Sequencing and Scheduling Constraints

Sequencing Constraints Associated with Production Scheduling 

The production scheduling model has been presented in detail in Chapter 2 of this textbook, but is briefly presented in this section of the chapter for purposes of continuity and facilitation of understanding. For a detailed explanation of each of the production scheduling constraints, the reader is referred to Chapter 2. 

The material balances ensure the conservation of mass around each unit and concerning each state involved in production scheduling. 

The duration constraints constitutes one of the most crucial constraints as it addresses the intrinsic aspect of time in batch plants. It simply states that the time at which a particular state is produced is dependent on the duration of task that produces the same state as follows. 

The assignment constraints ensures that only one task takes place in a given unit at a given point in time. 

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The constraints considered in the mathematical formulation are divided into two modules. The first deals with the mass balance constraints and the second with the sequencing and scheduling constraints. The mass balance constraints for the case where there is no central storage are slightly different to those for the case where there is. The mass balances for each are described in the mass balance module below. The sequencing and scheduling module will be described, for both cases, in a subsequent section. The nomenclature for all the sets, variables and parameters can be found in the nomenclature list. 

Sequencing and Scheduling Constraints Associated with Storage... 

The final group of sequencing and scheduling constraints comprise of feasibility constraints and time horizon constraints. 

The above constraints deal with the mass flows between the various units in a batch plant. They do not consider the timing of the streams, tasks and such. Therefore, further constraints have to be derived to ensure the correct sequencing and scheduling of the processes, streams and tasks. 

With classical structure, the proposed GA is implemented in Matlab to search the optimal/good solutions for the problem. This study considers the problem associated with soft precedence constraints, which will incur a penalty if violated rather rendering the sequence and schedule infeasible. A penalty implies that the respective chromosome is less likely to pass in the next generation, but still may have very valuable characteristics to pass on through the evolution process. 

In this chapter, a class of soft precedence-constrained production sequencing and scheduling problems for multiple production lines has been modelled. Due to the nature of constraints, the multi-objectives GA with new strategies for chromosome encoding, feasibility of chromosome, crossover as well as mutation operations have been developed to optimise the model. 

In this chapter, state sequence network (SSN) representation has been presented. Based on this representation, a continuous-time formulation for scheduling of multipurpose batch processes is developed. This representation involves states only, which are characteristic of the units and tasks present in the process. Due to the elimination of tasks and units which are encountered in formulations based on the state task network (STN), the SSN based formulation leads to a much smaller number of binary variables and fewer constraints. This eventually leads to much shorter CPU times as substantiated by both the examples presented in this chapter. This advantage becomes more apparent as the problem size increases. In the second literature example, which involved a multipurpose plant producing two products, this formulation required 40 binary variables and gave a performance index of 1513.35, whilst other continuous-time formulations required between 48 (Ierapetritou and Floudas, 1998) and 147 binary variables (Zhang, 1995). 

For the third example, our algorithm is compared to the results of the authors of [4] who solve the scheduling and sequencing problem by constraint programming (CP). It can be seen in Table 2 that it takes slightly more time to compute the heuristic ASAP solution than to find the first feasible solution by CP, but that the ASAP solution has a significantly smaller makespan. The EA improves the initial solution in less than half a minute to a solution which is very close to the optimum. 

Start-up is the transition from completion of construction to full operation and it impacts both construction and operations (Fig. 6). Many times, projects have construction scheduled to be completed simultaneously in all areas. This is neither accurate or the real world. Both construction and start-up personnel must think in terms of a phased completion because construction will not have sufficient people to complete every thing at once and start-up will not have sufficient people, or functionality, to start-up the facility all at once. The sequence of completion needs to be agreed upon early in the construction effort so that construction focuses on completion in the agreed sequence and start-up gains availability to start in a logical sequence. If the last item on the construction schedule is to set the main electrical transformer and connect the plant power, no transition to start-up is possible. There are many more subtle constraints in a construction schedule that can be prevented with proper planning. 

Note that the rules in Equations (12.1)-(12.4) do not consider the previously set due dates. Therefore, utilizing WEIN-NONPAR I and WEIN-NONPAR II, Wein proposes two other rules, WEIN-HOT-I and WEIN-HOT-II, for problems I and II, respectively. Under these rules, if there is enough slack in the system, a new job can be quoted a shorter lead time and scheduled ahead of some previous jobs of the same class. The sequencing policy is still SPT for different classes, but EDD (rather than FCFS) within each class. Although these rules may result in shorter due dates, they may violate the service level constraints. 

As used practically by schedulers in industry, and as capmred in common project scheduling tools, dependence amongst activities is represented as precedence relationships e.g. a task s start can begin only after another task finishes. As part of creating sequence and duration of a chain of activities, each dependence becomes a sequential relationship between a milestone in one activity with a milestone in another activity [6, 7]. The most frequently used dependencies relate the sequence of start and finish milestones [e.g. Finish to start (FS)]. If a precedent constraint is not precisely the point in time after which one milestone may follow another, a lag or delay can be characterized. 

Condition assessment of aU pipelines in a system may take years because of operational constraints, logistical issues, and cost. It is therefore important to determine priority, sequence, and long-term schedules for pipeline inspection. These decisions are usually driven by potential consequences of failure and perceived pipeline condition based on the history of performance and other pipeline risk factors. There are two important components in determining the risk associated with a pipeline and therefore the pipeline criticality and inspection priority (1) the likelihood of pipe failure and (2) the consequence of failure, should it occur on a given pipeline (Zarghamee et al., 2012). 

Casual constraints the precedence or required sequence of tasks and resource requirements. There are unexpected events, failures, and/or events that have not been included in the scheduling program. Off-specification batches occasionally disturb the schedule. 

Availability constraints the macroscopic limits on material resources and the availability or up-time of equipment. Availability of raw materials is an obvious constraint at scheduling. Obviously, no catalytic hydrogenation can be done if the catalyst is unavailable. Simultaneous operation of certain tasks is restricted by the limited availability of common utilities such as steam, electricity, or labour. The priority sequence in a product chain needs to be respected by ensuring that intermediate products are manufactured in time to be available when required by a batch of the consecutive product. 

Sequencing Constraints that Associate Production Scheduling and Water Recycle/Reuse... 

Production planning decides on production volumes and values by site and production resource. Production planning normally considers total volumes only, while production scheduling in operations decides on the respective schedule. However, cases exist where production lead times and change-over constraints may require also considering the sequence of products in production master planning. 

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