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Firstly, the characteristics and present situations of the prefabricated construction supply chain are analyzed; inventory cost models for construction material of every phase order, one-off order, and fractionated order are built based on traditional EOQ model and construction supply chain theory. Next, the order decision is represented in binary numbers 0 and 1, in which 0 stands for “no order” and 1 for “order.” The analysis uses the genetic algorithm, sets the objective function, and undergoes testing and assessing the individual fitness function, encoding, decoding, crossover, mutation, and selecting parameter. Moreover, inventory cost of construction supply chain is processed and optimized in Matlab. The research establishes a research paradigm on supply chain management of component manufacturing and materials supply. This study concludes the ordering strategy on construction material, identifies the optimal order points and order batches, and provides recommendations for further research.

Even though supply chain management (SCM) in the manufacturing industry has been widely studied and developed, the application of the same concepts in the construction industry reveals that the problems in construction supply chain (CSC) are extensively present and persistent. Analysis of these problems has shown that a major part originates from the interfaces between the various factors or functions and the complex nature of the construction environment [

The most significant issue for the material purchasing and inventory of a CSC is how to use an optimization model to reduce cost while maintaining the whole supply chain efficiency [

Qiurui et al. researched how to minimize the overall costs of the CSC by CSCO proposed an integrated-operational method. However, CSCO model describes the dynamics between the project owner and the fabrication contractor [

The classical economic order quantity (EOQ) model is at the heart of supply chain optimization and the theory of inventories [

There is significant difference between industrial products and prefabricated components in construction material requirement. The construction material requirement during the construction period consists of subperiods, each corresponding to an ordering strategy, which can refer to the EOQ model [

The supply chain is supplier and demander of a single construction material, and the construction material demander is core party, which is the prefabricated components manufacturer.

During production period of the components, the demand for construction material is uninterrupted.

There are no shortage and no shortage cost of the construction materials after setting up the safety inventory and its order strategy. Thus, the safety inventory will not have significant influence on the overall inventory cost, which means we do not need to take into consideration safety inventory cost.

The order cost includes the handling cost, transportation cost, order cost, and so on, which relates only to the order times by the prefabricated components manufacturer.

The communication between the demander and supplier in the CSC is barrier-free, without hiding or asymmetrical information.

The inventory capacity of the demander and supplier is large enough, and the cost relates only to the unit inventory cost.

The prefabricated components manufacturer can only choose whether or not to order after the production of a kind of component is completed instead of ordering when the production is going on.

The meanings of letters are as follows.

hr is unit inventory holding cost of the manufacturer during the producing period.

HCr is total inventory cost of the manufacturer during the producing period.

hs is unit inventory holding cost of the construction material supplier.

HCs are total inventory cost of the construction material supplier.

TC is total inventory cost of the supplier and demander in the CSC.

Total inventory cost of the supplier and demander for every phase order equals total inventory cost of the demander for every phase order adds total inventory cost of the supplier for every delivery; that is,

Figure

Chart of inventory changes of the prefabricated components manufacturer (every phase order).

The demand for the construction materials for each period and the average inventory in each period are as shown below.

The demand for the construction materials in the

Based on the experience of manufacturing supply, the production rate and demand of the construction materials for the construction material supplier for each period are explicit. Taking into account lead time and Figure

Chart of inventory changes of the construction material supplier (every phase order).

The production rate of the construction material supplier is

Under inventory management mode, total inventory cost of the construction materials in the CSC is as follows.

Every phase order is an extreme situation, and one-off order is another extreme situation which we need to consider. In this situation, all construction materials are ordered only once. The inventory cost in this situation is reduced to zero and only one-off order cost needs to be considered. For the construction material supplier in the CSC, all construction materials are produced only once. Similar to every phase order mentioned before, the total demand of the construction materials for one-off order is

The characteristics of change in inventory for the prefabricated components manufacturer for one-off order are shown in Figure

Inventory changes for the prefabricated components manufacturer (one-off order).

Then, the inventory holding cost for the prefabricated components manufacturer throughout the period is

Based on production and supply experience, the production rate of the construction materials is known as

Inventory change for the construction material supplier (one-off order).

In this order model, the construction material supplier in the CSC needs to supply only once, so the material needs to produce once. The total production of the construction materials is

The inventory cost for the construction material supplier throughout the period is

The total inventory cost of the construction materials under inventory management mode is

The above two models are two extreme cases of some main construction materials with unstable demand in the CSC, namely, one-off order and every phase order strategies throughout the period. For the inventory in the CSC, such order strategy and inventory management mode are unable to achieve the lowest-cost in most cases.

In general, the order strategy is an integrated decision considering multiple phases, which takes full advantage of the transportation, construction, and storage conditions. The fractionated order means the indentors combine several construction stages to order materials at specific time. The decision of order times and order selection mode is made based on personal experience of indentor and the inventory status of the construction materials. The assumptions of order model mentioned previously still apply, and the only differences are as follows.

Figure

Inventory change for the prefabricated components manufacturer (fractionated order).

The demand for some main construction material is different for the prefabricated components manufacturer during

The inventory holding cost for the prefabricated components manufacturer throughout the period is

The production rate of the construction material supplier is

Change in inventory for the construction material supplier (fractionated order).

The inventory cost for the construction material supplier throughout the period is

Total inventory cost of the construction materials in the CSC under inventory management mode is

To make the model more suitable for the analysis of inventory cost, the demand for construction materials should be treated as uniform and continuous. Bortolini et al. choose to use the 4D model to deal with the continuity and uniformity of the construction materials demand [

The choice of an appropriate algorithm is the core problem for the analysis of inventory cost. The genetic algorithm is a kind of multipoint searching algorithm, which is more likely to obtain a global optimal solution [

Take the order point of the construction materials as a variable. To ensure that the

One key problem is to express the objective function using the Matlab language because it is different from

Fitness function describes the quality of each individual created by the genetic algorithm. Its value is subsequently used to determine the probability that each individual will be copied to next generation (a genetic operator of the selection) [

There are many categories of fitness function values; the size of fitness function value determines the probability of the descendant moving to the next generation. When analyzing the practical problems, the analyzer must first define the category of the objective function and then transform the objective function into the fitness function.

In method 1, the objective function

In method 2, the objective function needs to be transformed to calculate the minimum value.

The selecting operator is set based on the individual fitness function value. This paper adopts the roulette method. By determining a threshold, the individuals above the threshold move into the next descendant individual for operation, and the individuals under the threshold are eliminated, and the calculated ratio of the fitness function is the threshold value. For example, if the total population size is

To solve the problems of minimum inventory cost of the construction materials, the fitness function is

The processes of inheritance and variation are to change all binary numbers, so before entering the next cycle, the numbers of the first column and the last column are not 1. Transformation of 1 needs to be forced again on the first column and the last column when calculating the built-in population; namely,

The probability of mutation operation in the genetic algorithm is quite low. The solving efficiency for local operation is good due to a small number of variation points. Importing mutation operator plays an important role in optimal solution convergence. Small probability value can effectively avoid the big shortcoming of genetic algorithm which is immature convergence. The crossover operation ensures the global search ability of the genetic algorithm in the entire solution region while the mutation operator ensures the search ability of the genetic algorithm in the local solution region. The two complemented each other and coordinated with each other until the mutation operator reaches the optimal value of the entire region. The two are closely related; thus the parameters need to be adjusted to make them coordinate perfectly.

Parameter selection of the genetic algorithm is key to solving the whole model correctly. There are four basic parameters in the genetic algorithm, namely, chromosome length, population size, crossover probability, and the mutation probability of the genetic algorithm [

The following four operating parameters of the genetic algorithm need to be preset, namely, NIND, MAXGEN, Pc, and Pm.

NIND is preset as the size of the genetic algorithm population, and the data selection range is 10–200. The operation time will increase significantly if the data selection range is too large while the operation is not universal if the data selection range is too small and the results may be limited to a small range.

MAXGEN is preset as the evolutionary operation generations of the genetic algorithm, which is the operator operation times and the range of data selection is 100–600.

The operator is selected by the roulette method.

For a prefabricated component, the reinforcement requirements are shown in Table

Reinforcement demand of a prefabricated component.

Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Demand ( |
50 | 20 | 60 | 0 | 30 | 20 | 70 | 35 | 53 | 74 | 59 | 22 | 43 | 44 | 24 | 58 | 22 | 52 | 37 | 48 | 0 | 48 | 52 | 35 |

Time ( |
1–3 | 3-4 | 4–8 | 8-9 | 9-10 | 10–13 | 13–15 | 15-16 | 16–18 | 18–21 | 21–24 | 24-25 | 25–28 | 28–30 | 30-31 | 31–34 | 34-35 | 35–38 | 38–40 | 40–43 | 43-44 | 44–47 | 47–50 | 50–52 |

Duration ( |
2 | 1 | 4 | 1 | 1 | 3 | 2 | 1 | 2 | 3 | 3 | 1 | 3 | 2 | 1 | 3 | 1 | 3 | 2 | 3 | 1 | 3 | 3 | 2 |

The reinforcement will be supplied when they are used up in every period.

The inventory holding cost for the reinforcement demander throughout the period is

The order cost for the reinforcement demander throughout the period is

The inventory cost for the reinforcement supplier throughout the period is

The inventory cost of the reinforcement in the whole CSC under this order model is 1,431,896 yuan.

The reinforcement will be supplied only once for all periods.

The inventory holding cost for the reinforcement demander throughout the period is

The order cost for the reinforcement demander throughout the period is

The inventory cost for the reinforcement supplier throughout the period is

The inventory cost of the reinforcement in the whole CSC under this order model is 963,035 yuan.

The reinforcement will be supplied as fractionated for all periods.

Substitute the following data into the inventory cost model of the construction materials in the CSC; namely,

Each operation involves 20

From the first operation, the following conclusions are concluded:

The meaning of the above binary code is as follows:

The reinforcement of the 1st, 2nd, and 3rd periods is ordered before the 1st period.

The reinforcement of the 4th and 5th periods is ordered before the 4th period.

The reinforcement of the 6th period is ordered before the 6th period.

The reinforcement of the 7th and 8th periods is ordered before the 7th period.

The reinforcement of the 9th and 10th periods is ordered before the 7th period.

The reinforcement of the 11th period is ordered before the 11th period.

The reinforcement of the 12th period is ordered before the 12th period.

The reinforcement of the 13th period is ordered before the 13th period.

The reinforcement of the 14th and 15th periods is ordered before the 14th period.

The reinforcement of the 16th, 17th, 18th, and 19th periods is ordered before the 16th period.

The reinforcement of the 20th period is ordered before the 20th period.

The reinforcement of the 21st and 22nd periods is ordered before the 21st period.

The reinforcement of the 23rd period is ordered before the 23rd period.

The reinforcement of the 24th period is ordered before the 24th period.

The diagram of performance tracing of the genetic algorithm visually reflects the continuous optimization of the subgeneration individuals in the process of reaction software operation, and the diagram of performance tracing of the first operation is shown in Figure

Diagram of performance tracing of the genetic algorithm.

The solid line in the diagram shows that the minimum value appeared at the 30th generation in this operation, which is consistent with the result in 605th generation. The average value of the objective function in this operation is stable since the 130th generation, as shown by the dotted line.

The ability of the genetic algorithm to explore the new region is limited, and it is easy to converge to the optimal local solution. To achieve rational, objective, and scientific data, the optimal value is obtained using the simplest multiple operations. In this study, 20 repeated operations are selected, and various data of each operation are shown in Table

Data of 20 times’ operation in Matlab.

Time index | Optimal value (yuan) | Descendant generation of optimal value | Operation time (s) | Optimal binary code | Performance tracing |
---|---|---|---|---|---|

1 | 656243 | 1514 | 244.893527 | 101111110010000101000001 | a |

2 | 622654 | 3485 | 219.106535 | 111100010110110100011101 | b |

3 | 628137 | 3580 | 252.787547 | 111010101010110011110001 | c |

4 | 638617 | 784 | 306.611929 | 111100101100000100000001 | d |

5 | 611373 | 2472 | 261.379150 | 101100000110011010100001 | e |

6 | 626497 | 157 | 249.771833 | 111010100110010011100101 | f |

7 | 653815 | 2998 | 172.502950 | 110000000110100001011011 | g |

8 | 688007 | 2093 | 168.465815 | 110110101101000000010001 | h |

9 | 600608 | 2903 | 159.715251 | 100100101110100000100101 | i |

10 | 647640 | 3467 | 190.351622 | 111110001111011111110101 | j |

11 | 611642 | 3614 | 219.169720 | 110101011000100010101111 | k |

12 | 611642 | 480 | 242.232776 | 111111101100111100011111 | l |

13 | 647915 | 572 | 182.389709 | 110000100110000010001101 | m |

14 | 653312 | 3024 | 219.162909 | 101110101100100001100001 | n |

15 | 658918 | 2100 | 236.762271 | 100010010010000110010001 | o |

16 | 672677 | 2870 | 263.718400 | 111001100010011010001101 | p |

17 | 617254 | 2266 | 251.924982 | 111011100010101101000101 | q |

18 | 589031 | 2344 | 239.436273 | 111111100110000110000001 | r |

19 | 587416 | 3469 | 213.099410 | 101010111110001001001111 | s |

20 | 638343 | 532 | 198.166484 | 101001110011001110000001 | t |

Diagram of number 1 times of performance tracings of the genetic algorithm

Diagram of number 2 times of performance tracings of the genetic algorithm

Diagram of number 3 times of performance tracings of the genetic algorithm

Diagram of number 4 times of performance tracings of the genetic algorithm

Diagram of number 5 times of performance tracings of the genetic algorithm

Diagram of number 6 times of performance tracings of the genetic algorithm

Diagram of number 7 times of performance tracings of the genetic algorithm

Diagram of number 8 times of performance tracings of the genetic algorithm

Diagram of number 9 times of performance tracings of the genetic algorithm

Diagram of number 10 times of performance tracings of the genetic algorithm

Diagram of number 11 times of performance tracings of the genetic algorithm

Diagram of number 12 times of performance tracings of the genetic algorithm

Diagram of number 13 times of performance tracings of the genetic algorithm

Diagram of number 14 times of performance tracings of the genetic algorithm

Diagram of number 15 times of performance tracings of the genetic algorithm

Diagram of number 16 times of performance tracings of the genetic algorithm

Diagram of number 17 times of performance tracings of the genetic algorithm

Diagram of number 18 times of performance tracings of the genetic algorithm

Diagram of number 19 times of performance tracings of the genetic algorithm

Diagram of number 20 times of performance tracings of the genetic algorithm

The operation results show that the genetic algorithm cannot obtain the absolute minimum or maximum value (minimum value in this paper), and only the minimum value of an operation can be obtained. By running 20 times of operations, the minimum cost can be obtained as 587,416 yuan by adopting the order strategy of 101010111110001001001111.

The result of minimum inventory cost and order strategy for every phase order, one-off order, and fractionated order is shown in Table

Comparison of the genetic algorithm results.

Inventory cost | Order strategy | |
---|---|---|

One-off supply | 963035 | 100000000000000000000001 |

Every supply | 1431896 | 111111111111111111111111 |

Optimal supply | 587416 | 101010111110001001001111 |

Data sources: operation result of Matlab software.

The results comparison shows that the optimized calculation result is significantly lower than the cost of the first two extreme cases, and the binary code calculated according to the optimal supply order strategy is 101010111110001001001111.

The meanings of the binary code and the corresponding order strategies are as follows:

The reinforcement of the 1st and 2nd periods is ordered before the 1st period, with an order quantity of 70

The construction materials of the 3rd and 4th periods are ordered before the 3rd period, with an order quantity of 60

The reinforcement of the 5th and 6th periods is ordered before the 5th period, with an order quantity of 50

The reinforcement of the 7th period is ordered before the 7th period, with an order quantity of 70

The reinforcement of the 8th period is ordered before the 8th period, with an order quantity of 35

The reinforcement of the 9th period is ordered before the 9th period, with an order quantity of 53

The reinforcement of the 10th period is ordered before the 10th period, with an order quantity of 74

The reinforcement of the 11th, 12th, 13th, and 14th periods is ordered before the 11th period, with an order quantity of 168

The reinforcement of the 15th, 16th, and 17th periods is ordered before the 15th period, with an order quantity of 104

The reinforcement of the 18th, 19th, and 20th periods is ordered before the 18th period, with an order quantity of 137

The reinforcement of the 21st period is ordered before the 21st period, with an order quantity of 0

The reinforcement of the 22nd period is ordered before the 22nd period, with an order quantity of 48

The reinforcement of the 23rd period is ordered before the 23rd period, with an order quantity of 52

The reinforcement of the 24th period is ordered before the 24th period, with an order quantity of 35

This optimal inventory cost model is suitable for the construction materials of high inventory cost and many order batches (order batch is greater than or equal to 2).

The paper takes into account the whole CSC process ranging from ordering to inventory and builds up the simplest economic order quantity model. The inventory management model of the construction materials is constructed, which combines the characteristics of construction engineering with the order strategy. The optimal value of inventory cost of the construction materials is achieved by solving the genetic algorithm.

The inventory statuses of construction materials in CSC are analyzed dynamically. The component manufacturer’s demands for construction materials are treated as uniform and continuous. This assumption fits the classic model of economic order quantity and lays the foundation for the model. The paper analyzes every phase order and one-off order strategy of prefabricated components production during all periods to achieve a model to select the order of the lowest whole inventory cost. By setting the order variable of order point (01) in combination with the binary algorithm of the genetic algorithm, the model of inventory cost of the construction materials is smoothly related to the genetic algorithm. By setting the order variable to be “order” point (01), the relationship between inventory cost model of the construction materials in the CSC and genetic algorithm is established. The order strategy for the prefabricated components manufacturer is obtained with Matlab simulations, and the optimal order point and order quantity are specified.

In the future, some heuristic algorithms can be adopted for improvement. Moreover, combining with the benefit distribution model, the researchers may analyze how to reduce the whole cost of the supply chain while the normal interests of the manufacturers in the supply chain are guaranteed.

The authors declare that they have no conflicts of interest.