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

  • * Corresponding author: Jufeng Wang

    * Corresponding author: Jufeng Wang
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  • 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.

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

    Citation:

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  • Figure 1.  The encode scheme for an example solution

    Figure 2.  Flowchart of the proposed RICA

    Figure 3.  Crossover of country

    Figure 4.  Mutation of country

    Figure 5.  The diagram of the Taguchi experiment

    Figure 6.  Convergence diagram of a typical example

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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)
     | Show Table
    DownLoad: CSV

    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 PROBi1 0.24 0.19 0.30
    Demand D1
    (S=300)
    73
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

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

     | Show Table
    DownLoad: CSV
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