1. Some Introductory Remarks on Operations Scheduling

2. The basic scheduling problem addressed in workflow management
How to prioritize the (exclusive) allocation of a finite set of reusable resources to a set of contesting “jobs” so that certain performance criteria are optimized.
In some more complex systems, the scheduling policy must also guarantee the correct operation of the underlying system from a more logical / behavioral standpoint (e.g., there might be a need to avoid potential deadlocks).
The last concern is particularly prominent in flexibly automated operations.

3. The need for behavioral control
J1 : R1 ® R2 ® R3
J2 : R3 ® R2 ® R1
Explain the system operation and the depicted deadlock
Emphasize that deadlock is a disruption, in general, and a “fatal error” in case of automated systems

4. Finite State Automata (FSA)-based modeling of RAS behaviorq 16 12 J 21 17 11 22 1 2 3 4 15 18 19
To start the exposition of the available results let us first describe the operation of the considered RAS and the corresponding deadlock avoidance problem by means of a finite state automaton:
the state of this automaton is defined by the active process instances at each processing stage; for instance, in the considered example, the state will be a vector having six components
The initial state is the empty state
the RAS behavior can be expressed by the STD, i.e., an enumeration of the state space of the RAS-modeling FSA (demonstrate on the right part of the slide)
The development of. deadlock
The RAS state is defined by the number of active process instances at each processing stage.

5. Safe vs. Unsafe Region and the Optimal Deadlock Avoidance Policyq q 6 13 J 5 11 12 7 23 8 21 22 9 10 14
A deadlock-free
unsafe state! q 1 11 J 2 21 q 15 q 3 12 J q 4 J J J 11 21 22
The complete reachable state space
Co-reachable states and their classification to safe and usafe
The differentiation between unsafe states and deadlocks
The optimal DAP, its uniqueness, and its one-step lookahead implementation q 16 q 17 J J J J 12 21 11 22 q 18 11 J 12 21 19 22

6. An Event-Driven RAS Control Scheme
System State Model
Logical Control
Performance Control
Event
Feasible
Actions
Admissible
Actions
Commanded
Action
A closed-loop control scheme:
Controller actions are responses to the events taking place in the RAS
Situation assessment based on a maintained RAS state model gives the feasible actions
A logical control policy filters out the admissible actions
A performance control policy selects the admissible action to be commanded on the system
The rest of the talk will report the progress that has been made in terms of materializing this control scheme.
Configuration Data
RAS Domain

7. Some factors defining a scheduling problem and its complexity
Structure of the contesting jobs: single tasks or multiple tasks per job, and in the case of multi-task jobs, the sequential logic that drives the execution of these tasks.
Number of distinct resource types and the “capacity” of each type (i.e., the number of distinct units from this type).
Processing-time distributions for the different tasks involved.
Resource operational modes and availabilities
Job arrival patterns: static vs. dynamic
Allowance for preemption
Possibility of insertion of deliberate idleness
Other possible dependencies among the different jobs in the form of priorities, synchronizations, etc.

8. Scheduling objectives
Maximize the throughput that can be delivered in a stable manner
Control the experienced delays by the various jobs
Control the accumulated WIP
Meet due dates and control the corresponding implications of failing to do so
Control set-up costs, preventive maintenance costs, etc.
Etc.

9. The complexity of the scheduling problems
Scheduling problems are combinatorial optimization problems that become intractable very fast, even for rather simple instantiations.
From a theoretical standpoint, they have been studied by IE / OR, Operations Management, and (Stochastic Optimal) Control theory. The relevant literature is vast and the corresponding results very interesting and technically savvy.
But in the context of operations / shop-floor scheduling, these problems are addressed by defining a rather simple sequencing policy for each workstation; these policies are collectively known as “dispatching rules” in the relevant literature.
Popular dispatching rules have established their broad acceptance on their ability to do well in some simpler settings, in particular, some single-machine scheduling problems.
Also, focusing on single-machine scheduling is further justified in many industrial settings by the presence of a well-defined bottleneck station. In such a case, the problem boils down to the efficient scheduling of the bottleneck station, while the scheduling of the other stations should align to the needs and the logic of the bottleneck schedule.

10. An example on bottleneck-based scheduling
Mashing
(1 mashing tun)
Boiling
(1 brew kettle)
Fermentation
(3 40-barrel
ferm. tanks)
Filtering
(1 filter tank)
Bottling
(1 bottling
station)
Grain cracking
(1 milling
machine)
Fermentation Times:

11. Single-Workstation Scheduling
Please, refer to:
your class notes from the in-class developments, and
the corresponding material from Nahmias’ textbook posted at the library electronic reserves