Mathematical Problems in Engineering

Volume 2018 (2018), Article ID 4062871, 16 pages

https://doi.org/10.1155/2018/4062871

## Ordering Strategy Analysis of Prefabricated Component Manufacturer in Construction Supply Chain

^{1}School of Management, Tianjin University of Technology, Binshuixi Road, Xiqing District, Tianjin 300384, China^{2}School of Design & Environment, National University of Singapore, 4 Architecture Drive, Singapore 117566^{3}College of Civil Engineering, Shenzhen University, Nanshan District, Shenzhen 518060, China

Correspondence should be addressed to Hongxiong Yang

Received 6 September 2017; Accepted 12 November 2017; Published 15 January 2018

Academic Editor: Jian G. Zhou

Copyright © 2018 Hongxiong Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

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 [1]. The prefabricated manufacturers produce components according to the split design and deepening design of architectural drawings, then deliver the products to the construction site, and finish assembly. A large amount of construction material is purchased and transported according to the manufacturing schedule. The characteristics of building itself and the construction materials limit the procurement mode of construction materials. Transportation distance, purchasing times, and quantity have a significant impact on cost, so it is important to make scientific and reasonable procurement strategies of construction materials to reduce costs. Because the assembly of components only takes a short time, a large number of manufactured components need temporary storage, which draws the attention of contractors to the inventory cost.

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 [2]. The inventory cost under management mode of CSC is significantly less than that of traditional mode [3]. The collaborative efforts reduce total supply chain costs efficiently [4]. The construction procedure sequence and procurement strategy affect inventory [5]. Demand variation influences the safety stock and inventory cost [6]. Large quantities and low-frequency orders will directly lead to high inventory cost; on the other hand, high frequency and small batch orders will cause higher reorder cost [7]. Currently, technologies, including JIT analysis technique [8], information integration technology on cloud platform [9], radio frequency identification (RFID) technology [10], third-party logistics [11], 4D BIM, and GIS technology [12, 13], have been applied to analyze cost, order, delivery of contractors, and components supplier. The technologies solve some practical problems of contractors and suppliers to an extent. However, they do not provide much analysis on the order and delivery time point. In the following sections, the genetic algorithm will be used to study the order and delivery time of the prefabricated components manufacturer and their material supplier. This research is expected to explain the ordering strategy from another angle in CSC.

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 [14]. Zhai et al. took into account lead time order issue in the prefabricated CSC, providing rigorous mathematical analysis of an operational hedging and coordination mechanism to mitigate the impact of production lead time uncertainty in the prefabrication construction industry [15]. The paper studied ordering and supplying problems between the component manufacturer and construction material supplier. The research assumes prefabricated components manufacturers (PCM) and their materials supplier have rich experience in production and that the construction materials supply rate and demand of each stage are known. So the lead time has no substantial influence on the inventory cost of the whole prefabricated component supply chain, which provides an alternative analysis the of the actual situation.

#### 2. Building Inventory Cost Model of Every Phase Order about Construction Materials

The classical economic order quantity (EOQ) model is at the heart of supply chain optimization and the theory of inventories [16]. Traditional inventory models attempt to optimize material lot sizes by minimizing total annual supply chain costs [17]. Taleizadeh, Khanbaglo, and Cárdenas-Barrón introduced distance factor to study partial backordering and reparation of damaged products [18]. De and Sana developed a cost minimization model by trading off setup cost, inventory cost, backordering cost, and cost for promotional effort based on some assumptions, which includes demand rate decreases over time during a shortage period [19]. Maddah and Noueihed considered a variant of the EOQ model, which assumes that demand occurs at random times with single order of the same amount [20]. Huang and Wu built a decision model to assist a wholesaler to hand ordering batch in a replenishment cycle and the maximal backorder level to minimize the average inventory cost [21]. Most of existing literatures consider the backlogging behavior only for retailers rather than wholesalers, and some assumptions are too far from the actual situation, such as stock-out cost, lead time, and order quantities [22].

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 [23]. For the construction project, its structure has been determined during the design period. Thus, the quantity and type of materials, as well as project duration and material average requirement planning, become explicit. Following the simple-to-complex research procedure, assumptions are as follows.

*Assumption 1. *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.

*Assumption 2. *During production period of the components, the demand for construction material is uninterrupted.

*Assumption 3. *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.

*Assumption 4. *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.

*Assumption 5. *The communication between the demander and supplier in the CSC is barrier-free, without hiding or asymmetrical information.

*Assumption 6. *The inventory capacity of the demander and supplier is large enough, and the cost relates only to the unit inventory cost.

*Assumption 7. *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. is demand rate of the construction materials during the producing period. is order cost of a certain construction material during the producing period. is the components completed by the manufacturer during the producing period. hr is unit inventory holding cost of the manufacturer during the producing period. is order quantity of the manufacturer during the producing period. HCr is total inventory cost of the manufacturer during the producing period. is time for the components completed by the manufacturer. is production rate of the construction material supplier, which is greater than consumption rate. hs is unit inventory holding cost of the construction material supplier. is delivery time of material supplier that is also order time of the demander, for every phase order. 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,

##### 2.1. Total Inventory Cost for Prefabricated Components Manufacturer for Every Phase Order

Figure 1 shows the inventory changes of the prefabricated components manufacturer for every phase order.