4.1. Conceptual Model
The objects of data acquisition are manufacturing resources in smart factories, such as machines, AGVs, WIP, etc. Under the IIoT environment, the internal producing department can obtain real-time data in time by industrial bus, wireless sensor network, RFID reader and camera, etc. The external can obtain real-time orders by industrial cloud platform, ERP\MES, and other upper-layer applications. The dynamic characteristics of workshop resource status and order arrival time require the smart workshop resource model to differ from the traditional one [
37]. The production resource service model of smart workshops should not only build its static serviceability, but also have the function of constructing a real-time service capability based on its own real-time state and task requirements.
Definition 1—Smart Work-in-progress (SWIP). It refers to goods in process with a passive recognition ability in physical space. SWIP can be perceived by manufacturing resources (e.g., manufacturing equipment, processing equipment, and people) in the manufacturing environment and read, related requirements (e.g., production process, emergency grade, and deadline) of SWIP. Manufacturing resources are dynamically adjusted in the manufacturing process to coordinate the completion of production tasks.
Definition 2—Smart Manufacturing Resources (SMRs). It refers to the production process based on WIP that complete the relevant handling, processing (assembly), and quality inspection and other related resources, including production resources, logistics resources, and people with wearable devices that are capable of sensing, communication interaction, learning, execution, self-control, etc., in physical space. After establishing the business association, smart manufacturing resources and SWIP jointly complete the manufacturing task in the form of cooperation/competition with the goal of the lowest manufacturing cost, the highest manufacturing efficiency, and the lowest energy consumption.
The smart modeling matrix set of PRs includes two parts: The attribute of resources and real-time status in the environment of IIoT. The real-time status includes dynamic queue, service load, and service process status, etc. Hence, the real-time perception of the state of key manufacturing resources in smart workshops is the basis of constructing the smart model [
38]. The purpose of introducing SWIP and SMRS into the self-adaption scheduling process is to formalize product requirements, resource capabilities, attributes, and constraints.
In order to manage the real-time state data of key resources more effectively, the real-time state model of PRs (e.g., machines and numerical control machining centers) and LRs (e.g., AGVs) are constructed as follows:
At time , the set of service types of can be described as , where is the number of service types that can be provided, and is one of them. Meanwhile, the set of service types of can be described as , where is the number of service types that can be provided, and is one of them.
The real-time status attribute of production equipment has six characteristics, including equipment number, service option, manufacturing energy consumption, idle energy consumption, and manufacturing time.
where
denotes the type of service that the machine can provide,
denotes the processing energy consumption of the machine tool for the current task,
denotes the idle energy consumption of the machine tool,
denotes the service time of the machine tool for the current task,
denotes the service queue of
.
The real-time status attribute of logistics equipment is defined as seven characteristics, including equipment number, service options, location of the handling equipment, handling energy consumption, standby energy consumption, and handling time.
where
denotes the type of service provided by the handling equipment
,
denotes the energy consumption of the handling equipment for the task,
denotes the location of the handling equipment,
denotes the idle energy consumption,
denotes the service time of the handling equipment for the current task,
denotes the service queue of
.
Definition 3—Real-time Tasks (RTs). Generally, in the field of manufacturing, there are two types of tasks, i.e., simple tasks and complex tasks. A simple task is a basic task that can be completed independently by a single service resource. It is a definite step of a complex task. Simple tasks have positive input conditions and output results. In addition, it also contains explicit attribute features, such as task arrival and end time, resource capability demand, and task execution time, etc. In this paper, RTs refer to complex tasks. It contains two simple tasks, such as production task ofand logistics task of.
The production and logistics collaborative manufacturing scenario in SSF, a manufacturing task includes a production task and a logistic task [
39]. In this study, the production task and logistics task of a manufacturing task are packaged and released in groups. We assume that task
will be performed by
and
. Hence, the
input set of
is denoted by (11).
where
is the status of the machine
which will be performing the production task of
,
is the status of the AGV
which will be performing the logistics task of
. It describes the serviceability of the required before
executes at time t, including the ability of processing resources and the ability of logistics resources.
When the task is completed at time
, the
output set of the
is denoted by (12).
It describes the status of service resources when has been executed at time .
4.2. Real-Time Information Model of Tasks for Multi-Customer
Entropy is defined as the product of information generated by an event and the probability of the event [
26]. In the scenario described in
Section 3, this paper focuses on orders with different arrival times and due dates. In a real-time distributed system, the remaining execution time and deadline are some fundamental attributes of real-time tasks that elucidate the activities of the manufacturing system [
35].
In the intelligent workshop layer, we can easily obtain the real-time process of jobs and the real-time status of PLs based on the conceptual model. We assume that the release time of
is time t,
. The predicted mean remaining processing time of
is denoted by (13).
where
is the total process number of
;
is the number of optional machines in each process (task) of
.
We assume that task
is processed on machine
, and task
will be processed on machine
. The distance between machine
and machine
is denoted by
. The predicted mean remaining delivery distance of
is denoted by (14).
where
,
is the predicted mean remaining delivery time of
,
is the predicted mean remaining delivery time from
to
.
The predicted mean remaining service time of
is denoted by (15).
where
represents the predicted mean remaining delivery time of
, i.e.,
.
Due to the fact that each task has its due date, at time
t, the remaining completion time of
is denoted by (16).
Subject to the constraints in Equations (13) to (16), we apply the information-theoretic concepts to define the following parameters [
40,
41,
42]:
The urgency of task
is the probability of execution of the task by the ratio between the predicted mean remaining service time (
) and the remaining completion time (
) of the task. At time
t, the urgency of
is denoted by (17).
The normalized urgency of a task is the probability of a task normalized by the sum of all the tasks’ urgency. We assume that the total number of the tasks in a task-pool at time
is
. The tasks in a task-pool can be described as
, where
. The normalized urgency of a task in a task-pool at time
is denoted by (18).
where
at time
.
The urgency of the task is a vital attribute under an uncertain scheduling environment. We define this attribute as a standard entropy of
, which is formulated as follows: