D B S －19－07｢Simulated annealing and genetic algorithm
based method for a bi-Level seru loading problem
with worker assignment in seru production systems｣

Lan Luo and Zhe Zhang_
School Economics and Management, Nanjing University of Science and Technology
Nanjing 210094, P. R. China

Yong Yin
Graduate School of Business, Doshisha University

September 2019

DBS Discussion Paper Series supported by the OMRON Foundation.DBS

（summary）
Seru production is one of the latest manufacturing modes arising from Japanese
production practice. Seru can achieve efficiency, flexibility, and responsivenesssimultaneously. To accommodate the current business environment with volatile demands
and fierce competitions, seru has attracted more and more attention both from researchersand practitioners. A new planning management system, just-in-time organization system(JIT-OS), is used to manage and control a seru production system. The JIT-OS contains two
decisions: seru formation and seru loading. By seru formation, a seru system with one or
multiple appropriate serus is configured; by seru loading, customer ordered products areallocated to serus to implement production plans. In the process of seru formation,
workers have to be assigned to serus. In this paper, a seru loading problem with worker
assignment is constructed as a bi-level programming model, and the worker assignmenton the upper level is to minimize total idle time while the lower level is to minimize themakespan by finding out optimal product allocation. A product lot can be splitted andallocated to different serus. The problem of this paper is shown to be NP-hard. Therefore,a simulated annealing and genetic algorithm (SA-GA) is developed. The SA is for theupper level programming and the GA is for the lower level programming. The practicality
and effectiveness of the model and algorithm are verified by two numerical examples, andthe results show that the SA-GA algorithm has good scalability.

Keywords: Assembly systems

DBS Discussion Paper Series supported by the OMRON Foundation.DBS

Manuscript submitted to

SIMULATED ANNEALING AND GENETIC ALGORITHM BASEDMETHOD FOR A BI-LEVEL SERU LOADING PROBLEM WITH
WORKER ASSIGNMENT IN SERU PRODUCTION SYSTEMS

Lan Luo and Zhe Zhang∗
School Economics and Management, Nanjing University of Science and Technology
Nanjing 210094, P. R. China

Yong Yin
Graduate School of Business, Doshisha University
Karasuma-Imadegawa, Kamigyo-ku, Kyoto, 602-8580, Japan

Abstract. Seru production is one of the latest manufacturing modes arising from Japanese production practice. Seru can achieve efficiency, flexibility,
and responsiveness simultaneously. To accommodate the current business environment with volatile demands and fierce competitions, seru has attracted
more and more attention both from researchers and practitioners. A new planning management system, just-in-time organization system (JIT-OS), is used
to manage and control a seru production system. The JIT-OS contains two
decisions: seru formation and seru loading. By seru formation, a seru systemwith one or multiple appropriate serus is configured; by seru loading, customer ordered products are allocated to serus to implement production plans.
In the process of seru formation, workers have to be assigned to serus. In
this paper, a seru loading problem with worker assignment is constructed as abi-level programming model, and the worker assignment on the upper level isto minimize total idle time while the lower level is to minimize the makespanby finding out optimal product allocation. A product lot can be splitted andallocated to different serus. The problem of this paper is shown to be NP-hard.
Therefore, a simulated annealing and genetic algorithm (SA-GA) is developed.
The SA is for the upper level programming and the GA is for the lower level
programming. The practicality and effectiveness of the model and algorithm
are verified by two numerical examples, and the results show that the SA-GA
algorithm has good scalability.

1. Introduction. In the past three decades, volatile and diversified demands, highcapital, and labor cost as well as the rapid revolution in technology have posed greatchallenges to manufacturing industries, especially to the high-tech like electronics.
Such tough environment motivates enterprises to modify traditional production
systems with high automated equipment and low worker involvement and to create2010 Mathematics Subject Classification. Primary: 58F15, 58F17; Secondary: 53C35.
Key words and phrases. Seru loading, bi-level programming, lot-splitting, worker assignment,
hybrid intelligent algorithm.
∗ Corresponding author: Zhe Zhang. This research was sponsored by Natural Science Foundation of China (NSFC Grant no. 71401075). We thank Professor Xiuli Wang and Ding Zhang fortheir valuable discussions and comments, and we would like to express our appreciation to all thereviewers and editors who contributed to this research.

1

2

LAN LUO, ZHE ZHANG AND YONG YIN

new production modes. In 1992, under the background of the economic crisis inJapan since 1990s, a new production system named seru was created at a factory inSony. Later on, many manufacturing enterprises such as Canon, Sharp, Panasonic,
etc. also adopted seru production systems (Liu et al., 2014 [25]). Taking Canon as
an example, the company dismantled assembly lines of its 54 factories with a total
length of about 20,000 meters and replaced them with serus. This replacement
saved 720,000 square meters of workshop space and reduced the average working
time of WIP from 3 days to 6 hours (D&M Nikkei Mechanical, 2003 [6]), andthe total cost was reduced by 230 million yen (Weekly Toyo Keizen, 2003 [45])
From 1999 to 2005, its subsidiary, Canon Electronics Corporation, increased profit
from 1.1 billion yen to 11.8 billion yen, reduced factory space by 70%, reduced
energy demand (water, electricity, etc.) and carbon dioxide emissions by 50% andincreased average productivity by 4 times (Hisashi Sakamaki, 2006 [11]; Yu andTang, 2019 [58]). Yin et al. (2017) provided more detailed data on the benefitsof implementing seru production in Canon and Sony [51]. Researches show that
seru is more adaptive and competitive in unpredictable environment with multiple
product models, fluctuated volumes, and short product life cycles (Sakamaki, 2006[36]; Zhang et al., 2017 [59]). Seru is considered as a potential production system
for Industry 4.0 (Yin et al., 2018 [52]).
Seru production system is a relatively new production mode arising from Japanese production practice (Yin et al., 2017 [51]), the research on seru is still few
because of its short history. Recently, seru has attracted attention from leading
scholars. For example, Roth et al. (2016) summed up the development of operations management over the past 25 years, pointing out 8 possible future research
directions. They listed seru as one of the new research fields worthy of attention,i.e., “seru production systems are more flexible than Toyota production system,and they represent the next generation of lean production that has recently been
introduced to operations” [34]. Similarly, Treville mentioned that although there
is little research on seru production systems outside Japan, its progressiveness has
been verified in practice. By applying seru production, some Japanese electronics
enterprises have been able to respond quickly to market demands and confront with
rapid development and upgrading of products (Treville et al., 2017 [5]). Althoughseru production mode has been successfully implemented in many manufacturing
enterprises, the academic research on it is not sufficient enough to guide production
practice. In this paper, we take a seru loading problem with worker assignment
and lot-sppliting into consideration, and hopefully this research could promote thepractice of seru production.
Seru is the Japanese pronunciation for cell. Seru is defined as a low automatedassembly system that is converted from traditional conveyor line. A seru system
consists one or more serus. A seru consists of simple equipment and multi-skilledworkers to complete one or more product types (Yin, Stecke and Kaku, 2008 [48];
Stecke et al., 2012 [39]). The difference between seru production and celluar manufacturing can be found in Yin et al. (2018) [52], Sakazume (2005) [35], and Liu etal. (2010) [24]. They stated that these two types of production systems are similarin layout such as U-sharped. Manufacturing cells are converted from functionallayout job shops into product layout flow shops using group technology. Seru is aconversion of conveyor lines. Cells are mainly used in machining processes but seru
is mainly adapted in the assembly process. Yin et al. (2017) [51] added that serus
are reconfigurable while cells are usually fixed.

BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

3

There are three types of seru, namely divisional seru, rotating seru and yatai(Akino, 1997 [2]), which reveal the evolution of seru production system, see Fig.
1. A divisional seru is configured at the first stage when converting a line into
several serus. As seru implementation and worker training carry on, the workers
possess the whole skill required for assembly, rotating serus can be constructed. The
equipment is shared by several fully skilled workers in rotating serus, they movefrom one workstation to another to complete all the operations from start to end
one by one in each seru. The operations on a single product are completed by a fully
skilled worker and not shared with other workers. When a product is finished, theworker returns to the first workstation and begins a new round (Liu et al., 2014 [25]).
The efficiency of each seru is mainly decided by the slowest worker in a rotating
seru, thus causing waste in processing time. Sometimes, a supervisor is required totake charge of managerial tasks in rotating serus. The benefit of rotating seru is
its flexibility to fluctuated volumes. The high the production volume, the more thenumber of workers within a rotating seru. On the contrary, the low the production
volume, the less the number of workers are assigned. Some rotating serus can finally
evolve into yatais. A yatai is a highly self-disciplined seru that contains only one
fully cross-trained worker who takes full charge of the processing procedure (Liuet al., 2010 [24]). There are hybrid seru systems in which different seru types andconveyor lines exist (Iwamuro, 2004 [15]; Miyake, 2006 [32]). Researches on seru
production usually focus on specific seru types and/or hybrid seru systems. Liuet al. (2014) [23] discussed the production planning problem in multi-stage multioption seru systems. Yu et al. (2017) [56] took line-hybrid seru conversion problem
into account. Some research on the practice of seru production is ongoing, including
seru-line conversion (Shao et al., 2016 [37]; Yu et al., 2017 [55]; Aboelfotoh et al.,2018 [1]; Zhang et al., 2019 [62]), seru formulation (Yu et al., 2018 [57]; Wang andTang, 2018 [46]) and reliability of seru systems (Han et al., 2018 [7]; Han et al., 2019[8]). This paper will focus on the seru loading problem with worker assignment in
the context of rotating serus.
5

4

6

5
3

4

6

4

5
3

6

3

7

2

7

2

7

2

8

1

8

1

8

1

divisional seru

rotating seru

yatai

Figure 1. Three types seru
A new planning system, JIT-OS, is used to manage and control a seru production
system. The industrial cases of JIT-OS can be found in Yin et al. (2008) [48] andStecke et al. (2012) [39]. JIT-OS is an extension, or upgrade, of traditional JIT material system (JIT-MS). Their mechanisms are similar: the correct materials/serus,
in the right place, at the appropriate time, in the exact amount. The difference isthe focus from materials to organizations (i.e., serus). According to Stecke et al.
(2012) [39], the application of JIT-OS is as follows. First, apply the principles of thecorrect serus, in the right place, at the appropriate time for product model changes.
This involves the relocation or relayout of either current serus or the creation of

4

LAN LUO, ZHE ZHANG AND YONG YIN

new serus for both new models or model changes. Second, determine the appropriate number of serus and/or number of workers within serus to handle production
volume fluctuation. The JIT-OS contains two decisions: seru formation and seru
loading. By seru formation, a seru system with one or multiple appropriate serus
is configured; by seru loading, customer ordered products are allocated to serus to
implement production plans. In the process of seru formation, workers have to be
assigned to serus. In this paper, a seru loading problem with worker assignment isconstructed as a bi-level programming model.
Seru loading is included in production planning problem, which plays an essential role in deciding the performance of a seru system. It contains two aspects: one
is to assign products to feasible serus (or assign feasible serus to products), andthe other is to give a preliminary order for products in each seru (Süer and Dagli,
2005 [40]). Tao et al. (2010) [43] developed a semi-online algorithm for schedulingproblem with bounded processing time. Yin et al. (2013) [50] studied schedulingproblem with past-sequence-dependent delivery times. Zhao et al. (2014) [63] considered scheduling and assignment problem with rejection and position dependent
processing time. Lot-splitting and setup time are two main factors when making
seru loading decision. On one hand, parallel production may reduce total makespanand increase the flexibility of the whole seru system. On the other hand, too small lot size brings about frequent setups which may in turn cause an increase in
makespan. Lot-splitting means the demand of a product can be divided and the
product can be allocated to more than one seru, it is usually neglected in researches
about seru on account of complexity. However, other researches have been carriedon with lot-splitting in the scenarios of jobshop, CM and traditional conveyor line.
Low et al. (2004) [27] studied the benefits of lot-splitting in job-shop production
system. Huang and Yu (2017) [14] designed an ant colony algorithm for solving
multi-objective job-shop scheduling problem with equal-size lot-splitting. What’smore, setup time is another deciding factor in loading problem which is usually considered to be zero in seru context. Some researches under other production modes
provide us with similar understandings. Hsu et al. (2010) [13] regarded setup time
to be proportional to the length of the already processed jobs. Luo et al. (2015)[28] solved scheduling problem for hybrid flowshop with family setup time. Pei etal. (2017) [33] considered time-dependent setup time which is a liner function ofstarting time. Luo et al. (2017) [29] estimated setup time by the number of different operations between two adjacent products in one seru. Apart from these
two main factors above, assignment of multi-skilled workers are the key factor that
deciding the performance of seru production system. Babayigit and Süer (2003) [3]considered minimizing tardy jobs with limited manpower. Liu et al. (2013) [26]
investigated training and assignment problem of workers with the aim of balance
workers’ workload. Ying and Tsai (2017) [53] worked on training and assigning
multi-skilled workers in seru system to minimize total cost. Lian et al. (2018) [22]considered a multi-skilled worker assignment problem with worker heterogeneity inseru systems. Sun et al. (2019) [41] developed a cooperative coevolution algorithm
which combining generic algorithm and local search, and the ant colony optimization algorithm for solving seru formulation and seru scheduling problem at the sametime with the objective of minimizing makespan. Sun et al. (2019) [42] used a cooperative coevolution algorithm to solve seru production problem aim at reducing
the total tardiness. Although the researches above took worker assignment into
account, few researches has considered the hierarchy of worker assignment decisionBI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

5

and production allocation decision. In that case, the seru loading problem withworker assignment in this paper is abstracted as a bi-level programming model.
Because of the complexity of practical production decision-making problems
which may be in the charge of different hierarchical decision makers, bi-level programming has been widely utilized in the field of engineering optimization. There
are mainly two aspects of methods for solving bi-level programming, one is analytical methods, and the other is heuristics (Sinha et al. 2018) [38]. Due to the nonconvexity and non-differentiability of bi-level programming, the heuristics including
meta-heuristic methods are widely used. Kasemset and Kachitvichyanukul (2010)[19] built a bi-level multi-objective model under Theory of Constraints (TOC) forjob shop scheduling. Kasemset and Kachitvichyanukul (2012) [20] developed a PSObased procedure for bi-level job-shop scheduling problem. Yang et al. (2013) [47]designed an electromagnetism-like optimization algorithm for bi-level programming
problems. Han et al. (2013) [9] proposed a bi-level model for scheduling problem with lot-splitting in virtual cell manufacturing system. Zhang et al. (2014)[61] introduced bi-level programming with MOBL-APSO algorithm to resourceconstrained multiple project scheduling problems in hydropower station. Behnia
et al. (2017) [4] built a bi-level mathematical model for cell formulation problem
considering workers’ interest. Zhang and Xu (2016) [60] developed a bi-level multiobjective MRCPSP (multi-mode resource-constrained projects scheduling problem)
model with fuzzy random coefficients and bi-random coefficients. In this paper,
we will design a simulated annealing and genetic algorithm (SA-GA) to solve theproposed bi-level seru loading model, where SA is for upper level programming and
the GA is for lower level programming.
The remainder of this paper is organized as follows: a detailed description forthe seru loading problem with worker assignment is presented in Section 2. Thenin Section 3, a bi-level model is formulated based on the problem description above.
To solve this NP-hard problem, a simulated annealing and genetic algorithm (SAGA) is designed in Section 4. Section 5 provides two numerical examples to test
the effectiveness of the proposed model and algorithm. The conclusions and future
research are finally shown in Section 6.
2. Problem description.
2.1. Seru loading problem with worker assignment. In this section, a seru
loading problem with worker assignment will be discussed. Since multi-skilled worker is the core of seru production system, so its assignment is one of the most important issues. Normally, when the orders are received, the worker assignment decision
is firstly made by the first-line managers. Then, the serus are constructed and theability of each seru (whether a product can be produced and its producing time) is
also determined. According to this worker assignment, the product allocation decision is made by the production planning department. Subsequently, the production
planning department feedbacks his result to the first-line managers to check it issatisfied or not. If it is not, the process above will be repeated until the optimal
worker assignment and loading results are obtained. In this decision making process, although the first-line managers cannot make product allocation decision oflower level directly, they can guide the decision. Besides, the product allocation
decision could in turn affects worker allocation on the upper level. Hence, the output of worker assignment in the upper level is the input of product allocation in
the lower level. Meanwhile, the output of lower level is also the input of the upper

6

LAN LUO, ZHE ZHANG AND YONG YIN

level. Therefore, the seru loading problem in this paper is formulated as a bi-levelproblem, see Fig. 2.
With regard to worker assignment, the workers’ processing time for each productare known and which seru the workers should be assigned to is needed to be decided.
The serus discussed in this paper are all rotating serus, the divisional serus andyatais are left for the future research. In a rotating seru, the workers are in chargeof the whole processing procedures of a single product but the equipments areshared with each other. They move along with the materials from one workstation
to another to complete the processing procedures. The ability of serus are decided
by workers assigned to them, and if at least one worker in the seru is capable ofprocessing a product, then the seru can process this product. And the efficiency ofeach seru is mainly decided by the slowest worker in the seru, and the other workers
in the seru should stop and wait for the slowest one. Thus, the waiting time is theiridle time. The aim of worker assignment is to balance the ability of workers in eachseru, i.e. to minimize the total idle time of the workers.
When it comes to seru loading, the demands of each product are known, andwhich seru the product should be allocated to along with the allocation quantity
is to be decided. The products are sorted by due dates in advance, so that the
products with the earlier due date will be prioritized. Lot-splitting is allowed inthis paper to ensure the solutions be more balanced and flexible. The aim of productallocation is to minimize the makespan. Makespan means the maximum processing
time of all the serus in the whole seru production system. The demands of the
products should be satisfied and there is an upper limit of processing time for eachseru. Except for the objective which is to minimize the maximum of several values,
the constraints of product allocation present the characteristics of transportation
problem.

2.2. Assumptions. The following assumptions are made to formulate the bi-level
programming model of seru loading problem with worker assignment:(1) The seru system has already been configured, and the reconfiguration
is not taken into consideration.
(2) Each product can be produced in at least one seru.
(3) The demand of each product have already been known.
(4) The manpower assignment is decided before product allocation.
(5) The raw materials are already in place, so the product can be assembled
immediately after setup.
(6) The serus are kanketsu, i.e. all the procedures required for producing
a product can be completed within the assigned serus.

2.3. Notation.
Indicesi seru index
i = 1, 2, · · · , I
j product index j = 1, 2, · · · , Jw worker index w = 1, 2 · · · , W
Parameters

BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

7First-line m anagers

Satisfied?

No
Upper level m odel

Worker assignm ent...

Som e w orker assignm ent result

Feedback

Production planning departm ent

Lower level m odel

Product allocation

Yes

Preliminary sorting by due dates

Product 1, 2, 3, 4, 5

Objective: Minimize makespan20.9mi n

Seru 11(638.4mi n)

10.4mi n2(319.2m i n)

32.7m i n

Seru 21294.4mi n

18.7mi n4(980. 5mi n)2(202mi n)

2400mi n3(305.5mi n)1603.5mi n

5(369.6mi n)

18.7mi n

Seru 32(772. 5mi n)Note: product 1

1771.6mi n

5(980.4mi n)

product 2

product 3

product 4

product 5

Seru loading result
Output optimal worker assignment withminimum idle time and the corresponding
product allocation

Figure 2. Whole bi-level decision procedure

8

LAN LUO, ZHE ZHANG AND YONG YIN

Qj
sj
tw
j
tij
Ti
Wil
Wiu

the demand for product j
setup time before producing product j
worker w’s producing time of product j
the processing time of product j in seru ithe maximum producing time of seru i in this period
the minmum number of workers can be assigned to seru ithe maximum number of workers can be assigned to seru i
1, if worker w can assemble product j,jew =0, otherwise.

Decision 
variables
1, if worker w is assigned to seru i,wyi =0, otherwise.
1, if seru i can process product j,fij =0, otherwise.
1, if product j is allocated to seru i,xij =0, otherwise.
Qij

the quantity of product j being assigned to seru i

There are some connections among these variables:
The efficiency of a rotating seru is decided by the slowest worker, i.e.:tij = max{w=1,··· ,W } {yiw twj }If worker w can assemble product j, then his/her processing time for product jcannot be zero, i.e.:1, twj 6= 0jew =0, otherwise.
If one of the worker in seru i can produce product j, then the seru can produce
product j, i.e.:
fij = max{w,··· ,W } {yiw ejw }Besides, the total number of workers that can produce product j in seru i is:WX

yiw ejw

w=1

If product j is allocated to seru i, then the allocated quantity cannot be zero, i.e.:
1, Qij 6= 0xij =0, otherwise.

Pj−1
0
1,
j 0 =1 xij = 0
Moreover, let vij =, then vij xij = 1 means that prod0, otherwise.
uct j will be firstly produced in seru i.
3. Modeling.
3.1. Upper level model. The objective of upper level model is to minimize thetotal idle time of all the workers in this seru production system, and it is the waitingtime of all the workers on average workload in their assigned seru, i.e.:
min

I X
J X
W
X

w
(tij − twj )yi PW

i=1 j=1 w=1

Qij

w j
w=1 yi ew(1)

BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

9

Since a worker can only be allocated to one seru, thus:IX

yiw = 1

∀w

(2)

i=1

Because of the space and equipment limits as well as the increase in management
difficulties as workers adding, the number of workers in each seru is supposed not
to exceed the maximum number. What’s more, the minimum number of workers ineach seru should be guaranteed in case that the workload of workers in serus whichhave small number of workers is too heavy, i.e.:

Wil ≤

W
X

yiw ≤ Wiu

∀i

(3)

w=1

Besides, there are also some logical constraints in upper level model:
yiw , fij ∈ {0, 1}(4)

3.2. Lower level model. The objective of lower level model is to minimize thetotal makespan, which is the finishing time of the latest product in the whole system,
i.e.:
!
J
X
Qij tij+ sj xij vij(5)
min M S = max{i∈{1,··· ,I}}PW
w j
w=1 yi ew
j=1
Because a product can only be assigned to feasible serus, so:xij ≤ fij

∀i, j

(6)

And, the total quantity of demand should be fulfilled when splitting into lots:
I
X

Qij = Qj

∀j

(7)

i

In addition, the total producing time of each seru cannot exceed its available timein the period,i.e.:J
X
j=1

Qij tijPWw j
w=1 yi ew!
+ sj xij

≤ Ti

(8)

Finally, there are also some logical constraints in lower model, i.e.:
Qij ≥ 0(9)

10LAN LUO, ZHE ZHANG AND YONG YIN

To sum up, the bi-level programming model formulated for the seru loading problem
in this paper is as follows:
PI PJ PW

Qij
w w
min

i=1
j=1
w=1 (tij − tj )yi PW y w ejw

w=1 i


PI


w


∀w


i=1 yi = 1,





P

W


l
w
 Wi ≤ w=1 yi ≤ Wiu , ∀i













tij = max{w=1,··· ,W } {yiw tw
∀i, j

j },









fij = max{w=1,··· ,W } {yiw ejw }, ∀i, j













1, tw


j 6= 0
j


e
=


w


0,
otherwise.








yiw , fij ∈ {0, 1}










 i = 1, 2, · · · , I; j = 1, 2, · · · , J; w = 1, 2, · · · , W ;
(10)



P
s.t.

Q
t
J
ij
ij


min M S = max{i∈{1,··· ,I}} j=1 PW yw ej + sj xij vij





w=1 i w







xij ≤ fij , ∀i, j












PI







∀j



i=1 Qij = Qj ,












P


Qij tij
J





P
+
s
x
≤ Ti , ∀i


j
j
ij

W
w
j=1




w=1 yi ew


s.t.




1, Qij 6= 0






xij =






0, otherwise.












Q
≥
0
ij
















i
=
1, 2, · · · , I; j = 1, 2, · · · , J; w = 1, 2, · · · , W
4. Bi-level simulated annealing and genetic algorithm (SA-GA). Bi-level
programming problem has been proven to be NP-hard (Jeroslow, 1985 [16]; Hansen,
Jaumard and Savard, 1992 [10]; Vicente, Savard and Judice, 1994 [44]). What’smore, the upper level programming of worker assignment has been proven by Yu
et al. (2014) [54] as an exact cover problem which is one of the Karp’s 21 NPcomplete problems (Karp, 1972 [18]) . Similarly, the seru loading problem has
also been proven to be NP-hard by Yin et al. (2011) [49]. Therefore, it can beconcluded that the bi-level seru loading problem with worker assignment is an NPhard problem. Considering the complexity of bi-level programming, especially with
mixed integer variables and minimax objective in lower level programming, a nonnumerical stochastic method i.e. SA-GA algorithm is designed to solve this problem.
In this algorithm, the SA is dedicated for the upper level programming because its
ability to jump out of the local optimum due to Metropolis rule, while GA is forlower level programming due to its robustness and global optimization. In theprocess of finding the optimal solution, when a particular worker assignment isdecided in upper level programming, then the GA is used to find out the optimal
product allocation for this particular worker assignment. The outline of the SAGA algorithm which can briefly show the connection between the upper and lower
programming is presented in Fig. 3.
4.1. Simulated annealing for the upper level programming. Simulated annealing (SA) is firstly introduced to combinatorial optimization by Kirk- patrick,BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

11

Upper level programming

Yes

Meet
termination
condition?

No
w
Generate worker assignment yi

Qij

yiw
Lower level programming

Generate corresponding
product allocation Qij underw
certain worker assignment yi

Output optimal yiw andcorresponding Qij

Figure 3. The outline of SA-GA algorithm
Gelatt and Vecchi (1983) [21]. The simulation of annealing procedure in solids provides a new method for solving complex problems with large number of variables.
Compared with hill-climbing method, SA provides a mechanism which is called Metropolis for inferior solution being accepted. The Metropolis procedure, proposedby Metropolis et al. (1953) [30], is used to generate a set of states under a certain temperature. Take minimization problem for example, let ∆E be the changing
quantity of evaluation i.e. ∆E = Enew − Eold . If ∆E ≤ 0, the old state will be
replaced by the new state. In other case, when ∆E > 0, the new state will be
accepted by the probability of
P = exp(−∆E/T )(11)

It can be concluded from Eq. (11) that the acceptance is close to 1 when thetemperature is at a higher level in the beginning. SA in this stage is similar tosimple random search. As the iteration goes on, the temperature drops, as well as
the acceptance of inferior solution. At the end of the iteration, the temperature is
at a very low level and the acceptance of inferior solution is close to 0, which makes
the SA has the same effect as iterated hill-climbing methods. In that case, it can bequickly convergent. SA is a local research method, but the Metropolis rule makes it
possible to jump out of the local optimum. Considering the global optimization andrapid convergence SA has, it is utilized in this paper for upper level programming.
In this paper, a kind of permutation encoding method is used to represent thesolution. A chromosome is combined with W genes which correspond to W workers.
Thus, the position of a gene represents the worker’s number, and the value of a genemeans the seru’s number which the worker is assigned to. By this way of encoding,the constraint in Eq. (2) which let a worker can only be assigned to one seru will
always be satisfied. An indicator variable y w to represent the value of a gene is12

LAN LUO, ZHE ZHANG AND YONG YIN

defined as follows:
y w = i when yiw = 1, ∀i, w(12)
A specific example of the encoding method is shown in Fig. 4. The numbers in thefirst row which note the locations represent the number of a certain worker, andthe number ( i.e. y w ) in the second row is the seru where the worker is assigned.
For instance, in Fig. 4 the first worker is assigned to seru 1 , the second worker isassigned to seru 2 and the third worker is assigned to seru 2, etc. The encoding
vector in programming is the second row.
worker (location)

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

seru

1

2

2

1

1

1

3

2

3

1

3

2

2

3

2

Figure 4. An example of SA encoding
The procedure of SA for upper level programming is summarized as follows:
Step 1: Initialize T max, T min, II, α, and set initial iteration T = T max,
t = 1;
Step 2: Generate initial random solution of worker assignment;
Step 3: Check constraints and repair the solution;
Step 4: Solve lower level programming by GA and get the best product allocation quantities;
Step 5: Evaluate the solution by the objective of total idle time;
Step 6: Set initial iteration ii = 1;
Step 7: Generate a random disturbance to the solution;
Step 8: Repeat Step 3-5;
Step 9: If eval new < eval old, receive the new solution; else receive the new
solution by Metropolis rule, ii = ii + 1;
Step 10: If ii ≤ II, then go to Step 7, else go to Step 11;
Step 11: Let T = αT , t = t+1, If T ≥ T min, go to Step 6, else output the bestsolution of worker assignment and its idle time, as well as the corresponding
product allocation quantities and makespan obtained by GA in lower level
programming.
Besides, the detailed procedure for generating initial solution and repairing is presented by the following pseudo codes in Algorithm 1, and the way of generating arandom disturbance to the current solution is shown in Algorithm 2. The pseudo
codes are based on MATLAB. And solving lower level programming by GA in step
4 will be explained in detail in the following section.
4.2. Genetic algorithm for the lower level programming. Since being proposed by Holland in 1975 [12], the genetic algorithm (GA) has been widely usedin engineering optimization problem. GA is inspired by the natural evolution procedure, it starts from an initial population of random solutions. The offspring
population is generated from the parent population by a series of genetic operations i.e. selection, crossover and mutation. In each generation, the populationconsists of a certain number of individuals, and each individual corresponds to apotential solution. The individuals will be evaluated by a certain fitness function.
After obtaining the fitness value of each individual, the parents will be selected.
The individuals with higher fitness value are more likely to be chosen, according
to the assumption that better parents will generate better offspring. Hopefully theBI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

13

Algorithm 1: Initialize and repair
Input: seru, worker, worker uplim, worker lowlim
Output: worker seru row
1 worker seru row = f ix(rand(1, worker) ∗ seru) + 1;
2 seru worker = zeros(seru, worker uplim);
3 for w = 1 : worker do
4
if the number of assigned workers in seru: worker seru row(w) is lessthan worker uplim then5
assign worker w to the seru;
6else
7while worker w has not been assigned do
8
a = f ix(rand ∗ seru) + 1;
9
if the number of workers in seru a is less than worker uplim then10
assign worker w to seru a;
11
end
12
end
13
end
14
while the seru where the number of workers is less than worker lowlim
exists do
15
find the first unsatisfied seru noted as c;
16
b = f ix(rand ∗ seru) + 1;
17
if b 6= c and the number of workers in seru b meets upper and lower
limits then18
assign the worker with maximum number in seru b to seru c;
19
end
20
end
21 end22 for w=1:worker do
23[worker seru row(w), no use] = f ind(seru worker == w);
24 endAlgorithm 2: Generate disturbance
Input: seru, worker, worker seru row old
Output: worker seru row new
1 worker seru row dis = worker seru row old;2 k = f ix(rand ∗ worker) + 1;
3 if worker seru row dis(k) < seru then4change worker k to the next seru;
5 else6change worker k to seru 1;
7 end
8 check constraints and repair worker seru row dis;
9 worker seru row new = worker seru row dis;

14

LAN LUO, ZHE ZHANG AND YONG YIN

Product 1

Product 2......

Product J

Seru 1

r11

r12......

r1J

Seru 2r21

r22......

r2 J......

......
¡- ¡-......

......

......

algorithm will converge to a best solution which may represent the optimal or suboptimal solution. GA is developed for solving lower level model due to its robustness
and global optimization (Jones and Soule, 2016 [17]). The genetic algorithm forlower level model is called repeatedly under different worker assignment results, therobustness of genetic algorithm ensures that the results of product allocation won’t
be greatly affected by parameters compared with other algorithms. Besides, GA isa global search method, and it can process multiple individuals at the same, which
speed up the velocity of finding solutions.
To meet the demand constraint in Eq. (7), allocation ratios are used in thispaper to represent the solution by real-number encoding. The genetic operators all
work on the allocation ratios. Fig. 5 intuitively shows the real-number encoding
way by allocation ratios. The algorithms for initialization and repairing solutions

Seru I

rI 1

rI 2......

rIJ

Reshapeallocation ratio(Chromosome)

r11

r12

......

r1J

r21 r22......

r2 J......

rI 1

rI 2......

rIJ

allocation quantity

Q11

Q12

......

Q1J

Q21 Q22......

Q2 J......

QI 1

QI 2......

QIJ

Figure 5. The genetic encoding based on allocation ratios
are as follows:
In this paper, a binary tournament selection method is used to select parents.
It chooses two chromosomes from the old population every time, the one withhigher fitness value will be introduced to the new population, the procedure will be
repeated until the number of individuals in the new population meets the population
size. After selection, the crossover operator used in the algorithm is arithmeticalcrossover. Let chromosome x1 and x2 be the parents, and introducing a random
number of λ, then the two children are:0x1 = λx1 + (1 − λ)x20x2 = (1 − λ)x1 + λx2

(13)
(14)

The mutation method used in the GA is nonuniform mutation, it is firstly raisedby Michalewicz (1996) [31]. For a chromosome x , if xk is the gene to be mutated,
there are two alternative ways of mutation, i.e.
0xk + ∆(g, xU
k − xk ), rand < 0.5
xk =
(15)
xk − ∆(g, xk − xL
otherwisek ),LxU
k and xk are the upper and lower limits of xk . In this paper, because the solutions
are represented by allocation ratios, the upper limit of allocation ratio is 1, and theBI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

15

lower limit is 0. The function ∆(g, y) is defined as follows:g∆(g, y) = y(1 − r(1− G )b )(16)

The parameter g represents the present genetic algebra when mutation occurs, andG notates the maximum genetic algebra. Besides, r is the random number in [0,1]interval while b marks the degree of nonuniformity (in this paper b is set to be 2
as normal). It can be known from the Eq. (16) that at early stage when g is verysmall, ∆(g, y) is close to y, such that the xk can mutate in the whole solution space.
While at the late stage, ∆(g, y) approaches to 0, xk only mutate in a very smallneighbourhood. Therefore, the nonuniform mutation method can avoid prematurityof the GA as well as improve the speed of convergence.
The detailed procedure of GA for lower level programming is as follows:
Step 1: Initialize pop size, GEN ;Step 2: Generate initial population by allocation ratios;
Step 2.1: Set initial iteration a=1;
Step 2.2: Generate the allocation ratio of product j in seru i (rij ) randomly,
set rij = 0 under the probability of p zero1, and normalize rij by rij =
r
PI ij
;
r
i=1

ij

Step 2.3: Let a = a + 1, If a > pop size, then go to step 3 , else go to Step
2.2 ;Step 3: Set initial iteration g = 1;
Step 4: Set initial iteration b = 1;
Step 5: Repair the solutions to meet the constraints of demands in Eq. (7);
Step 5.1: Calculate the allocation quantities (Qij ) of product j in seru i by
Qij = round(rij ∗ Qj );Step 5.2: Adjust the allocation quantity of product j in an allocated seru sPIwhich is randomly found by Qsj = Qj − i=1 Qij + Qsj ;Step 6: Evaluate the solutions;
Step 6.1: Calculate the total processing time of each seru i: P Ti and the
makespan M S is M S = max{i···I} P Ti ;Step 6.2: If for each seru, P Ti <= Ti , then f itness = max(Ti ) − M S, elsef itness = −M S;
Step 6.3: Let b = b + 1, If b > pop size, then go to step 7 , else go to step
5;
Step 7: Select the parents from the population by binary tournament selection;
Step 6: Generate the child population by arithmetical crossover operator asEq.( 13 - 14 );Step 8: Mutate the chromosomes by nonuniform mutation as Eq.( 15 - 16 ),and set some of the genes to be 0 under the probability of p zero2;
Step 9: Let g = g + 1, If g ≤ GEN , then go to Step 4, else output the bestsolution of Qij and its M S.
The probability of p zero1 and p zero2 decides the degree of lot-splitting in theseru production system.
To sum up, the overall procedure of the whole SA-GA algorithm is show in Fig.
6.

16

LAN LUO, ZHE ZHANG AND YONG YIN

The upper lev el programming ( SA )Start

The lower lev el programming ( GA )Initialize pop_size, GEN

Initialize T_m ax, T_m in, II, α

set initial iteration a=1

Set initial iteration T=T_m ax, t=1
Generate initial random solution
Check constraints and repair the solution

Generate the initial random allocation
ratio of ecah product in each seru
Set the ratios to be zero under the probability of p_zero1
and normalization

Solve lower level program m ing
by GA
Evaluate the solution by theobjective of total idle tim e

a=a+1
No

a>pop_size?

Yes

Set initial iteration ii=1

Set initial iteration g=1
Generate a random disturbance tothe solution

Set initial iteration b=1

Check constraints and repair the solution

Repair the solution to meet the constraints of demands

Solve lower level program m ing
by GA

Calculate makespan:MS(The maximum of all serus' processing time PTi)

Evaluate the solution by theobjective of total idle tim eNoeval_new<eval_old

No

PTi>TiYesfitness=-MS

fitness=m ax(Ti)-MS

Yes
b=b+1

Receive the new solution
Receive the new solution
by Metropolios

Nob>pop_size?

Yes
ii=ii+1

Binary tournem ent selection
Arithm etical crossover

Yesii<=II
No

Nonuniform m utation

T=alpha*T
t=t+1

g=g+1
g<=GEN?

Yes

T>=T_minNow

Output optim al yi and idle tim ealong with corresponding Qij and MS
End

Figure 6. The flowchart of SA-GA algorithm

No
End

Yes

BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

17

5. Numerical examples and analysis. In this section, numerical examples arepresented to verify the practicality and effectiveness of the bi-level model and SAGA algorithm proposed above. The parameter settings of SA-GA algorithm forsolving these two examples are presented in Table 1 based on various tests. The
algorithm is implemented by MATLAB R2015b on an Inter Core I5-7200U (basic
frequency of 2.5GHz) with 8G memory.
Table 1. The parameter setting of SA-GA algorithm
Level

Algorithm

Upper

SA

Lower

GA

Parameters
T max = 10000 T min = 0.1
II = 20
α = 0.9
pop size = 300 GEN = 500
p zero1 = 0.75 p zero2 = 0.25
p cross = 0.9
p muta = 0.1

5.1. Data collection. The example in this subsection is about a seru production
system of 15 workers, and 3 serus are to be configured for producing 8 types of
products. Besides, the maximum number of workers in a seru is 6 and the minimum
number is 4. The whole period is of 5 weekdays and each day has 8 working hours,
such that the available producing time for each seru (Ti ) is 2400 minutes. They
work from 8:00 to 12:00 in the morning and from 14:00 to 18:00 in the afternoon.
Table 2 lists the parameters about products, including each worker’s producing timefor each product (twj ), the demand of each product (Qj ) and the setup time before
producing each product (sj ). The number of the products are based on the orderof their due dates, and the one with earlier due date has smaller number, whichmakes it been arranged before the one with later due date in the allocated seru.
5.2. Results and analysis. Fig. 7 is the minimum idle time in every iterationof SA. It can be seen from the figure that the SA begins to converge around the100th iteration. Fig. 8 reveals the relationship between the two objectives of thebi-level model. It is clear that there is a high linear correlation between the total
idle time and the makespan. In that case, the realization of lower level objective
to some extent has a positive effect on the upper level objective. The dots close
to the origin have deeper color, which means that the SA-GA algorithm graduallyconverges to the optimal solution.
Moreover, Fig. 9 and 10 present the two optimal solutions of this problem respectively, the former has minimum idle time but with slightly longer makespan,
and the latter is the opposite. Because the model is a bi-level model and the worker
assignment is decided in the first place, so the first-line manager is more likely tochoose the solution with minimum idle time in Fig. 9. The worker assignment decision with minimum idle time is shown in Fig. 11, and the corresponding productallocation decision made by product planning department is presented in Table 3.
Fig. 11 shows that 6 workers are assigned to seru 1, 5 workers are assigned to seru 2
and 4 workers are assigned to seru 3. With the minimum idle time of all the workers, the working pace of the workers in each seru is relatively consistent. Besides,
according to Table 3, product 5 is allocated to seru 1 and seru 3, and product 6 isallocated to seru 2 and seru 3. Therefore, lot-splitting is occurred to product 5 and
6 in this loading decision. Fig. 12 illustrates the loading results intuitively. It can

18

LAN LUO, ZHE ZHANG AND YONG YIN

Table 2. Data about products

1

Worker’s processing time (min)Demand
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
23 23 21 22 21 24 22 – 21 24 22 – 24 24 23
95

2– 32 37 32 – 34 37 31 34 31 – 31 36 36 37

100

9

3

41 43 – – 44 47 42 42 – 41 47 45 44 42 –

130

8

4

29 28 29 28 26 27 26 27 27 28 26 31 31 – 28

105

6

5

17 – 17 16 19 17 – 18 16 16 20 20 18 16 17

120

5

6

42 23 20 33 38 33 27 29 – 34 33 29 30 36 19

145

6

7

– 68 48 63 43 71 49 21 66 59 53 – – 70 83

50

4

8

14 15 14 20 – 19 19 17 22 19 17 18 – 15 10

115

1

Product

Setup
(min)
4

7000

7000

6500

6500

6000

6000

5500

5500

Idle time/min

Idle time/min

1 The ‘–’ means that the worker cannot produce the product.

5000
4500
4000

5000
4500
4000

3500

3500

3000

3000

2500

2500

2000
0

20

40

60

80

Iteration Times

Figure 7. The minimum idle time in each iteration of SA

100

2000
120
1850

1900

1950

2000

2050

2100

2150

2200

Makespan/min

Figure 8. Idle time and makespanbe seen from the figure that seru 2 has the longest processing time of 1872 minutes
among the 3 serus, so the makespan of the whole seru production system is 1872
minutes. The processing time of seru 2 is only 43 minutes longer than seru 3 which
has the shortest processing time. In that case, the loading of the whole production
system is relatively balanced. Table 4 lists the detailed production timetable of eachproduct in this seru system. Hopefully, the practical production will be guided bythis table. It can be seen from Table 4 that on Friday the serus do not have anytasks, so it is possible for the seru production system to receive more orders.

2250

7000

7000

6500

6500

6000

6000

5500

5500

Idle time/min

Idle time/min

BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

5000
4500
4000
3500
3000

19

5000
4500
4000
3500

2500

X: 1872
Y: 2301

2000
1850

1900

3000

X: 1866
Y: 2323

2500

1950

2000

2050

2100

2150

2000
2250 1850

2200

1900

1950

2000

Makespan/min

2050

2100

2150

2200

2250

Makespan/min

Figure 9. Minimum idle time

Figure 10. Minimum makespan

worker

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Seru

3

2

1

1

3

1

2

2

1

1

3

2

2

1

3

Figure 11. The worker assignment decision
Table 3. Data about products
XX
XXX product
1
XXX
Seru
XX
1
–
2
–
95
3

2

3

4

5

6

7

8

100
–
–

–
–
130 –
– 105

80
–
40

–
116
29

50
–
–

115
–
–

1 The ‘–’ means that the product is not allocated to the seru.

Table 4. Production timetable
Product
1
2
3
4
5
Seru
3
1
2
3
1
Starting time
Monday 8:00
Monday 8:00
Monday 8:00
Tuesday 9:13
Tuesday10:22
Tuesday 10:17 Wednesday 11:30 Wednesday 15:54 Tuesday 16:09
Finishing time Tuesday 9:07
Product
5
6
6
7
8
Seru
3
2
3
1
1
Starting time Wednesday 15:59 Wednesday 11:36 Thursday 9:25
Tuesday 16:13 Thursday 8:05
Finishing time Thursday 9:19
Thursday 17:12 Thursday 16:29
Thursday 8:04 Thursday 17:07

Apart from the detailed result illustrated above, other results of 10 repeated runs
for this example are listed in Table 5.
5.3. Comparison with GA-GA algorithm. To better analyse the effectivenessof the SA-GA algorithm, a GA-GA algorithm which solve upper and lower level
model all by genetic algorithm is designed and the results of the two algorithms arecompared.

20

LAN LUO, ZHE ZHANG AND YONG YIN

4min

5min

Seru 12(616.67min)

5(226.67min)

2400min

1min

7(591.67min)

8(421.67min)

1866.67min

6min

Seru 23(1170min)

6(696min)

5min

6min

Seru 31(546.25min)

1872min

6min

4(761.25min)

5(200min)6(304.5min)

Note: product 1

product 2

product 3

product 4

product 5

product 6

product 7

product 8

1829minFigure 12. Loading results
Table 5. Results of the small case
No.
1
2
3
4
5
6
7
8
9
10
AverageSD

Idle time (min) Makespan (min) CPU time (s)2381.71910
8242.52629.4
1907.88193.52438.6
1932.38222.2
2446
1936
8228
2723.1
1933
8228.62022.3
1893
8064.82461.2
1895
8095.22300
1906.38098.52819
1859.58051.92566.8
1874.18135
2478.811904.78156.02214.16
24.07
70.94

The numerical example used to test the GA-GA algorithm is the same caseabove, and the parameter of GEN is set to 110 which is the same as the iteration
number of SA in this example and the parameter of pop size is set to be 20 whichequals to the number of neighbors in SA for each iteration. After ten runs for GAGA algorithm, we can get that the average and SD CPU time are 8353.08 (s) and
278.59 (s), where both of them are larger than SA-GA’s result. Hence, it can beconcluded that SA-GA algorithm has faster calculation than GA-GA. The resultsof ten runs by GA-GA algorithm are listed in Table 6.
5.4. Test on the large case. To show the superiority of SA-GA algorithm, a largecase which contains 20 products, 10 serus and 50 workers are tested. In this largecase, the workers’ processing time for each product is listed in Table. 7, and the
setup time and demand of each product is shown in Table. 8. The other data is thesame as the small case above.
The parameter settings of large case are the same as those of small case in Table
1, which is also based on various tests. The results of five runs are shown in Table

BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

21

Table 6. Results of GA-GA algorithm for small case
No.
1
2
3
4
5
6
7
8
9
10
AverageSD

Idle time (min) Makespan (min) CPU time (s)2519.5
1913.88220.8nonconvergent
2384.41851.88278.82375.6
1898.38230.3
nonconvergent
2409.5
1829
8284.82882
1894.29085.22213.2
1941.38244.52526
1941
8190.92526.91918
8289.32479.64
1898.438353.08
181.5537.55
278.598, which verified the designed SA-GA algorithm are also adapt to the large case.
In addition, the average CPU time only takes 7859.98s more than the small caseabove, so the scalability of the SA-GA algorithm in this paper are also proved.
6. Conclusions and further research. This paper studies a seru loading problem with worker assignment. The worker assignment is decided before the productallocation. Considering the hierarchy of decision-making, a bi-level model is proposed for this problem. In the upper level model, a best worker assignment should
be decided to minimize the total idle time, while the aim of the lower model is tofind best product allocation to minimize the total makespan under the certain worker assignment decided by upper level model. Then, a SA-GA algorithm is designed
for solving this model. The SA is for upper level model and GA is for lower level
model. The model and SA-GA algorithm are tested by a small case and a largecase, and the results show that the SA-GA algorithm has good scalability. Finally,
comparison with GA-GA algorithm is also presented to prove the superiority of
SA-GA algorithm.
Future research should concentrate on developing more efficient and scalable
algorithms. Although SA and GA are all effective meta-heuristic methods for combinatorial optimization problem, the GA will be called repeatedly while solving
upper level programming by SA, which contributes to an increase in computation
time. Hence, it is of great significance to introduce other mathematical methods
for solving this MIP and bi-level problem. The mathematical feature of the bi-level
model should be carefully examined for developing the algorithm. Besides, considering the complexity of decision-making in practical production and the conflictsof different decision goals, the multi-objective model should also be introduced toseru loading problem, as well as the multilevel programming. What’s more, studies
on seru loading problems in other seru types like divisional serus and yatais should
also be carried out. Lastly, software development for real application scenario is
supposed to be taken into account based on this research.
REFERENCES[1] A. Aboelfotoh, G. A. Süer and M. Abdullah, Selection of Assembly Systems; Assembly Lines
vs. Seru Systems, Procedia Computer Science, 140 (2018), 351-358.

22

LAN LUO, ZHE ZHANG AND YONG YIN

Table 7. Workers’ processing time for each productWorker
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50

Workers’ processing time for each product (min)1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
22 39 47 29 – 34 64 23 50 71 20 21 11 32 39 15 20 27 29 24
23 37 47 29 20 35 54 21 55 77 24 20 12 30 38 19 21 21 26 20
22 38 46 – 22 35 50 26 56 77 24 15 11 34 43 – 17 23 29 21– 37 46 32 – 35 56 – 50 78 22 19 12 34 42 17 21 21 25 23
23 40 47 27 – 34 59 20 50 81 – 17 10 34 42 15 17 22 28 –22 38 47 29 23 33 61 25 – – 21 20 10 32 39 18 17 27 28 21
21 37 – 28 19 32 59 – 52 73 23 21 11 30 35 16 22 22 25 19
23 38 49 27 18 – – 22 48 78 21 20 10 31 44 18 – 23 26 22
21 40 50 – 21 33 56 26 53 87 – 18 10 32 40 17 22 21 27 20
24 – 49 28 19 38 58 26 52 – 24 18 10 37 41 – 17 25 26 23
22 38 47 30 18 33 61 27 53 77 21 19 – 33 41 – 19 21 29 23
23 36 49 29 21 34 57 22 53 86 21 20 10 33 36 17 21 21 27 24
23 39 47 29 22 – 65 21 53 86 22 19 12 30 38 15 19 22 27 21
23 39 – 31 18 30 50 29 57 85 24 – 10 37 36 19 21 27 27 21
21 36 49 30 – 36 59 24 50 81 24 17 11 37 35 18 19 26 26 22
25 36 49 31 19 37 58 22 54 82 24 19 12 39 39 17 18 23 29 22– 37 45 30 22 38 60 23 55 – 21 18 – 37 44 – 21 22 27 –23 37 49 31 21 37 61 – 48 – 21 21 12 34 – 17 17 – 26 20
21 35 48 – 19 37 61 28 48 69 20 19 10 33 36 18 22 25 25 20
21 38 – 30 23 32 55 29 53 72 22 16 10 – 35 16 17 21 29 23
21 36 50 30 22 35 64 29 53 86 22 17 11 39 – 17 18 24 26 23
22 38 50 29 – 33 61 22 48 69 23 17 11 40 – 15 – 22 28 21
25 39 47 29 19 37 59 26 – – 24 16 12 39 – 17 22 25 25 23
20 37 49 29 22 30 62 22 47 71 21 18 12 40 42 19 21 27 25 21
23 39 47 30 21 38 63 – 55 – 23 15 11 31 38 19 22 27 27 24– 37 – 32 23 32 58 28 50 72 24 16 11 32 44 17 19 22 25 –24 37 49 30 22 – 56 30 51 78 24 19 11 34 40 – 19 – 29 21
24 39 47 – 18 37 – 24 47 85 23 16 10 39 35 17 22 20 26 20
25 – 47 29 19 36 54 20 49 79 24 16 11 35 41 18 – 23 25 –20 37 47 28 22 40 51 22 51 78 – 21 11 37 39 16 18 – 25 –23 38 48 29 19 35 53 20 56 72 22 16 11 – 37 16 20 25 25 20
23 36 45 29 – 37 63 29 50 79 20 16 11 37 – 18 21 27 29 25
23 38 47 30 23 40 59 26 56 78 23 18 11 41 40 – 21 22 – 23
21 35 50 27 23 38 65 22 47 71 24 16 10 38 36 16 20 27 27 24
20 35 48 32 21 33 61 25 – – 21 21 10 38 – 19 18 24 29 19– 38 45 30 19 31 63 24 56 85 23 – 10 41 37 19 19 24 26 21
24 36 – 30 22 38 55 24 50 87 23 19 12 – 39 17 20 26 – 25
24 39 49 32 21 37 52 – – 71 24 19 12 35 38 15 19 23 25 22
21 39 49 31 19 35 57 29 55 77 21 19 11 40 43 15 19 – 28 19
25 35 47 30 20 34 59 25 48 72 23 – 10 41 35 18 20 20 26 18
22 36 48 32 20 – 55 25 49 71 23 19 12 31 43 17 19 22 26 24
23 39 47 27 19 39 64 24 53 74 24 21 12 32 – 19 18 – 29 22
23 36 46 32 20 35 – 21 55 80 21 16 12 32 40 18 20 23 26 22– – 45 31 22 37 52 – 57 72 22 16 11 37 – 18 22 20 27 24
20 40 47 29 21 32 52 29 55 82 21 15 10 33 – 16 20 27 – 19
20 40 – 30 20 38 58 23 50 82 23 20 11 31 38 19 – – 25 19
23 39 49 – 21 39 61 25 – 78 24 19 11 38 39 17 22 27 27 25
22 38 49 28 18 33 – 25 49 74 23 18 12 30 43 16 20 21 29 –20 39 47 29 21 – 60 22 52 81 23 21 12 30 40 16 20 24 25 19
22 – 47 28 20 32 64 27 49 77 – 18 10 33 37 17 20 20 25 24

1 The ‘–’ means that the worker cannot produce the product.

BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

23

Table 8. Setup time and demand of products
Product
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Setup time (min) 4 9 8 6 5 6 4 1 10 12 24 2 5 7 11 3 15 4 2 7Demand14510713410514014511587 14512612515011810675 80 13283 65 89
Table 9. Results of large case
No.
1
2
3
4
5
AverageSD

Idle time (min) Makespan (min) CPU time (s)5587.3
1932
16236
5457.41848.3016376
5164.91865.416221
5258.91919
15754
5757.21806
15743
5445.14
1874.1416066
214.9246.36
264.84[2] S. Akino, Internationalization of Japanese company and change of production system, (Japanese), Rikkyo Economic Review, 51 (1997), 29-55.
[3] C. Babayigit, G. A. Süer, Cell loading to minimize the number of tardy jobs subject to the
manpower restriction, Proceedings of Group Technology/Cellular Manufacturing Symposium
OH, USA, 2003.
[4] B. Behnia, I. Mahdavi, B. Shirazi, M. M. Paydar, A bi-level mathematical programmingfor cell formation problem considering workers interest, International Journal of Industrial
Engineering & Production Research, 28 (2017), 267-277.
[5] S. Treville, M. Ketokivi, V. Singhal, Competitive manufacturing in a high-cost environment:
introduction to the special issue, Journal of Operations Management, 49-51 (2017), 1-5.
[6] D&M Nikkei Mechanical. The Challenge of Canon-Part 3, D&M Nikkei Mechanical, 588(2003), 70-73.
[7] X. Han, Z. Zhang and Y. Yin, ”Reliability Analysis for a Divisional Seru Production Systemwith Stochastic Capacity,” 2018 IEEE International Conference on Industrial Engineeringand Engineering Management (IEEM), Bangkok, (2018), 710-714.
[8] X. Han, Z. Zhang and Y. Yin, Reliability-oriented multi-resource allocation for seru production system with stochastic capacity, International Journal of Manufacturing Research,(2019), inpress.
[9] W. M. Han, J. Chen, X. Z. Bu, Batch splitting activity in scheduling of virtual cell withcapacity constraints based on bi-level mathematical model, Applied Mechanics & Materials,
263-266 (2013), 1257-1264.
[10] P. Hansen, B. Jaumard and G. Savard, New branch-and-bound rules for linear bilevel programming, SIAM Journal on Scientific & Statistical Computing, 13 (1992), 1194-1217.
[11] Sakamaki Hisashi . The Change of Consciousness and Company by Cellular Manufacturing
in Canon Way, (Japanese), Tokyo: JMAM, 2006.
[12] J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis With
Applications to Biology, Control, and Artificial Intelligence, Quarterly Review of Biology, 6(1975), 126-137.
[13] C. J. Hsu, W. H. Kuo and D. L. Yang, Unrelated parallel machine scheduling with pastsequence-dependent setup time and learning effects, Applied Mathematical Modeling, 35(2010), 1492-1496.
[14] R. H. Huang and T. H. Yu, An effective ant colony optimization algorithm for multi-objective
job-shop scheduling with equal-size lot-splitting, Applied Soft Computing., 57 (2017), 642-656.
[15] H. Iwamuro, An easy book about seru production, (Japanese), Nikkan Kogyo Shimbun Tokyo,
2004.
[16] R. G. Jeroslow, The polynomial hierarchy and a simple model for competitive analysis, Mathematical Programming, 32 (1985), 146-164.

24

LAN LUO, ZHE ZHANG AND YONG YIN[17] J. Jones and T. Soule, Comparing genetic robustness in generational vs. steady state evolutionary algorithms. In Proceedings of the 8th annual conference on genetic and evolutionary
computation, ACM (2006), 143-150.
[18] R. M. Karp, Reducibility among combinatorial problems, Complexity of Computer Computations Now York: Plenum, (1972), 85-103.
[19] C. Kasemset and V. Kachitvichyanukul, Bi-level multi-objective mathematical model for jobshop scheduling: the application of theory of constraints, International Journal of Production
Research, 48 (2010), 6137-6154.
[20] C. Kasemset and V. Kachitvichyanukul, A PSO-based procedure for a bi-level multi-objective
TOC-based job-shop scheduling problem, International Journal of Operational Research, 14(2012), 50-69.
[21] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by simulated annealing, Science,
220 (1983), 671-680.
[22] Jie Lian, ChenGuang Liu, WenJuan Li, Yong Yin, A multi-skilled worker assignment problem
in seru production systems considering the worker heterogeneity, Computers & Industrial
Engineering, 118 (2018), 366-382,[23] C. G. Liu, F. Dang, W. J. Li, J. Lian, S. Evans and Y. Yin, Production planning of multistage multi-option seru production systems with sustainable measures, Journal of Cleaner
Production, 105 (2014), 285-299.
[24] C. G. Liu, J. Lian, Y. Yin and W. J. Li, Seru seisan-an innovation of the production management mode in Japan, Asian Journal of Technology Innovation, 18 (2010), 89-113.
[25] C. G. Liu, K. E. Stecke, J. Lian and Y. Yin, An implementation framework for seru production, International Transactions in Operational Research, 21 (2014), 1-19.
[26] C. G. Liu, N. Yang, W. J. Li, J. Lian, S. Evans and Y. Yin, Training and assignment ofmulti-skilled workers for implementing seru production systems, The International Journalof Advanced Manufacturing Technology, 69 (2013), 937-959.
[27] C. Low, C. M. Hsu, K. I. Huang, Benefits of lot splitting in job-shop scheduling, The International Journal of Advanced Manufacturing Technology, 24 (2004), 773-780.
[28] H. Luo, A. Zhang, G. Q. Huang, Active scheduling for hybrid flowshop with family setup timeand inconsistent family formation, Journal of Intelligent Manufacturing, 26 (2015), 169-187.
[29] L. Luo, Z. Zhang and Y. Yin, Modelling and numerical analysis ofseru loading problem under
uncertainty, European J of Industrial Engineering, 11 (2017), 185-204.
[30] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Equationof state calculations by fast computing machines, Journal of Chemical Physics, 21 (1953),
1087-1092.
[31] Z. Michalewicz, Genetic Algorithm + Data Structure = Evolution Programs”, 3rd edition,
Springer-Verlag New York, 1996.
[32] D. I. Miyake, The shift from belt conveyor line to work-cell based assembly systems to copewith increasing demand variation in Japanese industries, International Journal of Automotive
Technology and Management, 6 (2006), 419C439.
[33] J. Pei, X. Liu, P. M. Pardalos, A. Migdalas and S. Yang, Serial-batching scheduling with timedependent setup time and effects of deterioration and learning on a single-machine, Journalof Global Optimization, 67 (2017), 1-12.
[34] A. Roth, J. Singhal, K. Singhal and C. S. Tang, Knowledge creation and dissemination in operations and supply chain management, Production and Operations Management, 25 (2016),
1473-1488.
[35] Y. Sakazume, Is Japanese Cell Manufacturing a New System? : A Comparative Study between Japanese Cell Manufacturing and Cellular Manufacturing, Journal of Japan Industrial
Management Association, 55 (2005), 341-349.
[36] H. Sakamaki, The Change of Consciousness and Company by Cellular Manufacturing inCanon Way, (Japanese), Japan Management AssociationManagement Center Tokyo, 2006.
[37] L. M. Shao, Z. Zhang and Y. Yin, A bi-objective combination optimisation model for line-seru
conversion based on queuing theory, International Journal of Manufacturing Research, 11(2016), 322-338.
[38] A. Sinha, P. Malo and K. Deb, A review on bilevel optimization: from classical to evolutionary
approaches and applications, IEEE Transactions on Evolutionary Computation, 22 (2018),
276-295.
[39] K. E. Stecke, Y. Yin, I. Kaku and Y. Murase, Seru: the organizational extension of JIT for a
super-talent factory, International Journal of Strategic Decision Sciences, 3 (2012), 105-118.

BI-LEVEL SERU LOADING PROBLEM WITH WORKER ASSIGNMENT

25[40] G. A. Süer and C. Dagli, Intra-cell manpower transfers and cell loading in labor-intensive
manufacturing cells, Computers & Industrial Engineering, 48 (2005), 643-655.
[41] W. Sun, Y. Wu, Q. Lou and Y. Yu, A Cooperative Coevolution Algorithm for the Seru
Production With Minimizing Makespan, IEEE Access, 7 (2019), 5662-5670.
[42] W. Sun, Y. Yu, J. W. Wang, Reducing the total tardiness by Seru Production: Model, exact
and cooperative coevolution solutions, International Journal of Production Research, in press.
[43] J. Tao, , Z. Chao and Y. Xi, A semi-online algorithm and its competitive analysis for asingle machine scheduling problem with bounded processing times, Journal of Industrial andManagement Optimization, 6 (2010), 269-282.
[44] L. Vicente, G. Savard and J. Judice, Descent approaches for quadratic bilevel programming,
Journal of Optimization Theory and Applications, 81 (1994), 379 - 399.
[45] Not only Toyota-Miraculous Canon Manufacturing System, (Japanese), Weekly Toyo Keizen,
2003.
[46] Y. Wang, J. F. Tang, Cost and service-level-based model for a seru production system formation problem with uncertain demand, Journal of Systems Science and Systems Engineering,27 (2018), 519C537.
[47] X. Yang, D. Qiu and J. Shen, Solving bi-level programming problem based onelectromagnetism-like algorithm, Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering (2013), 923-927.
[48] Y. Yin, K. E. Stecke and I. Kaku, The evolution of seru production systems throughout
canon, Operations Management Education Review, 2 (2008), 27-40.
[49] Y. Yin, K. E. Stecke, M. Li and I. Kaku, Prospering in a volatile market: Meeting uncertain
demand with seru, Working paper, Yamagata University, 2011.
[50] Y. Yin, T. C. E. Cheng, J. Xu, S. R. Cheng and C. C. Wu, (2013). Single-machine schedulingwith past-sequence-dependent delivery times and a linear deterioration, Journal of Industrial
and Management Optimization, 9 (2013), 323-339.
[51] Y. Yin, K. E. Stecke, M. Swink and I. Kaku, Lessons from seru, production on manufacturing
competitively in a high cost environment, Journal of Operations Management, 49-51 (2017),
67-76.
[52] Y. Yin, K. E. Stecke and D. Li, The evolution of production systems from Industry 2.0 throughIndustry 4.0, International Journal of Production Research, 56 (2018), 848-861.
[53] K. C. Ying and Y. J. Tsai, Minimising total cost for training and assigning multiskilled workers
in seru production systems, International Journal of Production Research, 55 (2017), 29782989.
[54] Y. Yu, J. Tang, J. Gong, Y. Yin and I. Kaku, Mathematical analysis and solutions for multiobjective line-cell conversion problem, European Journal of Operational Research, 236 (2014),
774-786.
[55] Y. Yu, W. Sun, J. Tang, I. Kaku and J. W. Wang, Line-seru conversion towards reducing
worker(s) without increasing makespan: models, exact and meta-heuristic solutions, International Journal of Production Research, 55 (2017), 2990-3007.
[56] Y. Yu, W. Sun, J. Tang, J. Wang, Line-hybrid seru system conversion, Computers & Industrial
Engineering, 103 (2017), 282-299.
[57] Y. Yu, J. W. Wang, K. Ma, W. Sun, Seru system balancing: Definition, formulation, andsolution, Computers & Industrial Engineering, 122 (2018), 318C325.
[58] Y. Yu , J. F. Tang, Review of seru production, Frontiers of Engineering Management, 6(2019), 183-192.
[59] X. L. Zhang, C. G. Liu, W. J. Li, S. Evans and Y. Yin, Effects of key enabling technologies
for seru production on sustainable performance, Omega, 66 (2017), 290-307.
[60] Z. Zhang and J. Xu, Bi-level multiple mode resource-constrained project scheduling problems
under hybrid uncertainty, Journal of Industrial & Management Optimization, 12 (2016),
565-593.
[61] Z. Zhang, J. Xu, H. Yang and Y. Wang, Bi-level optimization of resource-constrained multiple
project scheduling problems in hydropower station construction under uncertainty, Scientia
Iranica A, 22 (2014), 650-667.
[62] Z. Zhang, L. Shao, and Y. Yin, PSO-based algorithm for solving lot splitting in unbalanced seru production systems, International Journal of Industrial and Systems Engineering,(2019), inpress.

26

LAN LUO, ZHE ZHANG AND YONG YIN[63] C. Zhao, Y. Yin, T. C. E. Cheng and C. C. Wu, Single-machine scheduling and due dateassignment with rejection and position-dependent processing times, Journal of Industrial
and Management Optimization, 10 (2014), 691-700.
[64] P. Zwierzyski and H. Ahmad, Seru production as an alternative to a traditional assembly
line, Engineering Management in Production and Services, 10 (2018), 62-69.

Appendix. Further Reading – Recent Papers on Seru Production Systems
Abdullah, M. (2018). Impact of Skill: Seru vs Classical Assembly Line (Doctoral dissertation, Ohio
University).
Beber, J. (2019). Seru production system: Assembly cells implementation in a house appliancefactory. Journal of Lean Systems, 4(3), 23-43.
Han, X., Zhang, Z., & Yin, Y. (2018, December). Reliability Analysis for a Divisional Seru Production
System with Stochastic Capacity. In 2018 IEEE International Conference on Industrial Engineeringand Engineering Management (IEEM) (pp. 710-714). IEEE.
Kaku,

I.

(2016).

A Fundamental

Positive

Investigation

intoJapanese

Seru

Production

Systems. IFAC-PapersOnLine, 49(12), 337-342.
Kaku, I. (2017). Is Seru a Sustainable Manufacturing System?. Procedia Manufacturing, 8, 723-730.
Kaku, I., Zhang, X., & Yin, Y. (2017). DESCRIPTION AND EVALUATION OF SERU PRODUCTIONSYSTEM WITH SF SCHEME. DEStech Transactions on Engineering and Technology Research,(icpr).
Li, X., Li, D., Wu, X., Zheng, H., & Yin, Y. (2017, June). A cooperative co-evolution approach for aline-seru conversion problem. In 2017 IEEE Congress on Evolutionary Computation (CEC) (pp.
1406-1411). IEEE.
Lian, J., Liu, C., Li, W., & Yin, Y. (2018). A multi-skilled worker assignment problem in seru production
systems considering the worker heterogeneity. Computers & Industrial Engineering, 118, 366-382.
Liu, C., Dang, F., Li, W., Lian, J., Evans, S., & Yin, Y. (2015). Production planning of multi-stage
multi-option

seru

production

systemswithsustainablemeasures. Journalof

Cleaner

Production, 105, 285-299.
Liu, C., Li, W., Lian, J., & Yin, Y. (2012). Reconfiguration of assembly systems: From conveyor
assembly line to serus. Journal of Manufacturing Systems, 31(3), 312-325.
Liu, C., Stecke, K. E., Lian, J., & Yin, Y. (2014). An implementation framework for seru
production. International Transactions in Operational Research, 21(1), 1-19.
Liu, C., Yang, N., Li, W., Lian, J., Evans, S., & Yin, Y. (2013). Training and assignment of multi-skilledworkers for implementing seru production systems. The International Journal of Advanced
Manufacturing Technology, 69(5-8), 937-959.
Luo, L., Zhang, Z., & Yin, Y. (2016, December). Seru loading with worker-operation assignment insingle period. In 2016 IEEE International Conference on Industrial Engineering and Engineering
Management (IEEM) (pp. 1055-1058). IEEE.
Luo, L., Zhang, Z., & Yin, Y. (2017). Modelling and numerical analysis of seru loading problem under
uncertainty. European Journal of Industrial Engineering, 11(2), 185-204.
Manupati, V. K., Deepthi, T. V., Ramakotaiah, K., & Rao, S. S. (2015, March). Reconfiguration of
Networked seru production systems in an Indian Perspective. In 2015 International Conference on
Industrial Engineering and Operations Management (IEOM) (pp. 1-7). IEEE.
Ren, H., & Wang, D. (2019). Analysis of the Effect of the Line-Seru Conversion on the Waiting Timewith Batch Arrival. Mathematical Problems in Engineering, 2019.
Shao, L., Zhang, Z., & Yin, Y. (2016). A bi-objective combination optimisation model for line-seru
conversion based on queuing theory. International Journal of Manufacturing Research, 11(4),322-338.
Shao, L., Zhang, Z., & Yin, Y. (2017). Production System Performance Improvement by AssemblyLine-seru Conversion. In Proceedings of the Tenth International Conference on Management
Science and Engineering Management (pp. 1165-1180). Springer, Singapore.
Singh, S. (2017, July). A study on seru production system. In 3rd International Conference on
Emerging

Technologies

inEngineering,

Biomedical,

Management

andScience[3rd

ETEBMS-2017] (Vol. 9).
Sun, W., Li, Q., Huo, C., Yu, Y., & Ma, K. (2016). Formulations, features of solution space, andalgorithms for line-pure seru system conversion. Mathematical Problems in Engineering, 2016.
Sun, W., Wu, Y., Lou, Q., & Yu, Y. (2019). A cooperative coevolution algorithm for the seru production
with minimizing makespan. IEEE Access, 7, 5662-5670.
Villa, A., & Taurino, T. (2013). From JIT to Seru, for a production as lean as possible. Procedia
Engineering, 63, 956-965.
Wang, J., Liu, H., Qu, P., & Yin, Y. (2013). Design and operations of seru manufacturing: case study.
In The 6th PSU-UNS International Conference on Engineering and Technology (ICET-2013) (pp.
15-17).
Wang, Y., & Tang, J. (2017, June). Multi-objective optimization model for seru production systemformation under uncertain condition. In 2017 International Conference on Service Systems andService Management (pp. 1-6). IEEE.

Wang, Y., & Tang, J. (2018). Cost and service-level-based model for a seru production systemformation problem with uncertain demand. Journal of Systems Science and Systems
Engineering, 27(4), 519-537.
Wang, Y., & Tang, J. (2018, June). Is full skill the best configuration for seru production system?.
In 2018 Chinese Control And Decision Conference (CCDC) (pp. 3904-3909). IEEE.
Wu, L., Chan, F. T., Niu, B., & Li, L. (2018). Cross-trained worker assignment and comparative analysis
on throughput of divisional and rotating seru. Industrial Management & Data Systems, 118(5),1114-1136.
Yin, Y., Kaku, I., & Liu, C. (2016). Management of overlapped cross-training: with or without asupervisor?. Asian Journal of Management Science and Applications.
Yin, Y., Stecke, K. E., & Li, D. (2018). The evolution of production systems from Industry 2.0 throughIndustry 4.0. International Journal of Production Research, 56(1-2), 848-861.
Yin, Y., Stecke, K. E., Swink, M., & Kaku, I. (2017). Lessons from seru production on manufacturing
competitively in a high cost environment. Journal of Operations Management, 49, 67-76.
Ying, K. C., & Tsai, Y. J. (2017). Minimising total cost for training and assigning multiskilled workers inseru production systems. International Journal of Production Research, 55(10), 2978-2989.
Yu, Y., Gong, J., Tang, J., Yin, Y., & Kaku, I. (2012). How to carry out assembly line–cell conversion? A
discussion based on factor analysis of system performance improvements. International Journal of
Production Research, 50(18), 5259-5280.
Yu, Y., Sun, W., Tang, J., Kaku, I., & Wang, J. (2017). Line-seru conversion towards reducing worker(s) without increasing makespan: models, exact and meta-heuristic solutions. International Journalof Production Research, 55(10), 2990-3007.
Yu, Y., Sun, W., Tang, J., & Wang, J. (2017). Line-hybrid seru system conversion: Models, complexities,
properties, solutions and insights. Computers & Industrial Engineering, 103, 282-299.
Yu, Y., & Tang, J. (2019). Review of seru production. Frontiers of Engineering Management, 6(2),183-192.
Yu, Y., Tang, J., Gong, J., Yin, Y., & Kaku, I. (2014). Mathematical analysis and solutions for
multi-objective line-cell conversion problem. European Journal of Operational Research, 236(2),774-786.
Yu, Y., Tang, J., Sun, W., Yin, Y., & Kaku, I. (2013). Reducing worker (s) by converting assembly line

into a pure cell system. International Journal of Production Economics, 145(2), 799-806.
Yu, Y., Tang, J., Sun, W., Yin, Y., & Kaku, I. (2013). Combining local search into non-dominated sortingfor multi-objective line-cell conversion problem. International Journal of Computer Integrated
Manufacturing, 26(4), 316-326.
Yu, Y., Tang, J., Yin, Y., & Kaku, I. (2015). Comparison of two typical scheduling rules of line-seru
conversion problem. Asian Journal of Management Science and Applications, 2(2), 154-170.
Yu, Y., Wang, J., Ma, K., & Sun, W. (2018). Seru system balancing: Definition, formulation, and exact
solution. Computers & Industrial Engineering, 122, 318-325.
Yu, Y., Wang, S., Tang, J., Kaku, I., & Sun, W. (2016). Complexity of line-seru conversion for different
scheduling

rules

and

two

improved

exact

algorithms

for

the

multi-objective

optimization. SpringerPlus, 5(1), 809.
Zhang, X., Liu, C., Li, W., Evans, S., & Yin, Y. (2017). Effects of key enabling technologies for seru
production on sustainable performance. Omega, 66, 290-307.
Zwierzyński, P., & Ahmad, H. (2018). Seru production as an alternative to a traditional assembly
line. Engineering Management in Production and Services, 10(3), 62-69.
吴旭辉, 杜劭峰, 郝慧慧, 于洋, 殷勇, & 李冬妮. (2018). 一种基于协同进化的流水线向 Seru 系统转化方法. 自动化学报, 44(6), 1015-1027.