A revised imperialist competition algorithm for cellular manufacturing optimization based on product line design

Chunfeng Liu; Yuanyuan Liu; Jufeng Wang

doi:10.3934/jimo.2021175

Article Contents

2023, Volume 19, Issue 1: 69-104. Doi: 10.3934/jimo.2021175

This issue Previous Article Improved Lagrangian-PPA based prediction correction method for linearly constrained convex optimization Next Article Bounds for spectral radius of nonnegative tensors using matrix-digragh-based approach

A revised imperialist competition algorithm for cellular manufacturing optimization based on product line design

1.
School of Management, Hangzhou Dianzi University, Hangzhou 310018, China
2.
Department of Mathematics, China Jiliang University, Hangzhou 310018, China

^* Corresponding author: Jufeng Wang
^* Corresponding author: Jufeng Wang

Received: February 2021

Revised: August 2021

Early access: October 2021

Published: January 2023

Abstract / Introduction Full Text(HTML) Figure(6) / Table(8) Related Papers Cited by

Abstract

Due to the fierce market competition, enterprises try to satisfy customers' requirements for personalized products in order to maximize profit or market share of their products. This not only needs to determine the product variants through product line design, but also needs to pay attention to resource allocation in the manufacturing process. This paper proposes a cellular manufacturing optimization model that considers the market and production. If the company excessively pursues the satisfaction of customers' personalized needs, the manufacturing time and cost may increase accordingly. Of course, with the restriction of production capacity in manufacturing cells and the expectation of reducing cost, managers cannot design attributes' levels of a product line casually, which may result in its unstable marketing share and profit. Therefore, the product demand influenced by customers' preferences could be a key factor to link market and production. The objective of propose model is to maximize product profit which consists of revenue and miscellaneous costs (material, processing, transportation, final assembly and fixed costs). A revised imperialist competitive algorithm (RICA) is developed to optimize the discrete problem. Extensive numerical experiments and t-test are carried out to verify the effect of this method. The results demonstrate the proficiency of RICA over another imperialist competitive algorithm based method and genetic algorithm in terms of solution quality.

Keywords:

Mathematics Subject Classification: Primary: 90B30, 68W50; Secondary: 90B50.

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Figure 1. The encode scheme for an example solution

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Figure 2. Flowchart of the proposed RICA

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Figure 3. Crossover of country

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Figure 4. Mutation of country

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Figure 5. The diagram of the Taguchi experiment

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Figure 6. Convergence diagram of a typical example

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Table 1. Literature review of research scenario and solution method

Authors	Cell formation	Consumer preference	Product line design	Solution method
Gupta et al. ^[14]	$\surd$	-	-	GAs
Kashan et al. ^[19]	$\surd$	-	-	GBPSO
Kamalakannan and Pandian [17]	$ \surd $	-	-	TS, MGE
Bagheri and Bashiri [6]	$ \surd $	-	-	GICA
Zohrevand et al. [50]	$ \surd $	-	-	TS-GA
Jouzdani et al. [16]	$ \surd $	-	-	SA
Li et al. [24]	$ \surd $	-	-	HHS
Liu et al. [25]	$ \surd $	-	-	DBFA
Zhao [49]	$ \surd $	-	-	Memetic Algorithm
Mehdizadeh et al. [30]	$ \surd $	-	-	MOVDO
Bootaki et al. [8]	$ \surd $	-	-	GA-AUGMECON
Niakan et al. [36]	$ \surd $	-	-	NSGA-II
Liu et al. [26]	$ \surd $	-	-	DICAP
Howard and Sheth [15]	-	$ \surd $	-	Buyer Behavior Theory
Norton [37]	-	$ \surd $	-	Coase Theorem
Cao et al. [9]	-	$ \surd $	-	Ontology-based
Ng and Law [35]	-	$ \surd $	$ \surd $	Fuzzy-ER
Achabou et al. [2]	-	$ \surd $	-	Conjoint Analysis, Cluster Analysis
Agnew and Dargusch [3]	-	$ \surd $	$ \surd $	BWS, DCE
Grasso and Asioli[13]	-	$ \surd $	$ \surd $	DCMs
Michalek et al. [32]	-	$ \surd $	$ \surd $	Conjoint Analysis
Tookanlou and Wong [42]	-	$ \surd $	$ \surd $	Empirical Studies
Tsafarakis et al. [43,44]	-	$ \surd $	$ \surd $	Hybrid PSO, FSTDE
Kuzmanovic et al. [23]	-	$ \surd $	$ \surd $	Conjoint Analysis
This paper	$ \surd $	$ \surd $	$ \surd $	RICA

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Table 2. Attributes and levels of vacuum glass

Component	Attribute	Level
Component 1	Thickness	Thin, thick, superthick
	The shape of the support	Cylindrical, spherical, oval
	Glass shape	Square, circular, rhombic
Component 2	Color	Blue, gray, green
	Light transmission	Transparent, translucent, opaque
	Thermal insulation	General, great, excellent
	Edge banding material	Metallic, plastic, rubber
Component 3	Decoration	Retro, fashion, chinoiserie
	Welding of metallic layer	Metal brazing, gastight welding, laser welding

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Table 3. Preference scores of each attribute

	Attribute1 (A1)			Attribute 2 (A2)			Attribute 3(A3)
	Level₁₁ (L11)	Level₁₂ (L12)	Level₁₃ (L13)	Level₂₁ (L21)	Level₂₂ (L22)	Level₂₃ (L23)	Level₃₁ (L31)	Level₃₂ (L32)	Level₃₃ (L33)
Individual 1	2 (0.20)	3 (0.30)	5 (0.50)	1 (0.13)	4 (0.50)	3 (0.38)	2 (0.18)	5 (0.45)	4 (0.36)
Individual 2	2 (0.33)	3 (0.50)	1 (0.17)	3 (0.33)	4 (0.44)	2 (0.22)	3 (0.30)	4 (0.40)	3 (0.30)
Individual 3	4 (0.36)	2 (0.18)	5 (0.45)	4 (0.44)	3 (0.33)	2 (0.22)	5 (0.56)	1 (0.11)	3 (0.33)

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Table 4. Utility of different products

	A1	A2	A3	Individual 1	Individual 2	Individual 3
Product 1	L13	L23	L31	1.06	0.69	1.23
Competitive product 1	L12	L22	L33	1.16	1.24	0.84
Competitive product 2	L11	L23	L32	1.03	0.95	0.69
Competitive product 3	L13	L22	L31	1.18	0.91	1.34
Probability PROB_i1				0.24	0.19	0.30
Demand D₁ (S=300)					73

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Table 5. Control parameters of RICA

Control parameters	Levels
$ N_{pop} $ (Npop): Number of countries	40, 50, 60
$ N_{imp} $ (Nimp): Number of imperialists	8, 10, 12
$ \xi $ (Xi): Weight coefficient for colony profit	0.1, 0.2, 0.3
$ \rho $ (CORA): Cooling rate	0.6, 0.7, 0.8
$ U $ (UN): The number of times for which the optimal profit remains unchanged	10, 12, 15
$ \varepsilon $ (epsilon): A pre-given threshold	0.0001, 0.0005, 0,001

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Table 6. Parameters of the proposed problem

Parameter	Value	Min	Max
$ M $ : Number of components of each product type (or number of machines in each cell)	3
$ C $ : Number of cells	3
$ A $ : Number of attributes of each product type	9
$ L $ : Number of levels of each attribute	3
$ J $ : Number of company's product types	8
$ J $$ ^{'} $ : Number of competitive product types for each company's product type	5
$ I $ : Number of sample consumers	100
$ S $ : The size of represented population in the market	1000
$ \phi $ : Fixed cost per unit time	3
$ p $$ _{jsa} $ : Price of an attribute's level		10	20
$ h $$ _{jsa} $ : Material cost of an attribute's level		1	3
$ k $$ _{jsa} $ : Processing cost of an attribute's level		1	2
$ {\theta _j} $ : Material handling cost each time		25	40
$ {\Omega _j} $ : Unit assembly cost of each product type		2	5
$ {\tau _{jsa}} $ : Processing time of an attribute's level		3	8
$ \varphi $ : Preference score for an attribute's level		1	5

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Table 7. Performance comparison between RICA, ICASA and GA for impact parameters

$C=6, A=5, L=5$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$M$	6	398720	335469	322124	19	24	130
	12	607478	517620	489546	17	24	203
	18	797091	673714	657481	18	21	353
	24	1010046	860332	819408	17	23	519

$M=14, C=5, L=5$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$A$	3	1371713	1201124	1156277	14	19	308
	6	1000975	863354	829463	16	21	344
	9	963418	837029	796480	15	21	433
	12	978119	831539	791116	18	24	593

$M=12, C=5, A=10$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$L$	3	459945	402027	388192	14	18	176
	10	916115	788887	741580	16	24	283
	17	1343335	1154694	1104538	16	22	418
	24	1601637	1344834	1285988	19	25	819

$M=17, A=7, L=3$		$\mathop {\bar V}\nolimits_{RICA} $	$\mathop {\bar V}\nolimits_{ICASA} $	$\mathop {\bar V}\nolimits_{GA} $	$\mathop {\Delta \bar V}\nolimits_{ICASA}^{RICA} (\%)$	$\mathop {\Delta \bar V}\nolimits_{GA}^{RICA} (\%)$	$CPU$ (s)
$C$	3	1304929	1156539	1111787	13	17	294
	18	1427445	1198392	1155033	19	24	541
	13	1403110	1178416	1137835	19	23	813
	18	1421519	1222470	1173408	16	21	801

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Table 8. Statistical t-test results from SPSS for samples of entries 1-16

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