J. Oper. Res.

Comput. Chem. Eng.

Int. J. Prod. Econ.