(Table 4). After task composition, the cloud manufacturing platform
will schedule these tasks onto the services (as in the context of cloud
manufacturing) offered by the 10 enterprises mentioned above. Each
task has a specific workload, which can be expressed as the product of
resource efficiency and required completion time for a unit resource.
For instance, Milling-1/2/10 in Table 1 indicates that the operation
needs 1 unit milling equipment resource with the efficiency of 2 parts
per day to work for 10 days. There are constraints on task execution in
terms of time, cost, and reliability (reliability is measured by pass-rate)
(the last column of Table 4). For instance, 15/5K/0.96 means that the
task is required to be finished within 15 days with less than 5000USD
and the pass-rate should not be below 96%. Each task has a fixed
subtask execution flow (i.e. subtask structure). Fig. 1 shows the subtask
execution flow of all tasks shown in Table 3. It should be noted that
some subtasks of these tasks are identical and thus require the same
resources.
In this example, an important issue is how to schedule these tasks
with different workloads onto the services to better satisfy users’
requirements and achieve better system performance such as a shorter
makespan and higher service utilization. This is indeed a multi-task
scheduling problem. Solving this problem requires the establishment of
a suitable model.
4. A multi-task scheduling model
4.1. Enterprises and services
Assume that there are
registered enterprises in the current cloud
manufacturing system, which are denoted by
nt I E E E( )={ , …, ,…, }
iI1
(Fig. 2). Enterprise
i
(
iI1≤ ≤
)offers
l
i
(
lJ1≤ ≤
i
)different types of
manufacturing services (such as design services, production services,
and processing services), which are selected randomly from total
J
types of services in the entire cloud manufacturing system. The
s
th
(
sl1≤ ≤
i
) type of service is denoted by
S
is,
. The following attributes of
S
is,
, including type
R
i
,
, quantity
A
is,
, unit cost
is,
,efficiency coefficient
, and reliability
Rel
E
, are taken into account. The introduction of
efficiency coefficient
is motivated by the fact that different enter-
prises may have different efficiencies in fulfilling a task (or subtask)
with the same type of resource, which means that they may need
different amounts of time for fulfilling the same task (or subtask) even
using the same type and the same amount of manufacturing resources
[15,16]. For example, the efficiencies of the lathing resources provided
by Dengyun, Honda, Shili, and Huafeng are 5, 3, 6, and 6 parts per day,
respectively. The average efficiency is thus 5 parts per day. Hence, the
efficiency coefficients are 1.0 (5/5), 0.6 (3/5), 1.2 (6/5), and 1.2 (6/5),
respectively. The efficiency of
i
’s services depends on many factors
such as enterprise management level, resource quality. For the sake of
simplicity but without loss of generality, we assume that all services of
an enterprise have the same efficiency. The quantity
A
i,
of
S
i,
along
with its efficiency coefficient
characterizes the capacity of enterprise
with respect to
S
i,
, which is defined as
Cap A α=×
i,s
i,s
. The introduc-
tion of the concept of enterprise capacity facilitates the calculation of
the time required for
S
i,
to complete a subtask.
4.2. Requirement tasks
Requirement tasks come from the decomposition of users’ orders.
Assume that at a time there are
tasks to be processed in the current
cloud manufacturing system, which are represented by
ask K T T T( )={ ,…, , …, }
kK1
[21,22] (Fig. 2). A task may require one type
of service or multiple different types of services. Here, we deal with the
latter type of tasks so that
k
can be decomposed into
k
subtasks, with
the
u
th (
un1≤ ≤
k
) subtask being represented by
s
ku,
. Each subtask
requires a different type of service, which is selected randomly from the
total
J
types of services in the entire cloud manufacturing system.
k
has a certain subtask structure, which is usually a combination of the
four basic structures, including sequential, parallel, selective, and
circular [28]. For simplicity and without affecting the credibility of
our results, the sequential subtask structure is assumed, i.e.
k
’s
subtasks have a linear structure so that they are executed sequentially
[7,8].
For
s
ku,
, the following attributes, including the required service type
ku,
, the required service time
t
ku,
when using a unit service
a
ku,
, and the
benchmark efficiency coefficient
0
, are taken into account. The
introduction of the variables above is motivated by the fact that each
subtask has a certain workload
l
ku,
, which will take a period of time for
its completion using a certain amount of service (of a certain type and
with a certain efficiency coefficient) [18]. Based on the concepts
Table 2
Geographical distances between the case companies (km).
Dengyun Honda Hongtu Shili Power Hong Teo Delta Huafeng Sunspring Fenghua
Dengyun 0 355.4 245.5 272.3 20.2 126.2 55.2 10.8 19.3 170.3
Honda 355.4 0 100.2 21.5 153.9 200.2 24.5 15.4 148.9 298.1
Hongtu 245.5 100.2 0 292.6 60.2 28.7 73.2 22.2 21.1 18.4
Shili 272.3 21.5 292.6 0 113.5 175.8 178.1 301.6 156.9 279.3
Power 20.2 153.9 60.2 113.5 0 41.6 16.5 121.0 18.6 16.0
Hong Teo 126.2 200.2 28.7 175.8 41.6 0 19.6 63.1 92.4 186.2
Delta 55.2 24.5 73.2 178.1 16.5 19.6 0 16.6 48.9 32.5
Huafeng 10.8 15.4 22.2 301.6 121.0 63.1 16.6 0 102.7 64.3
Sunspring 19.3 148.9 21.1 156.9 18.6 92.4 48.9 102.7 0 136.1
Fenghua 170.3 298.1 18.4 279.3 16.0 186.2 32.5 64.3 136.1 0
Table 3
Subtask information of each task.
Task Subtask1 Subtask2 Subtask3 Subtask4 Subtask5 Subtask6
30207537 Valve Clutch housing Crankcase Oil pan Connecting rod Gear housing
30207538 EGR passage Crankcase Valve Oil pan Gear housing Connecting rod
30207540 Crankcase EGR passage Valve Clutch housing Connecting rod Gear housing
30207541 Gear housing EGR passage Valve Crankcase Valve Oil pan
30207543 Valve Crankcase Connecting rod Oil pan Gear housing EGR passage
30207568 Gear housing Clutch housing EGR passage Valve Crankcase Oil pan
30207573 Oil pan Gear housing Connecting rod Valve EGR passage Clutch housing
30201025 Crankcase Oil pan Connecting rod Valve EGR passage Clutch housing
Y. Liu et al.
Robotics and Computer–Integrated Manufacturing xx (xxxx) xxxx–xxxx
4