Sequencing/scheduling constraints

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. 

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. 

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). 

The sequencing set of constraints focuses on capturing the time dimension, which is intrinsic in batch operations. The following constraints, which apply irrespective of the chosen scenario (scenario 1 or scenario 2), constitute the scheduling set of constraints for the proposed mathematical model. 

Sequencing Constraints Associated with Production Scheduling... 

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

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. 

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. 

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. 

Analyze in detail. Identify limits (constraints, restrictions). Include variability in components and users. Meike machine adjust to person, not converse. Obteun specifications of components and assembly. Obtiun skills aveulability of people obteun capability/aveulability of equipment. Get restrictions in fabrication and assembly techniques and sequence. Obtain more details on cost accounting, scheduling, emd tradeoffs of criteria. 

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