Relative scheduling start time

The relative timing of the various operations is determined by the operation s duration and by scheduling relationships among operations. An operation s duration may be fixed, rate-based (i.e., dependent on the amount of material processed), inventory-dependent (i.e., related to the time it takes for a storage unit to reach a specified level), or specified to be equivalent to the duration of another operation. Each operation s timing may be set relative to the start of a batch or the start or end time of another operation. Flexible shifts related to operation start times can also be specified, in order to allow an operation to be delayed automatically if some of its required resources are not available at its scheduled start time [148]. 

Note that if there are no data-dependent delay vertices in the graph, then the start times of all operations will be specified in terms of time offsets from the source vertex, which reduces to the traditional scheduling formulation. We define the relative scheduling problem as follows. 

First, we improve significantly the efficiency of the scheduling algorithm (Section 6.3.5) by focusing on a smaller number of anchors. Second, we can achieve a smaller and faster control implementation of a relative schedule because the start time depends on fewer offsets, and hence on fewer synchronizations. 

The iterative incremental scheduling algorithm constructs a minimum relative schedule, or detects the presence of inconsistent timing constraints, with at most i + 1 iterations. This is a very desirable property, since the number of maximum timing constraints i is in general small. The proof follows the outline in [LW83]. Note that in the sequel the full anchor set A(v <) for a valex Vi is used in the computation of the start time and offsets. By Theorem 6.2.4 and Theorem 6.2.6, the result is applicable when the relevant anchor set R vi) or the irredundant anchor set IR(vi) are used instead. 

In relative scheduling, the start time of an operation is defined as time offsets with respect to the completion of anchors. Constraints are feasible or well-posed depending on whether they can be satisfied under restricted or general input conditions, respectively. Redundancy of anchors was introduced to simplify the start time of operations by removing redundant anchor dependencies. This can lead to a more efficient control implementation because operations need to be synchronized to a fewer number of signals. Analysis of these properties was presented in this chapter. 

Definition 8.0.1 Given a constraint graph G and a relative schedule 12(G), a control implementationfor G is precise w.r.L 12(G) if its control delay is exactly equal to the difference between the sink and source start times, T(v ) — T(vo). computed using the schedule Q G),for all input sequences. 

In relative scheduling, the activation of an operation is specified with respect to the completion of a set of anchors with data-dependent execution delays. In particular, the start time T v) for a vertex v e is defined in terms of the anchor offsets 12 = [Pg.214]

A mathematical formulation based on uneven discretization of the time horizon for the reduction of freshwater utilization and wastewater production in batch processes has been developed. The formulation, which is founded on the exploitation of water reuse and recycle opportunities within one or more processes with a common single contaminant, is applicable to both multipurpose and multiproduct batch facilities. The main advantages of the formulation are its ability to capture the essence of time with relative exactness, adaptability to various performance indices (objective functions) and its structure that renders it solvable within a reasonable CPU time. Capturing the essence of time sets this formulation apart from most published methods in the field of batch process integration. The latter are based on the assumption that scheduling of the entire process is known a priori, thereby specifying the start and/or end times for the operations of interest. This assumption is not necessary in the model presented in this chapter, since water reuse/recycle opportunities can be explored within a broader scheduling framework. In this instance, only duration rather start/end time is necessary. Moreover, the removal of this assumption allows problem analysis to be performed over an unlimited time horizon. The specification of start and end times invariably sets limitations on the time horizon over which water reuse/recycle opportunities can be explored. In the four scenarios explored in... 

Scheduling for the single study case is relatively simple. One should begin with the length of the actual study and then factor in the time needed before the study is started to secure the following resources ... 

Patients more than 12 years of age - The effective dose is 900 to 1800 mg/day in divided doses (3 times/day) using 300 or 400 mg capsules or 600 or 800 mg tablets. The starting dose is 300 mg 3 times/day. If necessary, the dose may be increased using 300 or 400 mg capsules or 600 or 800 mg tablets 3 times/day up to 1800 mg/day. Dosages up to 2400 mg/day have been well tolerated in long-term clinical studies. Doses of 3600 mg/day also have been administered to a small number of patients for a relatively short duration, and have been well tolerated. The maximum time between doses in the 3 times/day schedule should not exceed 12 hours. 

Obtaining approvals for off-site transport might cause delays. If the destruction of energetics must be completed by the CWC deadline, PMCD should set a date by which construction of the DFS must be started if no off-site permit has been received or if the receiving facility does not have a valid permit. A permit for DFS construction should be relatively easy to obtain because of its successful use at both JACADS and TOCDF. However, enough time must be allowed in the schedule for permit application and approval. In view of the opposition to incineration by some Pueblo stakeholders, the prompt receipt of a DFS permit cannot be assumed. 

Table 1 shows the relative improvement obtained by the proposed EA on the initial ASAP solution. The parameters of the EA were set to p=10 and k=2. The probability of a mutation was 80 %. The results are reported for a set of five runs with a time limit of 60 seconds. It can be seen that the improvement for the simple problem is larger than for the industrial problem. The best solutions for the simple problem do not run many batches simultaneously. It is a weakness of the ASAP solution to start too many batches at once. Thereby vessels are blocking each other and stations can be occupied only later in time. For the industrial problem, however, it seems that the ASAP solution is already a good schedule so that the EA cannot improve it much. We suppose that this is due to the plant layout which minimizes the probability of collisions. 

In model constraints given next, Q is a wrap-around operator (Shat et al., 1993), r, holds the duration of tasks in number of time intervals (5=8 h) and set K, gives the tasks belonging to chemical z. The objective function minimizes the total cost of the schedule in relative money units (r.m.u.). Eq 2 ensures that the volume handled by the task does not exceed the capacity of the vessel Vm. Eq 3 ensures that material production only occurs if the corresponding task is executed. The periodic schedule features exactly one batch of each chemical (eq 4). Eqs 5-6 are the excess resource balances. Eq 7 ensures that the start-up procedure does not require more units than those available. 

After the installation of each heater, the bentonite blocks, the instrumentation and backfilling of the surrounding area, the corresponding system was switched on. That is, heaters were turned on according to the installation time schedule. First heater started last September 2001 (Goudarzi Bbrgesson, 2003). Since that dale, temperature, relative humidity, total pressure and water pressure from the instrumentation have been collected. 

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